Recipe 8: Fractional Factorial Designs
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Recipes for the Design of Experiments
as of August 28, 2014, superceding the version of August 24. Always use the most recent version.
Fractional Factorial Design Analysis of Average State Unemployment Rate (Six-Factor, Two-Level Experiment)
Brendan Howell
Renselaer Polytechnic Institute
11/20/14 - Version 1.0
1. Setting
Dataset of Unemployment Rates of Blue Collar Workers in the United States (‘Benefits’).
Description: This dataframe contains a cross-section of information from 1972 pertaining to the unemployment rates of blue collar workers in the United States, collected for the research corresponding to the article entitled “The impact of unemployment insurance benefit levels on recipiency” (McCall, B.P. 1995) [1].
In this study that uses data collected from “The impact of unemployment insurance benefit levels on recipiency” (McCall, B.P. 1995), a six-factor, two-level experiment (analyzed via ANOVA and a fractional factorial design) is performed to see if either being white, attending school for more than 12 years, being male/female, being married, having kids, or having previously applied for UI benefits has a statistically significant effect on the state unemployment rate (in %). Respectively, these factors are denoted in the dataset as being ‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’. Additionally, this analysis’ response variable is referred to in the dataset as ‘stateur’, which denotes the state unemployment rate in the analysis. [1]
#Install and load the 'Ecdat' dataset into R.
rm(list=ls())
install.packages("Ecdat", repos='http://cran.us.r-project.org')## package 'Ecdat' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\howelb\AppData\Local\Temp\RtmpIF8syp\downloaded_packageslibrary("Ecdat",lib.loc="C:/Program Files/R/R-3.1.1/library")## Warning: package 'Ecdat' was built under R version 3.1.2## Loading required package: Ecfun## Warning: package 'Ecfun' was built under R version 3.1.2##
## Attaching package: 'Ecdat'
##
## The following object is masked from 'package:datasets':
##
## Orange#Assign a variable, 'benefits', to the complete dataframe, 'Benefits'. Then, determine the "head" and "tail" of the dataset, 'benefits'.
benefits<-Benefits
head(benefits)## stateur statemb state age tenure joblost nwhite school12 sex
## 1 4.5 167 42 49 21 other no no male
## 2 10.5 251 55 26 2 slack_work no no male
## 3 7.2 260 21 40 19 other no yes female
## 4 5.8 245 56 51 17 slack_work yes no female
## 5 6.5 125 58 33 1 slack_work no yes male
## 6 7.5 188 11 51 3 other no no male
## bluecol smsa married dkids dykids yrdispl rr head ui
## 1 yes yes no no no 7 0.2906 yes yes
## 2 yes yes no yes yes 10 0.5202 yes no
## 3 yes yes yes no no 10 0.4325 yes yes
## 4 yes yes yes no no 10 0.5000 no yes
## 5 yes yes yes yes yes 4 0.3906 yes no
## 6 yes yes yes no no 10 0.4822 yes yestail(benefits)## stateur statemb state age tenure joblost nwhite school12 sex
## 4872 8.6 125 59 21 2 slack_work no no male
## 4873 7.4 168 33 35 12 slack_work yes yes female
## 4874 7.0 189 74 39 5 slack_work no no male
## 4875 8.0 168 74 59 13 slack_work no no male
## 4876 6.3 191 41 33 11 slack_work no no male
## 4877 9.3 188 94 27 2 other no no male
## bluecol smsa married dkids dykids yrdispl rr head ui
## 4872 yes yes no no no 2 0.3125 yes no
## 4873 yes yes no yes no 6 0.4636 yes yes
## 4874 yes yes yes no no 4 0.3937 yes yes
## 4875 yes yes yes yes no 2 0.3724 yes yes
## 4876 yes yes yes yes yes 3 0.5000 yes no
## 4877 yes yes yes yes yes 7 0.4954 yes yesFactors and Levels
This analysis considers six factors (with each having two unique levels), which are denoted in the dataset as being ‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’. In the original dataset “Benefits”, the factors ‘nwhite’, ‘school12’, ‘married’, ‘dkids’, and ‘ui’ are characterized as being a factor (or, in other words, a categorical variable) with levels “yes” and “no”, and the factor ‘sex’ is characterized as being a factor (or, in other words, a categorical variable) with levels “male” and “female”. These factor were selected intuitively, since this analysis aims to determine the most important factors that may have a statistically significant effect on the state unemployment rate (in %).
#Display the summary statistics of "Benefits".
summary(benefits)## stateur statemb state age
## Min. : 2.20 Min. : 84 Min. :11.0 Min. :20.0
## 1st Qu.: 5.70 1st Qu.:150 1st Qu.:31.0 1st Qu.:28.0
## Median : 7.20 Median :177 Median :55.0 Median :34.0
## Mean : 7.51 Mean :181 Mean :52.8 Mean :36.1
## 3rd Qu.: 9.00 3rd Qu.:205 3rd Qu.:74.0 3rd Qu.:43.0
## Max. :18.00 Max. :293 Max. :95.0 Max. :61.0
## tenure joblost nwhite school12
## Min. : 1.00 other :1976 no :4159 no :3950
## 1st Qu.: 2.00 position_abolished: 402 yes: 718 yes: 927
## Median : 3.00 seasonal_job_ended: 177
## Mean : 5.66 slack_work :2322
## 3rd Qu.: 7.00
## Max. :41.00
## sex bluecol smsa married dkids dykids
## female:1150 yes:4877 no :1694 no :1791 no :2508 no :3796
## male :3727 yes:3183 yes:3086 yes:2369 yes:1081
##
##
##
##
## yrdispl rr head ui
## Min. : 1.0 Min. :0.0386 no :1558 no :1542
## 1st Qu.: 2.0 1st Qu.:0.3752 yes:3319 yes:3335
## Median : 5.0 Median :0.4904
## Mean : 5.2 Mean :0.4384
## 3rd Qu.: 8.0 3rd Qu.:0.5116
## Max. :10.0 Max. :0.6912#Display the names found in "Benefits".
names(benefits)## [1] "stateur" "statemb" "state" "age" "tenure" "joblost"
## [7] "nwhite" "school12" "sex" "bluecol" "smsa" "married"
## [13] "dkids" "dykids" "yrdispl" "rr" "head" "ui"#Display the structure of "Benefits".
str(benefits)## 'data.frame': 4877 obs. of 18 variables:
## $ stateur : num 4.5 10.5 7.2 5.8 6.5 7.5 5.8 5.8 7.7 6 ...
## $ statemb : int 167 251 260 245 125 188 166 214 213 187 ...
## $ state : int 42 55 21 56 58 11 93 84 84 33 ...
## $ age : int 49 26 40 51 33 51 30 26 54 31 ...
## $ tenure : int 21 2 19 17 1 3 5 3 20 1 ...
## $ joblost : Factor w/ 4 levels "other","position_abolished",..: 1 4 1 4 4 1 2 4 1 4 ...
## $ nwhite : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 1 1 1 ...
## $ school12: Factor w/ 2 levels "no","yes": 1 1 2 1 2 1 1 1 1 1 ...
## $ sex : Factor w/ 2 levels "female","male": 2 2 1 1 2 2 2 2 2 2 ...
## $ bluecol : Factor w/ 1 level "yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ smsa : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ married : Factor w/ 2 levels "no","yes": 1 1 2 2 2 2 2 2 2 2 ...
## $ dkids : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 2 2 1 1 ...
## $ dykids : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 2 2 1 1 ...
## $ yrdispl : int 7 10 10 10 4 10 6 8 6 8 ...
## $ rr : num 0.291 0.52 0.432 0.5 0.391 ...
## $ head : Factor w/ 2 levels "no","yes": 2 2 2 1 2 2 2 2 2 2 ...
## $ ui : Factor w/ 2 levels "no","yes": 2 1 2 2 1 2 2 2 1 2 ...Continuous variables (if any)
In this dataset, there are a few variables that can be considered to be continuous variables; these variables are the ones which are categorized as being numeric variables. By this standard, the continuous variables that exist in this dataset include ‘stateur’ (which refers to the state unemployment rate (in %)) and ‘rr’(which refers to the replacement rate of blue collar workers). Additionally, five variables in this dataset currently exist as integer variables, including the state maximum benefit level (‘statemb’), the state of residence code (‘state’), the age in years of each blue collar worker (‘age’), the years of tenure that a blue collar worker had in the job that they lost (‘tenure’), and the year of a blue collar worker’s job displacement (‘yrdispl’).
Response variables
This analysis will consider one response variable, ‘stateur’, which denotes the state unemployment rate in the analysis.
The Data: How is it organized and what does it look like?
As a whole, this dataset contains a cross-section of information from 1972 pertaining to the unemployment rates of blue collar workers in the United States, collected for the research corresponding to the article entitled “”The impact of unemployment insurance benefit levels on recipiency" (McCall, B.P. 1995) [1]. It includes data pertaining to state unemployment rates and to the reasons for job loss among blue collar workers. It contains 4877 observations of 18 variables, which are defined below:
Variable ID [Description]
stateur [state unemployment rate (in %)]
statemb [state maximum benefit level]
state [state of residence code]
age [age in years]
tenure [years of tenure in job lost]
joblost [a factor with four levels (“slack_work”, “position_abolished”, “seasonal_job_ended”, “other”)]
nwhite [non-white ?]
school12 [more than 12 years of school ?]
sex [a factor with two levels (“male”, “female”)]
bluecol [blue collar worker ?]
smsa [lives is smsa ?]
married [married ?]
dkids [has kids ?]
dykids [has young kids (0-5 yrs) ?]
yrdispl [year of job displacement (1982=1,…, 1991=10)]
rr [replacement rate]
head [is head of household ?]
ui [applied for (and received) UI benefits ?]
Randomization
According to the research publication being considered in this analysis (McCall, B.P. 1995), the observations contained within this dataset were simply the results of taking survey data. Therefore, we can likely make the assumption that this experiment exhibits sufficient randomization.
2. (Experimental) Design
How will the experiment be organized and conducted to test the hypothesis?
In this experiment, we are trying to determine whether or not the variation that is observed in the response variable (which corresponds to ‘stateur’ in this analysis) can be explained by the variation existent in any of the six factor-treatments of the experiment (which correspond to ‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’). Therefore, the null hypothesis that is being tested states that being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits does not have have a statistically significant effect on the state unemployment rate (in %). In carrying out this analysis, we perform an analysis of variance (ANOVA) for the state unemployment rate (‘stateur’) to see if there is a significant difference in the means for this response variable when considering the information pertaining to blue collar workers being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits, which are contained in this dataset. Additionally, in further testing this experiment, a fractional factorial design [2^(6-1)] is created and analyzed.
What is the rationale for this design?
The rationale for this design lies primarily in the fact that we’re trying to determine if blue collar workers being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits have any effect on the state unemployment rate. So, since the state unemployment rate (in %) is a useful and relevant metric to consider when determining the GDP and the economic performance/status of the United States, this design of a six-factor, two-level experiment (as it corresponds to an analysis of variance and a fractional factorial design) was crafted to see if blue collar workers being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits have a statistically significant effect on the state unemployment rate. By performing this analysis, we can hope to receive some insight regarding the different factors that come into play that typically result in a given level of the rate of state unemployment.
Randomize: What is the Randomization Scheme?
Since the observations contained within this dataset were simply the results of taking survey data (McCall, B.P. 1995), we can likely make the assumption that this experiment exhibits sufficient randomization.
Replicate: Are there replicates and/or repeated measures?
In this experiment, there are no replicates or repeated measures present.
Block: Did you use blocking in the design?
In designing this experiment in such a way that can be classified as a six-factor, two-level experiment that allows for the functionality of fractional factorial designs to be demonstrated, blocking was not built into the experiment’s design. The non-inclusion of blocking here ultimately serves to avoid adding further complexity to the experiment’s design, allowing for the functionality of fractional factorial designs to be showcased more effectively.
3. (Statistical) Analysis
(Exploratory Data Analysis) Graphics and Descriptive Summary
In beginning to display this data graphically, summary statistics were gathered for the dataset being considered here, “benefits”. Additionally, histograms and box plots were created to represent the different state unemployment rates.
#Display the summary statistics of "Benefits".
summary(benefits)## stateur statemb state age
## Min. : 2.20 Min. : 84 Min. :11.0 Min. :20.0
## 1st Qu.: 5.70 1st Qu.:150 1st Qu.:31.0 1st Qu.:28.0
## Median : 7.20 Median :177 Median :55.0 Median :34.0
## Mean : 7.51 Mean :181 Mean :52.8 Mean :36.1
## 3rd Qu.: 9.00 3rd Qu.:205 3rd Qu.:74.0 3rd Qu.:43.0
## Max. :18.00 Max. :293 Max. :95.0 Max. :61.0
## tenure joblost nwhite school12
## Min. : 1.00 other :1976 no :4159 no :3950
## 1st Qu.: 2.00 position_abolished: 402 yes: 718 yes: 927
## Median : 3.00 seasonal_job_ended: 177
## Mean : 5.66 slack_work :2322
## 3rd Qu.: 7.00
## Max. :41.00
## sex bluecol smsa married dkids dykids
## female:1150 yes:4877 no :1694 no :1791 no :2508 no :3796
## male :3727 yes:3183 yes:3086 yes:2369 yes:1081
##
##
##
##
## yrdispl rr head ui
## Min. : 1.0 Min. :0.0386 no :1558 no :1542
## 1st Qu.: 2.0 1st Qu.:0.3752 yes:3319 yes:3335
## Median : 5.0 Median :0.4904
## Mean : 5.2 Mean :0.4384
## 3rd Qu.: 8.0 3rd Qu.:0.5116
## Max. :10.0 Max. :0.6912#Display the names found in "Benefits".
names(benefits)## [1] "stateur" "statemb" "state" "age" "tenure" "joblost"
## [7] "nwhite" "school12" "sex" "bluecol" "smsa" "married"
## [13] "dkids" "dykids" "yrdispl" "rr" "head" "ui"#Display the structure of "Benefits".
str(benefits)## 'data.frame': 4877 obs. of 18 variables:
## $ stateur : num 4.5 10.5 7.2 5.8 6.5 7.5 5.8 5.8 7.7 6 ...
## $ statemb : int 167 251 260 245 125 188 166 214 213 187 ...
## $ state : int 42 55 21 56 58 11 93 84 84 33 ...
## $ age : int 49 26 40 51 33 51 30 26 54 31 ...
## $ tenure : int 21 2 19 17 1 3 5 3 20 1 ...
## $ joblost : Factor w/ 4 levels "other","position_abolished",..: 1 4 1 4 4 1 2 4 1 4 ...
## $ nwhite : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 1 1 1 ...
## $ school12: Factor w/ 2 levels "no","yes": 1 1 2 1 2 1 1 1 1 1 ...
## $ sex : Factor w/ 2 levels "female","male": 2 2 1 1 2 2 2 2 2 2 ...
## $ bluecol : Factor w/ 1 level "yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ smsa : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ married : Factor w/ 2 levels "no","yes": 1 1 2 2 2 2 2 2 2 2 ...
## $ dkids : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 2 2 1 1 ...
## $ dykids : Factor w/ 2 levels "no","yes": 1 2 1 1 2 1 2 2 1 1 ...
## $ yrdispl : int 7 10 10 10 4 10 6 8 6 8 ...
## $ rr : num 0.291 0.52 0.432 0.5 0.391 ...
## $ head : Factor w/ 2 levels "no","yes": 2 2 2 1 2 2 2 2 2 2 ...
## $ ui : Factor w/ 2 levels "no","yes": 2 1 2 2 1 2 2 2 1 2 ...#Display the head and tail of "Benefits".
head(benefits)## stateur statemb state age tenure joblost nwhite school12 sex
## 1 4.5 167 42 49 21 other no no male
## 2 10.5 251 55 26 2 slack_work no no male
## 3 7.2 260 21 40 19 other no yes female
## 4 5.8 245 56 51 17 slack_work yes no female
## 5 6.5 125 58 33 1 slack_work no yes male
## 6 7.5 188 11 51 3 other no no male
## bluecol smsa married dkids dykids yrdispl rr head ui
## 1 yes yes no no no 7 0.2906 yes yes
## 2 yes yes no yes yes 10 0.5202 yes no
## 3 yes yes yes no no 10 0.4325 yes yes
## 4 yes yes yes no no 10 0.5000 no yes
## 5 yes yes yes yes yes 4 0.3906 yes no
## 6 yes yes yes no no 10 0.4822 yes yestail(benefits)## stateur statemb state age tenure joblost nwhite school12 sex
## 4872 8.6 125 59 21 2 slack_work no no male
## 4873 7.4 168 33 35 12 slack_work yes yes female
## 4874 7.0 189 74 39 5 slack_work no no male
## 4875 8.0 168 74 59 13 slack_work no no male
## 4876 6.3 191 41 33 11 slack_work no no male
## 4877 9.3 188 94 27 2 other no no male
## bluecol smsa married dkids dykids yrdispl rr head ui
## 4872 yes yes no no no 2 0.3125 yes no
## 4873 yes yes no yes no 6 0.4636 yes yes
## 4874 yes yes yes no no 4 0.3937 yes yes
## 4875 yes yes yes yes no 2 0.3724 yes yes
## 4876 yes yes yes yes yes 3 0.5000 yes no
## 4877 yes yes yes yes yes 7 0.4954 yes yes#Display the levels of the 6 factors being considered within "Benefits".
levels(benefits$nwhite)## [1] "no" "yes"levels(benefits$school12)## [1] "no" "yes"levels(benefits$sex)## [1] "female" "male"levels(benefits$married)## [1] "no" "yes"levels(benefits$dkids)## [1] "no" "yes"levels(benefits$ui)## [1] "no" "yes"par(mfrow=c(1,1))
#Create a histogram of state unemployment rate ('stateur').
hist(benefits$stateur, xlim=c(2,18), main = "State Unemployment Rates in 1972", xlab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$nwhite, main = "Boxplot of State Unemployment Rates in 1972 (for 'nwhite')", ylim = c(2,18), xlab = "Non-white?", ylab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$school12, main = "Boxplot of State Unemployment Rates in 1972 (for 'school12')", ylim = c(2,18), xlab = "Attend School for More than 12 Years?", ylab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$sex, main = "Boxplot of State Unemployment Rates in 1972 (for 'sex')", ylim = c(2,18), xlab = "Male or Female?", ylab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$married, main = "Boxplot of State Unemployment Rates in 1972 (for 'married')", ylim = c(2,18), xlab = "Married?", ylab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$dkids, main = "Boxplot of State Unemployment Rates in 1972 (for 'dkids')", ylim = c(2,18), xlab = "Has Kids?", ylab = "State Unemployment Rate (in %)")
par(mfrow=c(1,1))
#Create a boxplot of state unemployment rate ('stateur').
boxplot(benefits$stateur~benefits$ui, main = "Boxplot of State Unemployment Rates in 1972 (for 'ui')", ylim = c(2,18), xlab = "Applied for UI Benefits?", ylab = "State Unemployment Rate (in %)")
Upon generating a histogram of ‘stateur’ data (which seems to exhibit a somewhat non-normal trend of data with its seemingly bi-modal nature) and box plots for each of the factors being considered in this analysis against the response variable ‘stateur’, the results suggest (at a glance) that the factors ‘nwhite’, ‘school12’, ‘sex’, ‘married’, and ‘dkids’ contain levels that are not statistically different from each other (in other words, the median values generated for the state unemployment rate when considering each of these five factors’ unique levels against each other are very similar). However, the factor ‘ui’ does seem to contain levels that are statistically different from each other (in other words, the median values generated for the state unemployment rate when considering each of these five factors’ unique levels against each other aren’t similar).
Testing - ANOVA
In order to determine if the variation that is observed in the response variable (which corresponds to the state unemployment rate in this analysis) can be explained by the variation existent in the treatment of the experiment (which corresponds to blue collar workers being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits), an analysis of variance (ANOVA) is performed as a means for analyzing the differences in state unemployment rate values for each of the six factors being considered in this experiment (‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’).
For the ANOVA model that is designed in this experiment, the null hypothesis that is being tested (which we will either reject or fail to reject by the end of our analysis) states that blue collar workers being white, attending school for more than 12 years, being male/female, being married, having kids, and having previously applied for UI benefits does not have have a statistically significant effect on the state unemployment rate (in %), implying that the differences in the mean values of the state unemployment rate were solely the result of randomization in this experiment. In other words, if we reject the null hypothesis, we would infer that the differences in mean values of the state unemployment rate for each of the six factors being considered in this dataset is caused by something other than randomization, leading us to believe that the variation that is observed in the mean values of the state unemployment rate can be explained by the variation existent in the six different factors being considered in this analysis. Alternately, if we fail to reject the null hypothesis, we would infer that the variation that is observed in the mean values of the state unemployment rate cannot be explained by the variation existent in the six different factors being considered in this analysis and, as such, is likely caused by randomization.
#Perform an analysis of variance (ANOVA) for the different mean values observed in the state unemployment rate, given the factors 'nwhite', 'school12', 'sex', 'married', 'dkids', and 'ui'.
model_stateur <- aov(stateur~nwhite+school12+sex+married+dkids+ui,benefits)
anova(model_stateur)## Analysis of Variance Table
##
## Response: stateur
## Df Sum Sq Mean Sq F value Pr(>F)
## nwhite 1 0 0 0.00 0.9586
## school12 1 3 3 0.42 0.5187
## sex 1 50 50 8.15 0.0043 **
## married 1 3 3 0.54 0.4609
## dkids 1 110 110 17.95 2.3e-05 ***
## ui 1 518 518 84.70 < 2e-16 ***
## Residuals 4870 29805 6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For the analysis of variance (ANOVA) that is performed where ‘nwhite’ is analyzed against the response variable ‘stateur’, a p-value = 0.958579 is returned, indicating that there is roughly a probability of 0.958579 that the resulting associated F-value (0.0027) is the result of solely randomization. Therefore, based on this result, we would fail to reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate cannot be explained by the factor ‘nwhite’ being considered in this analysis and, as such, is likely caused solely by randomization. (See above results for p-value and F-value.)
For the analysis of variance (ANOVA) that is performed where ‘school12’ is analyzed against the response variable ‘stateur’, a p-value = 0.518687 is returned, indicating that there is roughly a probability of 0.518687 that the resulting associated F-value (0.4166) is the result of solely randomization. Therefore, based on this result, we would fail to reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate cannot be explained by the factor ‘school12’ being considered in this analysis and, as such, is likely caused solely by randomization. (See above results for p-value and F-value.)
For the analysis of variance (ANOVA) that is performed where ‘sex’ is analyzed against the response variable ‘stateur’, a p-value = 0.004332 is returned, indicating that there is roughly a probability of 0.004332 that the resulting associated F-value (8.1469) is the result of solely randomization. Therefore, based on this result, we would reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate can be explained by the factor ‘sex’ being considered in this analysis and, as such, is not likely caused solely by randomization. (See above results for p-value and F-value.)
For the analysis of variance (ANOVA) that is performed where ‘married’ is analyzed against the response variable ‘stateur’, a p-value = 0.460868 is returned, indicating that there is roughly a probability of 0.460868 that the resulting associated F-value (0.5439) is the result of solely randomization. Therefore, based on this result, we would fail to reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate cannot be explained by the factor ‘married’ being considered in this analysis and, as such, is likely caused solely by randomization. (See above results for p-value and F-value.)
For the analysis of variance (ANOVA) that is performed where ‘dkids’ is analyzed against the response variable ‘stateur’, a p-value = 2.307e-05 is returned, indicating that there is roughly a probability of 2.307e-05 that the resulting associated F-value (17.9521) is the result of solely randomization. Therefore, based on this result, we would reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate can be explained by the factor ‘dkids’ being considered in this analysis and, as such, is not likely caused solely by randomization. (See above results for p-value and F-value.)
For the analysis of variance (ANOVA) that is performed where ‘ui’ is analyzed against the response variable ‘stateur’, a p-value < 2.2e-16 is returned, indicating that there is roughly a probability of < 2.2e-16 that the resulting associated F-value (84.6982) is the result of solely randomization. Therefore, based on this result, we would reject the null hypothesis, leading us to believe that the variation that is observed in the mean values of the state unemployment rate can be explained by the factor ‘ui’ being considered in this analysis and, as such, is not likely caused solely by randomization. (See above results for p-value and F-value.)
Tukey Honest Significant Differences
In further carrying out this analysis, we can compute Tukey Honest Significant Differences (via “TukeyHSD()”) as a means for determining the specific levels of the single factor existent in this analysis that are truly independent from each other and that significantly affect the response variable, ‘stateur’.
#Perform a TukeyHSD Test for "model_stateur".
Tukey_stateur = TukeyHSD(model_stateur, ordered = FALSE, conf.level = 0.95)
Tukey_stateur## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = stateur ~ nwhite + school12 + sex + married + dkids + ui, data = benefits)
##
## $nwhite
## diff lwr upr p adj
## yes-no 0.005193 -0.1908 0.2012 0.9586
##
## $school12
## diff lwr upr p adj
## yes-no -0.05827 -0.2353 0.1187 0.5187
##
## $sex
## diff lwr upr p adj
## male-female 0.2366 0.07299 0.4002 0.0046
##
## $married
## diff lwr upr p adj
## yes-no 0.05348 -0.09059 0.1975 0.4668
##
## $dkids
## diff lwr upr p adj
## yes-no 0.271 0.1321 0.41 1e-04
##
## $ui
## diff lwr upr p adj
## yes-no 0.6982 0.5489 0.8476 0par(mfrow=c(1,1))
plot(Tukey_stateur)
After observing the results of these Tukey Honest Significant Differences for “model_stateur”, it’s seemingly clear that half of the different “within-factor” level-comparisons suggest a not-so-significant difference in means among the different level-pairs in this experiment (these include the “within-factor” level-pairs for the factors ‘nwhite’, ‘school12’, and ‘married’). This is largely due to the fact that, unlike the other level-pairs for the factors ‘sex’, ‘dkids’, and ‘ui’, their respective p-values are greater than 0.05, which does not really serve to suggest any sort of statistical significance for those factors (‘nwhite’, ‘school12’, and ‘married’) that were analyzed in the above ANOVA model “model_stateur”.
Testing - Fractional Factorial Design [2^(6-1)]
In further analyzing the differences in state unemployment rate values for each of the six different factors being considered in this dataset, we can create a Fractional Factorial Design that will allow for the main effects and the interaction effects of our ANOVA model to be determined. The Fractional Factorial Design that will be used in this analysis can be denoted by 2^(k-1), where k = 6 factors.
#Load in fractional factorial design package, 'FrF2'.
install.packages("FrF2", repos='http://cran.us.r-project.org')## package 'FrF2' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\howelb\AppData\Local\Temp\RtmpIF8syp\downloaded_packageslibrary("FrF2",lib.loc="C:/Program Files/R/R-3.1.1/library")## Warning: package 'FrF2' was built under R version 3.1.2## Loading required package: DoE.base## Warning: package 'DoE.base' was built under R version 3.1.2## Loading required package: grid
## Loading required package: conf.design## Warning: package 'conf.design' was built under R version 3.1.2##
## Attaching package: 'DoE.base'
##
## The following objects are masked from 'package:stats':
##
## aov, lm
##
## The following object is masked from 'package:graphics':
##
## plot.design#Remove unnecessary variables from "benefits".
benefits_clean = subset(benefits, select = -c(statemb, state, age, tenure, joblost, bluecol, smsa, dykids, yrdispl, rr, head))
#Set up fractional factorial design [2^(6-1)].
FrDesign<-FrF2(32,6, estimable = formula("~nwhite+school12+sex+married+dkids+ui+nwhite:(school12+sex+married+dkids+ui)"), factor.names = list(
nwhite = c("yes", "no"), school12 = c("yes", "no"),
sex = c("male", "female"), married = c("yes", "no"),
dkids = c("yes", "no"), ui = c("yes", "no")), res4 = TRUE)
#Display the design matrix and the alias of "FrDesign".
FrDesign## nwhite school12 sex married dkids ui
## 1 no no male yes no no
## 2 yes yes male no no yes
## 3 no no male no no yes
## 4 yes yes female no yes yes
## 5 no no male no yes no
## 6 yes no male yes no yes
## 7 yes no female yes yes yes
## 8 yes yes female yes yes no
## 9 yes no male no no no
## 10 yes yes female no no no
## 11 yes no female no yes no
## 12 no no female yes no yes
## 13 no no female no no no
## 14 yes no female no no yes
## 15 no yes female no no yes
## 16 yes no male no yes yes
## 17 no yes female yes yes yes
## 18 yes no male yes yes no
## 19 no no male yes yes yes
## 20 no yes male no yes yes
## 21 yes yes male yes yes yes
## 22 no yes female no yes no
## 23 no yes female yes no no
## 24 no yes male yes no yes
## 25 no no female no yes yes
## 26 no no female yes yes no
## 27 yes yes female yes no yes
## 28 yes yes male no yes no
## 29 no yes male no no no
## 30 yes no female yes no no
## 31 yes yes male yes no no
## 32 no yes male yes yes no
## class=design, type= FrF2.estimablealiasprint(FrDesign)## $legend
## [1] A=nwhite B=school12 C=sex D=married E=dkids F=ui
##
## [[2]]
## [1] no aliasing among main effects and 2fis#Merge "FrDesign"" with "benefits_clean".
FFD_benefits <- merge(FrDesign, benefits_clean, by = c("nwhite", "school12", "sex", "married", "dkids", "ui"), all = FALSE)
#Display "FFD_benefits".
FFD_benefits## nwhite school12 sex married dkids ui stateur
## 1 no no female no no no 5.0
## 2 no no female no no no 5.8
## 3 no no female no no no 4.9
## 4 no no female no no no 5.8
## 5 no no female no no no 5.3
## 6 no no female no no no 3.6
## 7 no no female no no no 10.3
## 8 no no female no no no 8.4
## 9 no no female no no no 3.7
## 10 no no female no no no 8.0
## 11 no no female no no no 6.3
## 12 no no female no no no 10.2
## 13 no no female no no no 5.8
## 14 no no female no no no 5.1
## 15 no no female no no no 9.4
## 16 no no female no no no 5.3
## 17 no no female no no no 4.5
## 18 no no female no no no 6.2
## 19 no no female no no no 7.3
## 20 no no female no no no 4.7
## 21 no no female no no no 5.1
## 22 no no female no no no 7.8
## 23 no no female no no no 6.9
## 24 no no female no no no 5.3
## 25 no no female no no no 4.3
## 26 no no female no no no 9.4
## 27 no no female no no no 12.6
## 28 no no female no no no 5.1
## 29 no no female no no no 9.0
## 30 no no female no no no 6.2
## 31 no no female no no no 9.7
## 32 no no female no no no 3.1
## 33 no no female no no no 6.0
## 34 no no female no no no 3.5
## 35 no no female no no no 7.6
## 36 no no female no no no 8.1
## 37 no no female no no no 4.1
## 38 no no female no no no 4.5
## 39 no no female no no no 4.8
## 40 no no female no no no 5.9
## 41 no no female no no no 10.0
## 42 no no female no no no 6.8
## 43 no no female no no no 8.9
## 44 no no female no no no 7.8
## 45 no no female no no no 10.8
## 46 no no female no no no 6.7
## 47 no no female no no no 11.5
## 48 no no female no no no 8.1
## 49 no no female no no no 15.0
## 50 no no female no no no 6.4
## 51 no no female no no no 5.0
## 52 no no female no no no 11.6
## 53 no no female no no no 12.1
## 54 no no female no no no 10.3
## 55 no no female no no no 9.2
## 56 no no female no no no 3.9
## 57 no no female no no no 7.2
## 58 no no female no no no 6.4
## 59 no no female no no no 9.0
## 60 no no female no no no 8.6
## 61 no no female no no no 5.9
## 62 no no female no no no 8.9
## 63 no no female no no no 7.2
## 64 no no female no no no 7.5
## 65 no no female no no no 4.3
## 66 no no female no no no 6.9
## 67 no no female no no no 7.3
## 68 no no female no no no 7.5
## 69 no no female no no no 6.8
## 70 no no female no no no 9.0
## 71 no no female no no no 4.2
## 72 no no female no no no 5.9
## 73 no no female no no no 6.6
## 74 no no female no no no 5.4
## 75 no no female no no no 8.8
## 76 no no female no yes yes 5.0
## 77 no no female no yes yes 4.9
## 78 no no female no yes yes 6.5
## 79 no no female no yes yes 5.6
## 80 no no female no yes yes 14.6
## 81 no no female no yes yes 7.1
## 82 no no female no yes yes 8.0
## 83 no no female no yes yes 6.3
## 84 no no female no yes yes 6.0
## 85 no no female no yes yes 9.9
## 86 no no female no yes yes 7.2
## 87 no no female no yes yes 6.3
## 88 no no female no yes yes 6.1
## 89 no no female no yes yes 9.7
## 90 no no female no yes yes 8.5
## 91 no no female no yes yes 12.2
## 92 no no female no yes yes 5.7
## 93 no no female no yes yes 5.5
## 94 no no female no yes yes 9.1
## 95 no no female no yes yes 9.2
## 96 no no female no yes yes 7.2
## 97 no no female no yes yes 7.0
## 98 no no female no yes yes 3.3
## 99 no no female no yes yes 7.8
## 100 no no female no yes yes 6.1
## 101 no no female no yes yes 5.0
## 102 no no female no yes yes 9.2
## 103 no no female no yes yes 3.3
## 104 no no female no yes yes 7.2
## 105 no no female no yes yes 9.2
## 106 no no female no yes yes 5.2
## 107 no no female no yes yes 11.1
## 108 no no female no yes yes 11.9
## 109 no no female no yes yes 14.3
## 110 no no female no yes yes 7.2
## 111 no no female no yes yes 9.7
## 112 no no female no yes yes 6.6
## 113 no no female no yes yes 11.6
## 114 no no female no yes yes 7.0
## 115 no no female no yes yes 9.4
## 116 no no female no yes yes 11.7
## 117 no no female no yes yes 5.0
## 118 no no female no yes yes 6.7
## 119 no no female no yes yes 8.9
## 120 no no female no yes yes 11.2
## 121 no no female no yes yes 4.3
## 122 no no female no yes yes 11.7
## 123 no no female no yes yes 11.4
## 124 no no female no yes yes 9.2
## 125 no no female no yes yes 11.6
## 126 no no female no yes yes 5.7
## 127 no no female no yes yes 6.8
## 128 no no female no yes yes 11.1
## 129 no no female no yes yes 8.0
## 130 no no female no yes yes 5.7
## 131 no no female no yes yes 6.3
## 132 no no female no yes yes 8.4
## 133 no no female no yes yes 6.1
## 134 no no female no yes yes 6.0
## 135 no no female no yes yes 5.8
## 136 no no female no yes yes 7.3
## 137 no no female no yes yes 4.0
## 138 no no female no yes yes 8.0
## 139 no no female yes no yes 4.5
## 140 no no female yes no yes 7.5
## 141 no no female yes no yes 5.8
## 142 no no female yes no yes 8.9
## 143 no no female yes no yes 8.9
## 144 no no female yes no yes 5.6
## 145 no no female yes no yes 5.3
## 146 no no female yes no yes 7.1
## 147 no no female yes no yes 12.2
## 148 no no female yes no yes 3.8
## 149 no no female yes no yes 9.3
## 150 no no female yes no yes 9.3
## 151 no no female yes no yes 8.6
## 152 no no female yes no yes 4.5
## 153 no no female yes no yes 6.2
## 154 no no female yes no yes 4.1
## 155 no no female yes no yes 4.9
## 156 no no female yes no yes 5.3
## 157 no no female yes no yes 5.8
## 158 no no female yes no yes 8.0
## 159 no no female yes no yes 8.9
## 160 no no female yes no yes 8.2
## 161 no no female yes no yes 5.3
## 162 no no female yes no yes 6.0
## 163 no no female yes no yes 8.0
## 164 no no female yes no yes 6.1
## 165 no no female yes no yes 5.7
## 166 no no female yes no yes 8.0
## 167 no no female yes no yes 8.3
## 168 no no female yes no yes 8.5
## 169 no no female yes no yes 5.3
## 170 no no female yes no yes 5.8
## 171 no no female yes no yes 8.7
## 172 no no female yes no yes 6.7
## 173 no no female yes no yes 5.8
## 174 no no female yes no yes 12.2
## 175 no no female yes no yes 9.0
## 176 no no female yes no yes 9.0
## 177 no no female yes no yes 4.2
## 178 no no female yes no yes 4.9
## 179 no no female yes no yes 5.6
## 180 no no female yes no yes 12.3
## 181 no no female yes no yes 7.1
## 182 no no female yes no yes 6.2
## 183 no no female yes no yes 9.0
## 184 no no female yes no yes 4.3
## 185 no no female yes no yes 7.5
## 186 no no female yes no yes 12.4
## 187 no no female yes no yes 6.5
## 188 no no female yes no yes 3.6
## 189 no no female yes no yes 6.7
## 190 no no female yes no yes 12.2
## 191 no no female yes no yes 3.3
## 192 no no female yes no yes 6.4
## 193 no no female yes no yes 4.5
## 194 no no female yes no yes 6.0
## 195 no no female yes no yes 8.6
## 196 no no female yes no yes 6.9
## 197 no no female yes no yes 6.3
## 198 no no female yes no yes 9.7
## 199 no no female yes no yes 9.0
## 200 no no female yes no yes 8.9
## 201 no no female yes no yes 5.2
## 202 no no female yes no yes 8.6
## 203 no no female yes no yes 6.3
## 204 no no female yes no yes 5.2
## 205 no no female yes no yes 7.7
## 206 no no female yes no yes 7.4
## 207 no no female yes no yes 9.2
## 208 no no female yes no yes 6.3
## 209 no no female yes no yes 8.0
## 210 no no female yes no yes 11.8
## 211 no no female yes no yes 5.5
## 212 no no female yes no yes 9.4
## 213 no no female yes no yes 12.2
## 214 no no female yes no yes 7.1
## 215 no no female yes no yes 7.1
## 216 no no female yes no yes 9.4
## 217 no no female yes no yes 3.6
## 218 no no female yes no yes 6.3
## 219 no no female yes no yes 8.5
## 220 no no female yes no yes 10.1
## 221 no no female yes no yes 9.3
## 222 no no female yes no yes 5.7
## 223 no no female yes no yes 6.9
## 224 no no female yes no yes 9.2
## 225 no no female yes no yes 6.7
## 226 no no female yes no yes 5.0
## 227 no no female yes no yes 6.6
## 228 no no female yes no yes 4.9
## 229 no no female yes no yes 5.1
## 230 no no female yes no yes 6.6
## 231 no no female yes no yes 8.0
## 232 no no female yes no yes 7.8
## 233 no no female yes no yes 5.2
## 234 no no female yes no yes 9.7
## 235 no no female yes no yes 7.2
## 236 no no female yes no yes 14.2
## 237 no no female yes no yes 9.1
## 238 no no female yes no yes 4.3
## 239 no no female yes no yes 7.4
## 240 no no female yes no yes 6.2
## 241 no no female yes no yes 6.6
## 242 no no female yes no yes 9.2
## 243 no no female yes no yes 7.2
## 244 no no female yes no yes 5.1
## 245 no no female yes no yes 5.4
## 246 no no female yes no yes 9.8
## 247 no no female yes no yes 7.2
## 248 no no female yes no yes 6.7
## 249 no no female yes no yes 8.6
## 250 no no female yes no yes 11.7
## 251 no no female yes no yes 4.0
## 252 no no female yes no yes 5.0
## 253 no no female yes no yes 7.7
## 254 no no female yes no yes 6.7
## 255 no no female yes no yes 9.0
## 256 no no female yes no yes 6.2
## 257 no no female yes no yes 8.8
## 258 no no female yes no yes 8.6
## 259 no no female yes no yes 5.7
## 260 no no female yes no yes 8.6
## 261 no no female yes no yes 5.6
## 262 no no female yes no yes 4.8
## 263 no no female yes no yes 3.7
## 264 no no female yes no yes 10.5
## 265 no no female yes no yes 6.7
## 266 no no female yes no yes 11.7
## 267 no no female yes no yes 8.7
## 268 no no female yes no yes 6.3
## 269 no no female yes no yes 6.5
## 270 no no female yes no yes 7.1
## 271 no no female yes no yes 7.0
## 272 no no female yes no yes 6.0
## 273 no no female yes no yes 5.1
## 274 no no female yes no yes 11.1
## 275 no no female yes no yes 6.9
## 276 no no female yes no yes 4.5
## 277 no no female yes no yes 5.8
## 278 no no female yes no yes 3.8
## 279 no no female yes no yes 5.4
## 280 no no female yes no yes 11.1
## 281 no no female yes no yes 9.0
## 282 no no female yes no yes 6.7
## 283 no no female yes no yes 4.2
## 284 no no female yes no yes 4.3
## 285 no no female yes no yes 5.1
## 286 no no female yes no yes 6.7
## 287 no no female yes no yes 7.9
## 288 no no female yes no yes 5.9
## 289 no no female yes no yes 4.1
## 290 no no female yes no yes 8.9
## 291 no no female yes no yes 7.2
## 292 no no female yes no yes 9.4
## 293 no no female yes no yes 11.9
## 294 no no female yes no yes 10.8
## 295 no no female yes no yes 9.9
## 296 no no female yes yes no 7.3
## 297 no no female yes yes no 5.2
## 298 no no female yes yes no 11.8
## 299 no no female yes yes no 5.4
## 300 no no female yes yes no 11.4
## 301 no no female yes yes no 8.4
## 302 no no female yes yes no 4.5
## 303 no no female yes yes no 5.3
## 304 no no female yes yes no 5.0
## 305 no no female yes yes no 7.0
## 306 no no female yes yes no 7.8
## 307 no no female yes yes no 8.8
## 308 no no female yes yes no 6.4
## 309 no no female yes yes no 5.2
## 310 no no female yes yes no 3.5
## 311 no no female yes yes no 9.4
## 312 no no female yes yes no 8.9
## 313 no no female yes yes no 9.0
## 314 no no female yes yes no 8.9
## 315 no no female yes yes no 5.1
## 316 no no female yes yes no 6.3
## 317 no no female yes yes no 5.5
## 318 no no female yes yes no 6.7
## 319 no no female yes yes no 7.8
## 320 no no female yes yes no 7.3
## 321 no no female yes yes no 8.9
## 322 no no female yes yes no 5.9
## 323 no no female yes yes no 6.3
## 324 no no female yes yes no 5.6
## 325 no no female yes yes no 7.3
## 326 no no female yes yes no 7.0
## 327 no no female yes yes no 9.8
## 328 no no female yes yes no 5.6
## 329 no no female yes yes no 12.2
## 330 no no female yes yes no 7.9
## 331 no no female yes yes no 6.2
## 332 no no female yes yes no 5.0
## 333 no no female yes yes no 6.2
## 334 no no female yes yes no 5.8
## 335 no no female yes yes no 4.6
## 336 no no female yes yes no 5.8
## 337 no no female yes yes no 5.8
## 338 no no female yes yes no 5.3
## 339 no no female yes yes no 7.3
## 340 no no female yes yes no 9.2
## 341 no no female yes yes no 5.8
## 342 no no female yes yes no 6.9
## 343 no no female yes yes no 8.6
## 344 no no female yes yes no 7.6
## 345 no no female yes yes no 6.6
## 346 no no female yes yes no 10.3
## 347 no no female yes yes no 5.6
## 348 no no female yes yes no 8.0
## 349 no no female yes yes no 6.7
## 350 no no female yes yes no 4.3
## 351 no no female yes yes no 12.4
## 352 no no female yes yes no 6.7
## 353 no no female yes yes no 6.8
## 354 no no female yes yes no 14.6
## 355 no no female yes yes no 11.2
## 356 no no female yes yes no 9.7
## 357 no no female yes yes no 7.0
## 358 no no female yes yes no 6.0
## 359 no no female yes yes no 7.3
## 360 no no female yes yes no 7.5
## 361 no no female yes yes no 5.4
## 362 no no female yes yes no 6.3
## 363 no no female yes yes no 6.3
## 364 no no female yes yes no 3.2
## 365 no no female yes yes no 9.9
## 366 no no female yes yes no 5.8
## 367 no no female yes yes no 6.3
## 368 no no female yes yes no 5.9
## 369 no no female yes yes no 11.7
## 370 no no male no no yes 6.2
## 371 no no male no no yes 9.7
## 372 no no male no no yes 8.0
## 373 no no male no no yes 6.6
## 374 no no male no no yes 3.9
## 375 no no male no no yes 8.0
## 376 no no male no no yes 11.2
## 377 no no male no no yes 6.8
## 378 no no male no no yes 6.0
## 379 no no male no no yes 5.0
## 380 no no male no no yes 8.0
## 381 no no male no no yes 5.7
## 382 no no male no no yes 4.5
## 383 no no male no no yes 4.3
## 384 no no male no no yes 10.1
## 385 no no male no no yes 9.0
## 386 no no male no no yes 5.3
## 387 no no male no no yes 14.2
## 388 no no male no no yes 8.1
## 389 no no male no no yes 7.1
## 390 no no male no no yes 11.7
## 391 no no male no no yes 7.4
## 392 no no male no no yes 5.7
## 393 no no male no no yes 11.9
## 394 no no male no no yes 4.5
## 395 no no male no no yes 7.7
## 396 no no male no no yes 7.2
## 397 no no male no no yes 9.1
## 398 no no male no no yes 7.5
## 399 no no male no no yes 7.1
## 400 no no male no no yes 11.2
## 401 no no male no no yes 7.5
## 402 no no male no no yes 3.7
## 403 no no male no no yes 10.0
## 404 no no male no no yes 5.4
## 405 no no male no no yes 12.1
## 406 no no male no no yes 5.0
## 407 no no male no no yes 10.9
## 408 no no male no no yes 10.8
## 409 no no male no no yes 10.3
## 410 no no male no no yes 10.3
## 411 no no male no no yes 7.3
## 412 no no male no no yes 9.2
## 413 no no male no no yes 9.7
## 414 no no male no no yes 10.3
## 415 no no male no no yes 9.0
## 416 no no male no no yes 7.8
## 417 no no male no no yes 7.7
## 418 no no male no no yes 3.5
## 419 no no male no no yes 9.0
## 420 no no male no no yes 5.8
## 421 no no male no no yes 10.4
## 422 no no male no no yes 4.0
## 423 no no male no no yes 11.4
## 424 no no male no no yes 6.0
## 425 no no male no no yes 6.7
## 426 no no male no no yes 5.0
## 427 no no male no no yes 6.9
## 428 no no male no no yes 6.8
## 429 no no male no no yes 11.8
## 430 no no male no no yes 15.0
## 431 no no male no no yes 5.4
## 432 no no male no no yes 8.5
## 433 no no male no no yes 10.5
## 434 no no male no no yes 8.6
## 435 no no male no no yes 6.0
## 436 no no male no no yes 5.7
## 437 no no male no no yes 9.7
## 438 no no male no no yes 8.8
## 439 no no male no no yes 11.4
## 440 no no male no no yes 9.7
## 441 no no male no no yes 11.5
## 442 no no male no no yes 6.8
## 443 no no male no no yes 4.0
## 444 no no male no no yes 8.1
## 445 no no male no no yes 8.9
## 446 no no male no no yes 6.9
## 447 no no male no no yes 5.4
## 448 no no male no no yes 4.4
## 449 no no male no no yes 6.2
## 450 no no male no no yes 6.6
## 451 no no male no no yes 14.3
## 452 no no male no no yes 7.3
## 453 no no male no no yes 6.2
## 454 no no male no no yes 6.4
## 455 no no male no no yes 5.5
## 456 no no male no no yes 5.2
## 457 no no male no no yes 6.6
## 458 no no male no no yes 13.1
## 459 no no male no no yes 3.2
## 460 no no male no no yes 9.4
## 461 no no male no no yes 8.8
## 462 no no male no no yes 13.7
## 463 no no male no no yes 7.3
## 464 no no male no no yes 4.4
## 465 no no male no no yes 6.3
## 466 no no male no no yes 8.9
## 467 no no male no no yes 2.5
## 468 no no male no no yes 5.6
## 469 no no male no no yes 6.7
## 470 no no male no no yes 8.9
## 471 no no male no no yes 9.5
## 472 no no male no no yes 10.8
## 473 no no male no no yes 7.0
## 474 no no male no no yes 4.0
## 475 no no male no no yes 9.0
## 476 no no male no no yes 6.7
## 477 no no male no no yes 5.7
## 478 no no male no no yes 14.6
## 479 no no male no no yes 5.3
## 480 no no male no no yes 5.6
## 481 no no male no no yes 7.8
## 482 no no male no no yes 6.2
## 483 no no male no no yes 9.9
## 484 no no male no no yes 7.5
## 485 no no male no no yes 12.3
## 486 no no male no no yes 6.4
## 487 no no male no no yes 9.7
## 488 no no male no no yes 5.4
## 489 no no male no no yes 7.5
## 490 no no male no no yes 4.0
## 491 no no male no no yes 8.9
## 492 no no male no no yes 6.8
## 493 no no male no no yes 4.8
## 494 no no male no no yes 5.9
## 495 no no male no no yes 9.4
## 496 no no male no no yes 5.9
## 497 no no male no no yes 9.1
## 498 no no male no no yes 11.0
## 499 no no male no no yes 3.6
## 500 no no male no no yes 5.0
## 501 no no male no no yes 5.1
## 502 no no male no no yes 5.5
## 503 no no male no no yes 5.2
## 504 no no male no no yes 9.7
## 505 no no male no no yes 9.9
## 506 no no male no no yes 10.3
## 507 no no male no no yes 7.3
## 508 no no male no no yes 5.4
## 509 no no male no no yes 8.6
## 510 no no male no no yes 11.1
## 511 no no male no no yes 9.7
## 512 no no male no no yes 10.5
## 513 no no male no no yes 6.8
## 514 no no male no no yes 5.2
## 515 no no male no no yes 10.1
## 516 no no male no no yes 8.0
## 517 no no male no no yes 7.2
## 518 no no male no no yes 5.8
## 519 no no male no no yes 7.2
## 520 no no male no no yes 9.7
## 521 no no male no no yes 11.0
## 522 no no male no no yes 4.4
## 523 no no male no no yes 9.4
## 524 no no male no no yes 8.9
## 525 no no male no no yes 10.0
## 526 no no male no no yes 4.2
## 527 no no male no no yes 7.2
## 528 no no male no no yes 10.3
## 529 no no male no no yes 12.4
## 530 no no male no no yes 3.8
## 531 no no male no no yes 8.2
## 532 no no male no no yes 7.0
## 533 no no male no no yes 7.5
## 534 no no male no no yes 6.0
## 535 no no male no no yes 5.1
## 536 no no male no no yes 5.3
## 537 no no male no no yes 4.5
## 538 no no male no no yes 9.4
## 539 no no male no no yes 5.5
## 540 no no male no no yes 6.0
## 541 no no male no no yes 7.3
## 542 no no male no no yes 6.5
## 543 no no male no no yes 7.2
## 544 no no male no no yes 9.2
## 545 no no male no no yes 7.0
## 546 no no male no no yes 9.4
## 547 no no male no no yes 8.7
## 548 no no male no no yes 11.8
## 549 no no male no no yes 9.2
## 550 no no male no no yes 4.6
## 551 no no male no no yes 18.0
## 552 no no male no no yes 11.4
## 553 no no male no no yes 8.0
## 554 no no male no no yes 6.7
## 555 no no male no no yes 9.2
## 556 no no male no no yes 8.2
## 557 no no male no no yes 6.2
## 558 no no male no no yes 11.6
## 559 no no male no no yes 5.7
## 560 no no male no no yes 7.2
## 561 no no male no no yes 5.5
## 562 no no male no no yes 11.7
## 563 no no male no no yes 13.0
## 564 no no male no no yes 6.8
## 565 no no male no no yes 6.7
## 566 no no male no no yes 12.1
## 567 no no male no no yes 4.3
## 568 no no male no no yes 11.7
## 569 no no male no no yes 6.6
## 570 no no male no no yes 10.8
## 571 no no male no no yes 4.6
## 572 no no male no no yes 5.4
## 573 no no male no no yes 5.1
## 574 no no male no no yes 5.7
## 575 no no male no no yes 5.7
## 576 no no male no no yes 6.2
## 577 no no male no no yes 4.5
## 578 no no male no no yes 9.7
## 579 no no male no no yes 9.7
## 580 no no male no no yes 7.6
## 581 no no male no no yes 5.5
## 582 no no male no no yes 8.1
## 583 no no male no no yes 6.9
## 584 no no male no no yes 6.2
## 585 no no male no no yes 6.5
## 586 no no male no no yes 5.6
## 587 no no male no no yes 5.4
## 588 no no male no no yes 4.9
## 589 no no male no no yes 5.1
## 590 no no male no no yes 9.0
## 591 no no male no no yes 5.0
## 592 no no male no no yes 5.1
## 593 no no male no no yes 4.0
## 594 no no male no no yes 12.3
## 595 no no male no no yes 5.1
## 596 no no male no no yes 5.6
## 597 no no male no no yes 7.6
## 598 no no male no no yes 9.2
## 599 no no male no no yes 10.3
## 600 no no male no no yes 7.5
## 601 no no male no no yes 5.6
## 602 no no male no no yes 4.5
## 603 no no male no no yes 7.1
## 604 no no male no no yes 7.1
## 605 no no male no no yes 6.3
## 606 no no male no no yes 4.5
## 607 no no male no no yes 7.5
## 608 no no male no no yes 9.4
## 609 no no male no no yes 7.1
## 610 no no male no no yes 6.3
## 611 no no male no no yes 6.6
## 612 no no male no no yes 7.5
## 613 no no male no no yes 5.9
## 614 no no male no no yes 8.9
## 615 no no male no no yes 7.5
## 616 no no male no no yes 4.9
## 617 no no male no no yes 9.1
## 618 no no male no no yes 6.2
## 619 no no male no no yes 7.5
## 620 no no male no no yes 10.8
## 621 no no male no no yes 6.2
## 622 no no male no no yes 8.7
## 623 no no male no no yes 7.9
## 624 no no male no no yes 10.8
## 625 no no male no no yes 11.6
## 626 no no male no no yes 8.6
## 627 no no male no no yes 8.8
## 628 no no male no no yes 9.2
## 629 no no male no no yes 6.6
## 630 no no male no no yes 9.7
## 631 no no male no no yes 5.2
## 632 no no male no no yes 6.3
## 633 no no male no no yes 5.8
## 634 no no male no no yes 5.4
## 635 no no male no no yes 7.6
## 636 no no male no no yes 11.8
## 637 no no male no no yes 8.9
## 638 no no male no no yes 4.0
## 639 no no male no no yes 9.0
## 640 no no male no no yes 7.1
## 641 no no male no no yes 4.0
## 642 no no male no no yes 5.6
## 643 no no male no no yes 6.7
## 644 no no male no no yes 6.3
## 645 no no male no no yes 5.2
## 646 no no male no no yes 7.1
## 647 no no male no no yes 9.4
## 648 no no male no no yes 8.8
## 649 no no male no no yes 6.7
## 650 no no male no no yes 4.0
## 651 no no male no no yes 6.9
## 652 no no male no no yes 9.0
## 653 no no male no no yes 6.3
## 654 no no male no no yes 5.0
## 655 no no male no no yes 11.6
## 656 no no male no no yes 6.2
## 657 no no male no no yes 4.2
## 658 no no male no no yes 11.9
## 659 no no male no no yes 4.0
## 660 no no male no no yes 7.7
## 661 no no male no no yes 6.2
## 662 no no male no no yes 14.3
## 663 no no male no no yes 11.8
## 664 no no male no no yes 12.1
## 665 no no male no no yes 8.2
## 666 no no male no no yes 6.0
## 667 no no male no no yes 9.0
## 668 no no male no no yes 8.4
## 669 no no male no no yes 6.7
## 670 no no male no no yes 6.1
## 671 no no male no no yes 6.2
## 672 no no male no no yes 7.3
## 673 no no male no no yes 5.0
## 674 no no male no no yes 10.3
## 675 no no male no no yes 9.7
## 676 no no male no no yes 5.7
## 677 no no male no no yes 11.8
## 678 no no male no no yes 9.1
## 679 no no male no no yes 14.3
## 680 no no male no no yes 6.7
## 681 no no male no no yes 4.6
## 682 no no male no no yes 4.0
## 683 no no male no no yes 7.2
## 684 no no male no no yes 7.4
## 685 no no male no no yes 10.2
## 686 no no male no no yes 8.9
## 687 no no male no no yes 9.4
## 688 no no male no no yes 7.2
## 689 no no male no no yes 11.9
## 690 no no male no no yes 7.5
## 691 no no male no no yes 4.4
## 692 no no male no no yes 8.1
## 693 no no male no no yes 5.7
## 694 no no male no no yes 8.5
## 695 no no male no no yes 2.5
## 696 no no male no no yes 5.4
## 697 no no male no no yes 9.0
## 698 no no male no no yes 5.7
## 699 no no male no no yes 10.5
## 700 no no male no no yes 5.3
## 701 no no male no no yes 7.3
## 702 no no male no no yes 7.4
## 703 no no male no no yes 6.6
## 704 no no male no no yes 5.4
## 705 no no male no no yes 10.3
## 706 no no male no no yes 7.5
## 707 no no male no no yes 11.5
## 708 no no male no no yes 7.0
## 709 no no male no no yes 7.7
## 710 no no male no no yes 7.0
## 711 no no male no no yes 8.0
## 712 no no male no no yes 6.2
## 713 no no male no no yes 8.0
## 714 no no male no no yes 9.2
## 715 no no male no no yes 6.2
## 716 no no male no no yes 6.4
## 717 no no male no no yes 15.0
## 718 no no male no no yes 5.6
## 719 no no male no no yes 7.5
## 720 no no male no no yes 3.9
## 721 no no male no no yes 5.6
## 722 no no male no no yes 7.1
## 723 no no male no no yes 15.0
## 724 no no male no no yes 8.1
## 725 no no male no no yes 9.0
## 726 no no male no no yes 8.0
## 727 no no male no no yes 6.7
## 728 no no male no no yes 6.4
## 729 no no male no no yes 11.4
## 730 no no male no no yes 6.2
## 731 no no male no no yes 9.0
## 732 no no male no no yes 8.9
## 733 no no male no no yes 6.6
## 734 no no male no no yes 10.8
## 735 no no male no no yes 11.4
## 736 no no male no no yes 5.7
## 737 no no male no no yes 6.2
## 738 no no male no no yes 6.2
## 739 no no male no no yes 4.1
## 740 no no male no no yes 6.2
## 741 no no male no no yes 4.1
## 742 no no male no no yes 10.5
## 743 no no male no no yes 8.9
## 744 no no male no no yes 3.3
## 745 no no male no no yes 4.8
## 746 no no male no no yes 6.9
## 747 no no male no no yes 11.6
## 748 no no male no no yes 4.8
## 749 no no male no no yes 7.0
## 750 no no male no no yes 6.6
## 751 no no male no no yes 7.5
## 752 no no male no no yes 8.9
## 753 no no male no no yes 9.0
## 754 no no male no no yes 12.2
## 755 no no male no no yes 6.0
## 756 no no male no no yes 9.1
## 757 no no male no no yes 5.1
## 758 no no male no no yes 5.0
## 759 no no male no no yes 4.3
## 760 no no male no no yes 6.9
## 761 no no male no no yes 9.4
## 762 no no male no no yes 5.1
## 763 no no male no no yes 6.5
## 764 no no male no no yes 6.0
## 765 no no male no no yes 11.8
## 766 no no male no no yes 5.7
## 767 no no male no no yes 8.0
## 768 no no male no no yes 7.1
## 769 no no male no no yes 5.8
## 770 no no male no no yes 2.6
## 771 no no male no no yes 9.0
## 772 no no male no no yes 5.7
## 773 no no male no no yes 8.2
## 774 no no male no no yes 6.8
## 775 no no male no no yes 10.4
## 776 no no male no no yes 4.0
## 777 no no male no no yes 4.4
## 778 no no male no no yes 7.2
## 779 no no male no no yes 6.0
## 780 no no male no no yes 6.3
## 781 no no male no no yes 14.2
## 782 no no male no no yes 8.7
## 783 no no male no no yes 8.0
## 784 no no male no no yes 5.6
## 785 no no male no no yes 7.4
## 786 no no male no no yes 5.8
## 787 no no male no no yes 9.4
## 788 no no male no no yes 5.6
## 789 no no male no no yes 7.1
## 790 no no male no no yes 5.6
## 791 no no male no no yes 2.7
## 792 no no male no no yes 6.2
## 793 no no male no no yes 6.5
## 794 no no male no no yes 4.9
## 795 no no male no no yes 9.1
## 796 no no male no no yes 5.1
## 797 no no male no no yes 10.3
## 798 no no male no no yes 14.4
## 799 no no male no no yes 11.0
## 800 no no male no no yes 9.9
## 801 no no male no no yes 6.3
## 802 no no male no no yes 10.2
## 803 no no male no no yes 8.1
## 804 no no male no no yes 4.7
## 805 no no male no no yes 6.0
## 806 no no male no no yes 4.1
## 807 no no male no no yes 12.2
## 808 no no male no yes no 11.4
## 809 no no male no yes no 8.4
## 810 no no male no yes no 3.8
## 811 no no male no yes no 6.6
## 812 no no male no yes no 9.1
## 813 no no male no yes no 3.9
## 814 no no male no yes no 7.1
## 815 no no male no yes no 9.0
## 816 no no male no yes no 6.6
## 817 no no male no yes no 6.2
## 818 no no male no yes no 7.6
## 819 no no male no yes no 11.8
## 820 no no male no yes no 7.5
## 821 no no male no yes no 5.1
## 822 no no male no yes no 9.1
## 823 no no male no yes no 6.0
## 824 no no male no yes no 7.1
## 825 no no male no yes no 5.7
## 826 no no male no yes no 4.0
## 827 no no male no yes no 6.3
## 828 no no male no yes no 9.3
## 829 no no male no yes no 8.4
## 830 no no male no yes no 14.6
## 831 no no male no yes no 8.8
## 832 no no male no yes no 7.2
## 833 no no male no yes no 7.9
## 834 no no male no yes no 9.7
## 835 no no male no yes no 4.9
## 836 no no male no yes no 9.9
## 837 no no male no yes no 6.8
## 838 no no male no yes no 9.0
## 839 no no male no yes no 9.0
## 840 no no male no yes no 6.8
## 841 no no male no yes no 7.3
## 842 no no male no yes no 6.3
## 843 no no male no yes no 7.2
## 844 no no male no yes no 10.1
## 845 no no male no yes no 5.4
## 846 no no male no yes no 6.6
## 847 no no male no yes no 6.3
## 848 no no male no yes no 6.1
## 849 no no male no yes no 10.5
## 850 no no male no yes no 5.8
## 851 no no male no yes no 5.7
## 852 no no male no yes no 8.0
## 853 no no male no yes no 4.3
## 854 no no male no yes no 6.9
## 855 no no male no yes no 14.2
## 856 no no male no yes no 8.8
## 857 no no male no yes no 9.0
## 858 no no male no yes no 5.6
## 859 no no male no yes no 5.1
## 860 no no male no yes no 12.0
## 861 no no male yes no no 6.7
## 862 no no male yes no no 5.6
## 863 no no male yes no no 5.1
## 864 no no male yes no no 5.5
## 865 no no male yes no no 6.7
## 866 no no male yes no no 9.0
## 867 no no male yes no no 9.7
## 868 no no male yes no no 9.4
## 869 no no male yes no no 3.8
## 870 no no male yes no no 5.9
## 871 no no male yes no no 8.9
## 872 no no male yes no no 6.1
## 873 no no male yes no no 6.8
## 874 no no male yes no no 9.1
## 875 no no male yes no no 7.2
## 876 no no male yes no no 5.5
## 877 no no male yes no no 6.7
## 878 no no male yes no no 6.7
## 879 no no male yes no no 4.0
## 880 no no male yes no no 5.0
## 881 no no male yes no no 5.4
## 882 no no male yes no no 9.4
## 883 no no male yes no no 5.6
## 884 no no male yes no no 5.7
## 885 no no male yes no no 4.0
## 886 no no male yes no no 7.7
## 887 no no male yes no no 3.6
## 888 no no male yes no no 4.5
## 889 no no male yes no no 6.4
## 890 no no male yes no no 5.9
## 891 no no male yes no no 6.6
## 892 no no male yes no no 6.7
## 893 no no male yes no no 7.2
## 894 no no male yes no no 12.2
## 895 no no male yes no no 6.2
## 896 no no male yes no no 6.3
## 897 no no male yes no no 6.5
## 898 no no male yes no no 12.3
## 899 no no male yes no no 7.2
## 900 no no male yes no no 9.2
## 901 no no male yes no no 8.0
## 902 no no male yes no no 5.6
## 903 no no male yes no no 4.1
## 904 no no male yes no no 6.1
## 905 no no male yes no no 4.6
## 906 no no male yes no no 7.3
## 907 no no male yes no no 4.9
## 908 no no male yes no no 5.4
## 909 no no male yes no no 11.7
## 910 no no male yes no no 10.2
## 911 no no male yes no no 6.0
## 912 no no male yes no no 7.2
## 913 no no male yes no no 5.6
## 914 no no male yes no no 10.0
## 915 no no male yes no no 6.9
## 916 no no male yes no no 6.7
## 917 no no male yes no no 10.8
## 918 no no male yes no no 7.0
## 919 no no male yes no no 8.4
## 920 no no male yes no no 5.2
## 921 no no male yes no no 5.0
## 922 no no male yes no no 6.3
## 923 no no male yes no no 6.9
## 924 no no male yes no no 5.7
## 925 no no male yes no no 9.8
## 926 no no male yes no no 9.1
## 927 no no male yes no no 6.8
## 928 no no male yes no no 8.0
## 929 no no male yes no no 4.6
## 930 no no male yes no no 7.3
## 931 no no male yes no no 6.4
## 932 no no male yes no no 5.3
## 933 no no male yes no no 11.5
## 934 no no male yes no no 6.3
## 935 no no male yes no no 8.0
## 936 no no male yes no no 7.7
## 937 no no male yes no no 8.5
## 938 no no male yes no no 11.5
## 939 no no male yes no no 4.6
## 940 no no male yes no no 5.3
## 941 no no male yes no no 5.9
## 942 no no male yes no no 3.7
## 943 no no male yes no no 7.2
## 944 no no male yes no no 13.0
## 945 no no male yes no no 5.5
## 946 no no male yes no no 5.0
## 947 no no male yes no no 12.3
## 948 no no male yes no no 5.6
## 949 no no male yes no no 6.0
## 950 no no male yes no no 3.9
## 951 no no male yes no no 8.9
## 952 no no male yes no no 5.2
## 953 no no male yes no no 4.0
## 954 no no male yes no no 3.9
## 955 no no male yes no no 8.6
## 956 no no male yes no no 7.7
## 957 no no male yes no no 4.5
## 958 no no male yes no no 7.0
## 959 no no male yes no no 8.0
## 960 no no male yes no no 6.8
## 961 no no male yes no no 6.0
## 962 no no male yes no no 5.9
## 963 no no male yes no no 6.2
## 964 no no male yes no no 7.0
## 965 no no male yes no no 12.3
## 966 no no male yes no no 11.5
## 967 no no male yes no no 5.5
## 968 no no male yes no no 8.4
## 969 no no male yes no no 5.2
## 970 no no male yes no no 4.6
## 971 no no male yes no no 4.2
## 972 no no male yes no no 5.9
## 973 no no male yes no no 5.3
## 974 no no male yes no no 6.2
## 975 no no male yes no no 6.0
## 976 no no male yes no no 5.8
## 977 no no male yes no no 4.3
## 978 no no male yes no no 7.8
## 979 no no male yes no no 7.3
## 980 no no male yes no no 9.1
## 981 no no male yes no no 9.7
## 982 no no male yes no no 4.0
## 983 no no male yes no no 3.5
## 984 no no male yes no no 7.2
## 985 no no male yes no no 7.3
## 986 no no male yes no no 3.1
## 987 no no male yes no no 6.0
## 988 no no male yes no no 8.5
## 989 no no male yes no no 2.8
## 990 no no male yes no no 7.1
## 991 no no male yes no no 3.6
## 992 no no male yes no no 5.0
## 993 no no male yes no no 5.1
## 994 no no male yes no no 8.5
## 995 no no male yes no no 5.0
## 996 no no male yes no no 6.0
## 997 no no male yes no no 10.0
## 998 no no male yes no no 10.1
## 999 no no male yes no no 6.2
## 1000 no no male yes no no 11.8
## 1001 no no male yes no no 5.7
## 1002 no no male yes no no 6.5
## 1003 no no male yes no no 8.8
## 1004 no no male yes no no 11.5
## 1005 no no male yes no no 8.5
## 1006 no no male yes no no 2.7
## 1007 no no male yes no no 7.8
## 1008 no no male yes no no 6.1
## 1009 no no male yes no no 5.7
## 1010 no no male yes no no 5.0
## 1011 no no male yes no no 9.3
## 1012 no no male yes no no 5.1
## 1013 no no male yes no no 7.6
## 1014 no no male yes no no 9.2
## 1015 no no male yes no no 2.5
## 1016 no no male yes no no 3.4
## 1017 no no male yes no no 8.6
## 1018 no no male yes no no 8.9
## 1019 no no male yes no no 5.2
## 1020 no no male yes no no 5.7
## 1021 no no male yes no no 5.0
## 1022 no no male yes no no 7.5
## 1023 no no male yes no no 4.6
## 1024 no no male yes no no 6.2
## 1025 no no male yes no no 5.4
## 1026 no no male yes no no 5.0
## 1027 no no male yes no no 7.8
## 1028 no no male yes no no 4.3
## 1029 no no male yes no no 9.1
## 1030 no no male yes no no 7.3
## 1031 no no male yes no no 5.9
## 1032 no no male yes yes yes 5.8
## 1033 no no male yes yes yes 7.5
## 1034 no no male yes yes yes 5.2
## 1035 no no male yes yes yes 12.2
## 1036 no no male yes yes yes 9.1
## 1037 no no male yes yes yes 11.5
## 1038 no no male yes yes yes 10.3
## 1039 no no male yes yes yes 7.7
## 1040 no no male yes yes yes 7.1
## 1041 no no male yes yes yes 6.0
## 1042 no no male yes yes yes 8.9
## 1043 no no male yes yes yes 9.4
## 1044 no no male yes yes yes 6.9
## 1045 no no male yes yes yes 8.9
## 1046 no no male yes yes yes 6.1
## 1047 no no male yes yes yes 6.6
## 1048 no no male yes yes yes 7.1
## 1049 no no male yes yes yes 14.3
## 1050 no no male yes yes yes 11.8
## 1051 no no male yes yes yes 3.8
## 1052 no no male yes yes yes 9.9
## 1053 no no male yes yes yes 3.7
## 1054 no no male yes yes yes 3.7
## 1055 no no male yes yes yes 6.6
## 1056 no no male yes yes yes 6.4
## 1057 no no male yes yes yes 7.5
## 1058 no no male yes yes yes 9.1
## 1059 no no male yes yes yes 11.8
## 1060 no no male yes yes yes 7.4
## 1061 no no male yes yes yes 6.2
## 1062 no no male yes yes yes 13.0
## 1063 no no male yes yes yes 7.4
## 1064 no no male yes yes yes 5.0
## 1065 no no male yes yes yes 14.2
## 1066 no no male yes yes yes 11.7
## 1067 no no male yes yes yes 6.0
## 1068 no no male yes yes yes 6.9
## 1069 no no male yes yes yes 9.0
## 1070 no no male yes yes yes 4.1
## 1071 no no male yes yes yes 9.4
## 1072 no no male yes yes yes 7.8
## 1073 no no male yes yes yes 9.2
## 1074 no no male yes yes yes 7.5
## 1075 no no male yes yes yes 3.2
## 1076 no no male yes yes yes 9.5
## 1077 no no male yes yes yes 5.4
## 1078 no no male yes yes yes 9.9
## 1079 no no male yes yes yes 7.2
## 1080 no no male yes yes yes 13.1
## 1081 no no male yes yes yes 8.5
## 1082 no no male yes yes yes 9.0
## 1083 no no male yes yes yes 11.8
## 1084 no no male yes yes yes 9.0
## 1085 no no male yes yes yes 8.2
## 1086 no no male yes yes yes 5.0
## 1087 no no male yes yes yes 9.1
## 1088 no no male yes yes yes 5.5
## 1089 no no male yes yes yes 8.0
## 1090 no no male yes yes yes 6.5
## 1091 no no male yes yes yes 7.6
## 1092 no no male yes yes yes 6.7
## 1093 no no male yes yes yes 8.7
## 1094 no no male yes yes yes 5.9
## 1095 no no male yes yes yes 10.8
## 1096 no no male yes yes yes 7.7
## 1097 no no male yes yes yes 7.2
## 1098 no no male yes yes yes 10.9
## 1099 no no male yes yes yes 7.2
## 1100 no no male yes yes yes 6.2
## 1101 no no male yes yes yes 7.2
## 1102 no no male yes yes yes 8.8
## 1103 no no male yes yes yes 6.6
## 1104 no no male yes yes yes 8.6
## 1105 no no male yes yes yes 7.7
## 1106 no no male yes yes yes 5.6
## 1107 no no male yes yes yes 5.7
## 1108 no no male yes yes yes 8.6
## 1109 no no male yes yes yes 12.4
## 1110 no no male yes yes yes 5.7
## 1111 no no male yes yes yes 8.9
## 1112 no no male yes yes yes 7.8
## 1113 no no male yes yes yes 11.2
## 1114 no no male yes yes yes 14.4
## 1115 no no male yes yes yes 6.0
## 1116 no no male yes yes yes 9.0
## 1117 no no male yes yes yes 7.1
## 1118 no no male yes yes yes 4.0
## 1119 no no male yes yes yes 10.3
## 1120 no no male yes yes yes 8.0
## 1121 no no male yes yes yes 7.8
## 1122 no no male yes yes yes 3.0
## 1123 no no male yes yes yes 6.6
## 1124 no no male yes yes yes 10.3
## 1125 no no male yes yes yes 9.0
## 1126 no no male yes yes yes 11.7
## 1127 no no male yes yes yes 5.4
## 1128 no no male yes yes yes 6.2
## 1129 no no male yes yes yes 6.7
## 1130 no no male yes yes yes 5.9
## 1131 no no male yes yes yes 6.0
## 1132 no no male yes yes yes 11.8
## 1133 no no male yes yes yes 10.3
## 1134 no no male yes yes yes 10.3
## 1135 no no male yes yes yes 4.5
## 1136 no no male yes yes yes 5.8
## 1137 no no male yes yes yes 7.8
## 1138 no no male yes yes yes 5.5
## 1139 no no male yes yes yes 8.2
## 1140 no no male yes yes yes 11.6
## 1141 no no male yes yes yes 9.7
## 1142 no no male yes yes yes 8.6
## 1143 no no male yes yes yes 7.4
## 1144 no no male yes yes yes 7.4
## 1145 no no male yes yes yes 7.2
## 1146 no no male yes yes yes 9.4
## 1147 no no male yes yes yes 7.1
## 1148 no no male yes yes yes 8.9
## 1149 no no male yes yes yes 7.5
## 1150 no no male yes yes yes 6.3
## 1151 no no male yes yes yes 6.0
## 1152 no no male yes yes yes 8.0
## 1153 no no male yes yes yes 14.4
## 1154 no no male yes yes yes 7.1
## 1155 no no male yes yes yes 11.8
## 1156 no no male yes yes yes 10.0
## 1157 no no male yes yes yes 4.2
## 1158 no no male yes yes yes 9.9
## 1159 no no male yes yes yes 8.5
## 1160 no no male yes yes yes 10.8
## 1161 no no male yes yes yes 8.8
## 1162 no no male yes yes yes 5.7
## 1163 no no male yes yes yes 9.7
## 1164 no no male yes yes yes 7.5
## 1165 no no male yes yes yes 5.2
## 1166 no no male yes yes yes 11.0
## 1167 no no male yes yes yes 5.7
## 1168 no no male yes yes yes 14.4
## 1169 no no male yes yes yes 4.9
## 1170 no no male yes yes yes 7.6
## 1171 no no male yes yes yes 5.8
## 1172 no no male yes yes yes 9.9
## 1173 no no male yes yes yes 3.9
## 1174 no no male yes yes yes 4.6
## 1175 no no male yes yes yes 6.2
## 1176 no no male yes yes yes 7.0
## 1177 no no male yes yes yes 8.2
## 1178 no no male yes yes yes 8.8
## 1179 no no male yes yes yes 5.0
## 1180 no no male yes yes yes 9.3
## 1181 no no male yes yes yes 4.8
## 1182 no no male yes yes yes 12.9
## 1183 no no male yes yes yes 9.4
## 1184 no no male yes yes yes 6.0
## 1185 no no male yes yes yes 4.6
## 1186 no no male yes yes yes 7.2
## 1187 no no male yes yes yes 8.7
## 1188 no no male yes yes yes 11.8
## 1189 no no male yes yes yes 9.7
## 1190 no no male yes yes yes 7.7
## 1191 no no male yes yes yes 7.4
## 1192 no no male yes yes yes 7.4
## 1193 no no male yes yes yes 7.6
## 1194 no no male yes yes yes 5.6
## 1195 no no male yes yes yes 3.7
## 1196 no no male yes yes yes 4.9
## 1197 no no male yes yes yes 8.5
## 1198 no no male yes yes yes 5.4
## 1199 no no male yes yes yes 10.8
## 1200 no no male yes yes yes 8.8
## 1201 no no male yes yes yes 6.3
## 1202 no no male yes yes yes 9.2
## 1203 no no male yes yes yes 6.2
## 1204 no no male yes yes yes 9.7
## 1205 no no male yes yes yes 12.2
## 1206 no no male yes yes yes 3.1
## 1207 no no male yes yes yes 7.4
## 1208 no no male yes yes yes 11.7
## 1209 no no male yes yes yes 8.6
## 1210 no no male yes yes yes 7.7
## 1211 no no male yes yes yes 7.2
## 1212 no no male yes yes yes 6.2
## 1213 no no male yes yes yes 5.4
## 1214 no no male yes yes yes 7.6
## 1215 no no male yes yes yes 12.1
## 1216 no no male yes yes yes 11.8
## 1217 no no male yes yes yes 9.4
## 1218 no no male yes yes yes 5.8
## 1219 no no male yes yes yes 5.7
## 1220 no no male yes yes yes 7.5
## 1221 no no male yes yes yes 4.4
## 1222 no no male yes yes yes 5.2
## 1223 no no male yes yes yes 7.0
## 1224 no no male yes yes yes 4.8
## 1225 no no male yes yes yes 11.6
## 1226 no no male yes yes yes 6.7
## 1227 no no male yes yes yes 6.8
## 1228 no no male yes yes yes 11.8
## 1229 no no male yes yes yes 6.2
## 1230 no no male yes yes yes 7.2
## 1231 no no male yes yes yes 6.1
## 1232 no no male yes yes yes 7.5
## 1233 no no male yes yes yes 5.1
## 1234 no no male yes yes yes 14.6
## 1235 no no male yes yes yes 9.7
## 1236 no no male yes yes yes 8.9
## 1237 no no male yes yes yes 5.9
## 1238 no no male yes yes yes 3.5
## 1239 no no male yes yes yes 6.8
## 1240 no no male yes yes yes 11.4
## 1241 no no male yes yes yes 5.4
## 1242 no no male yes yes yes 6.1
## 1243 no no male yes yes yes 7.2
## 1244 no no male yes yes yes 3.8
## 1245 no no male yes yes yes 5.5
## 1246 no no male yes yes yes 8.2
## 1247 no no male yes yes yes 7.7
## 1248 no no male yes yes yes 12.6
## 1249 no no male yes yes yes 7.2
## 1250 no no male yes yes yes 12.9
## 1251 no no male yes yes yes 4.9
## 1252 no no male yes yes yes 10.3
## 1253 no no male yes yes yes 11.7
## 1254 no no male yes yes yes 3.8
## 1255 no no male yes yes yes 5.1
## 1256 no no male yes yes yes 7.6
## 1257 no no male yes yes yes 9.1
## 1258 no no male yes yes yes 11.7
## 1259 no no male yes yes yes 5.2
## 1260 no no male yes yes yes 9.0
## 1261 no no male yes yes yes 5.5
## 1262 no no male yes yes yes 9.3
## 1263 no no male yes yes yes 7.2
## 1264 no no male yes yes yes 7.1
## 1265 no no male yes yes yes 9.7
## 1266 no no male yes yes yes 8.8
## 1267 no no male yes yes yes 6.3
## 1268 no no male yes yes yes 14.6
## 1269 no no male yes yes yes 4.3
## 1270 no no male yes yes yes 7.8
## 1271 no no male yes yes yes 7.6
## 1272 no no male yes yes yes 7.7
## 1273 no no male yes yes yes 12.4
## 1274 no no male yes yes yes 9.0
## 1275 no no male yes yes yes 15.0
## 1276 no no male yes yes yes 10.3
## 1277 no no male yes yes yes 9.7
## 1278 no no male yes yes yes 6.4
## 1279 no no male yes yes yes 10.1
## 1280 no no male yes yes yes 9.1
## 1281 no no male yes yes yes 6.5
## 1282 no no male yes yes yes 2.7
## 1283 no no male yes yes yes 8.6
## 1284 no no male yes yes yes 8.5
## 1285 no no male yes yes yes 10.3
## 1286 no no male yes yes yes 8.9
## 1287 no no male yes yes yes 5.9
## 1288 no no male yes yes yes 11.5
## 1289 no no male yes yes yes 3.0
## 1290 no no male yes yes yes 5.8
## 1291 no no male yes yes yes 11.4
## 1292 no no male yes yes yes 5.4
## 1293 no no male yes yes yes 10.8
## 1294 no no male yes yes yes 5.0
## 1295 no no male yes yes yes 5.2
## 1296 no no male yes yes yes 8.7
## 1297 no no male yes yes yes 8.6
## 1298 no no male yes yes yes 7.5
## 1299 no no male yes yes yes 7.1
## 1300 no no male yes yes yes 8.5
## 1301 no no male yes yes yes 9.9
## 1302 no no male yes yes yes 14.3
## 1303 no no male yes yes yes 7.5
## 1304 no no male yes yes yes 6.1
## 1305 no no male yes yes yes 7.5
## 1306 no no male yes yes yes 5.3
## 1307 no no male yes yes yes 6.9
## 1308 no no male yes yes yes 6.6
## 1309 no no male yes yes yes 4.1
## 1310 no no male yes yes yes 5.6
## 1311 no no male yes yes yes 7.8
## 1312 no no male yes yes yes 6.9
## 1313 no no male yes yes yes 9.4
## 1314 no no male yes yes yes 8.0
## 1315 no no male yes yes yes 11.7
## 1316 no no male yes yes yes 6.3
## 1317 no no male yes yes yes 5.8
## 1318 no no male yes yes yes 7.5
## 1319 no no male yes yes yes 9.7
## 1320 no no male yes yes yes 3.7
## 1321 no no male yes yes yes 5.6
## 1322 no no male yes yes yes 7.2
## 1323 no no male yes yes yes 5.4
## 1324 no no male yes yes yes 9.2
## 1325 no no male yes yes yes 10.3
## 1326 no no male yes yes yes 7.2
## 1327 no no male yes yes yes 8.6
## 1328 no no male yes yes yes 9.2
## 1329 no no male yes yes yes 15.0
## 1330 no no male yes yes yes 10.8
## 1331 no no male yes yes yes 9.0
## 1332 no no male yes yes yes 10.8
## 1333 no no male yes yes yes 7.5
## 1334 no no male yes yes yes 6.1
## 1335 no no male yes yes yes 8.6
## 1336 no no male yes yes yes 7.3
## 1337 no no male yes yes yes 7.0
## 1338 no no male yes yes yes 6.1
## 1339 no no male yes yes yes 10.3
## 1340 no no male yes yes yes 6.3
## 1341 no no male yes yes yes 4.5
## 1342 no no male yes yes yes 3.7
## 1343 no no male yes yes yes 11.7
## 1344 no no male yes yes yes 8.1
## 1345 no no male yes yes yes 11.1
## 1346 no no male yes yes yes 11.0
## 1347 no no male yes yes yes 7.7
## 1348 no no male yes yes yes 9.2
## 1349 no no male yes yes yes 10.2
## 1350 no no male yes yes yes 5.7
## 1351 no no male yes yes yes 4.5
## 1352 no no male yes yes yes 6.7
## 1353 no no male yes yes yes 11.0
## 1354 no no male yes yes yes 6.4
## 1355 no no male yes yes yes 6.2
## 1356 no no male yes yes yes 7.4
## 1357 no no male yes yes yes 8.2
## 1358 no no male yes yes yes 6.5
## 1359 no no male yes yes yes 9.9
## 1360 no no male yes yes yes 9.0
## 1361 no no male yes yes yes 6.7
## 1362 no no male yes yes yes 6.2
## 1363 no no male yes yes yes 9.4
## 1364 no no male yes yes yes 7.2
## 1365 no no male yes yes yes 12.3
## 1366 no no male yes yes yes 8.4
## 1367 no no male yes yes yes 9.2
## 1368 no no male yes yes yes 6.0
## 1369 no no male yes yes yes 8.0
## 1370 no no male yes yes yes 18.0
## 1371 no no male yes yes yes 8.0
## 1372 no no male yes yes yes 9.4
## 1373 no no male yes yes yes 7.5
## 1374 no no male yes yes yes 8.1
## 1375 no no male yes yes yes 5.4
## 1376 no no male yes yes yes 8.9
## 1377 no no male yes yes yes 9.4
## 1378 no no male yes yes yes 9.4
## 1379 no no male yes yes yes 4.5
## 1380 no no male yes yes yes 5.3
## 1381 no no male yes yes yes 6.0
## 1382 no no male yes yes yes 8.8
## 1383 no no male yes yes yes 7.0
## 1384 no no male yes yes yes 7.0
## 1385 no no male yes yes yes 5.7
## 1386 no no male yes yes yes 5.1
## 1387 no no male yes yes yes 7.5
## 1388 no no male yes yes yes 9.7
## 1389 no no male yes yes yes 14.3
## 1390 no no male yes yes yes 8.9
## 1391 no no male yes yes yes 5.9
## 1392 no no male yes yes yes 8.4
## 1393 no no male yes yes yes 5.0
## 1394 no no male yes yes yes 5.4
## 1395 no no male yes yes yes 9.1
## 1396 no no male yes yes yes 9.2
## 1397 no no male yes yes yes 5.8
## 1398 no no male yes yes yes 8.0
## 1399 no no male yes yes yes 5.9
## 1400 no no male yes yes yes 7.5
## 1401 no no male yes yes yes 12.3
## 1402 no no male yes yes yes 8.0
## 1403 no no male yes yes yes 7.5
## 1404 no no male yes yes yes 7.3
## 1405 no no male yes yes yes 9.3
## 1406 no no male yes yes yes 9.9
## 1407 no no male yes yes yes 7.8
## 1408 no no male yes yes yes 7.6
## 1409 no no male yes yes yes 3.9
## 1410 no no male yes yes yes 14.4
## 1411 no no male yes yes yes 7.7
## 1412 no no male yes yes yes 7.6
## 1413 no no male yes yes yes 5.3
## 1414 no no male yes yes yes 8.0
## 1415 no no male yes yes yes 5.2
## 1416 no no male yes yes yes 7.5
## 1417 no no male yes yes yes 4.2
## 1418 no no male yes yes yes 5.8
## 1419 no no male yes yes yes 8.0
## 1420 no no male yes yes yes 7.4
## 1421 no no male yes yes yes 8.0
## 1422 no no male yes yes yes 6.8
## 1423 no no male yes yes yes 11.6
## 1424 no no male yes yes yes 4.4
## 1425 no no male yes yes yes 8.0
## 1426 no no male yes yes yes 7.3
## 1427 no no male yes yes yes 6.0
## 1428 no no male yes yes yes 10.8
## 1429 no no male yes yes yes 9.4
## 1430 no no male yes yes yes 7.1
## 1431 no no male yes yes yes 5.3
## 1432 no no male yes yes yes 6.7
## 1433 no no male yes yes yes 8.9
## 1434 no no male yes yes yes 8.0
## 1435 no no male yes yes yes 7.5
## 1436 no no male yes yes yes 7.7
## 1437 no no male yes yes yes 11.8
## 1438 no no male yes yes yes 12.3
## 1439 no no male yes yes yes 4.5
## 1440 no no male yes yes yes 7.2
## 1441 no no male yes yes yes 9.0
## 1442 no no male yes yes yes 11.8
## 1443 no no male yes yes yes 4.9
## 1444 no no male yes yes yes 6.5
## 1445 no no male yes yes yes 4.4
## 1446 no no male yes yes yes 11.8
## 1447 no no male yes yes yes 18.0
## 1448 no no male yes yes yes 12.4
## 1449 no no male yes yes yes 9.7
## 1450 no no male yes yes yes 10.3
## 1451 no no male yes yes yes 3.9
## 1452 no no male yes yes yes 4.7
## 1453 no no male yes yes yes 5.6
## 1454 no no male yes yes yes 5.0
## 1455 no no male yes yes yes 10.3
## 1456 no no male yes yes yes 6.6
## 1457 no no male yes yes yes 6.4
## 1458 no no male yes yes yes 3.9
## 1459 no no male yes yes yes 5.7
## 1460 no no male yes yes yes 5.4
## 1461 no no male yes yes yes 8.9
## 1462 no no male yes yes yes 11.8
## 1463 no no male yes yes yes 9.0
## 1464 no no male yes yes yes 5.7
## 1465 no no male yes yes yes 8.0
## 1466 no no male yes yes yes 7.7
## 1467 no no male yes yes yes 14.4
## 1468 no no male yes yes yes 8.0
## 1469 no no male yes yes yes 7.2
## 1470 no no male yes yes yes 7.6
## 1471 no no male yes yes yes 5.9
## 1472 no no male yes yes yes 12.0
## 1473 no no male yes yes yes 5.6
## 1474 no no male yes yes yes 9.0
## 1475 no no male yes yes yes 9.1
## 1476 no no male yes yes yes 9.4
## 1477 no no male yes yes yes 5.6
## 1478 no no male yes yes yes 7.1
## 1479 no no male yes yes yes 10.0
## 1480 no no male yes yes yes 8.1
## 1481 no no male yes yes yes 10.3
## 1482 no no male yes yes yes 3.5
## 1483 no no male yes yes yes 7.9
## 1484 no no male yes yes yes 12.1
## 1485 no no male yes yes yes 7.7
## 1486 no no male yes yes yes 5.0
## 1487 no no male yes yes yes 10.5
## 1488 no no male yes yes yes 7.4
## 1489 no no male yes yes yes 14.4
## 1490 no no male yes yes yes 5.2
## 1491 no no male yes yes yes 8.8
## 1492 no no male yes yes yes 7.1
## 1493 no no male yes yes yes 9.7
## 1494 no no male yes yes yes 11.0
## 1495 no no male yes yes yes 7.7
## 1496 no no male yes yes yes 9.0
## 1497 no no male yes yes yes 9.1
## 1498 no no male yes yes yes 5.8
## 1499 no no male yes yes yes 8.8
## 1500 no no male yes yes yes 14.3
## 1501 no no male yes yes yes 6.0
## 1502 no no male yes yes yes 11.1
## 1503 no no male yes yes yes 6.3
## 1504 no no male yes yes yes 4.9
## 1505 no no male yes yes yes 11.6
## 1506 no no male yes yes yes 5.2
## 1507 no no male yes yes yes 10.1
## 1508 no no male yes yes yes 5.1
## 1509 no no male yes yes yes 10.5
## 1510 no no male yes yes yes 8.9
## 1511 no no male yes yes yes 10.1
## 1512 no no male yes yes yes 6.6
## 1513 no no male yes yes yes 7.5
## 1514 no no male yes yes yes 7.4
## 1515 no no male yes yes yes 8.4
## 1516 no no male yes yes yes 14.2
## 1517 no no male yes yes yes 10.0
## 1518 no no male yes yes yes 7.9
## 1519 no no male yes yes yes 6.2
## 1520 no no male yes yes yes 7.1
## 1521 no no male yes yes yes 5.4
## 1522 no no male yes yes yes 7.8
## 1523 no no male yes yes yes 6.5
## 1524 no no male yes yes yes 9.8
## 1525 no no male yes yes yes 7.5
## 1526 no no male yes yes yes 6.4
## 1527 no no male yes yes yes 6.3
## 1528 no no male yes yes yes 5.4
## 1529 no no male yes yes yes 7.7
## 1530 no no male yes yes yes 5.2
## 1531 no no male yes yes yes 5.2
## 1532 no no male yes yes yes 7.9
## 1533 no no male yes yes yes 12.2
## 1534 no no male yes yes yes 8.2
## 1535 no no male yes yes yes 4.1
## 1536 no no male yes yes yes 11.8
## 1537 no no male yes yes yes 6.4
## 1538 no no male yes yes yes 10.8
## 1539 no no male yes yes yes 10.1
## 1540 no no male yes yes yes 8.5
## 1541 no no male yes yes yes 9.2
## 1542 no no male yes yes yes 12.3
## 1543 no no male yes yes yes 6.7
## 1544 no no male yes yes yes 7.6
## 1545 no no male yes yes yes 9.5
## 1546 no no male yes yes yes 11.7
## 1547 no no male yes yes yes 6.9
## 1548 no no male yes yes yes 6.0
## 1549 no no male yes yes yes 5.0
## 1550 no no male yes yes yes 6.6
## 1551 no no male yes yes yes 5.0
## 1552 no no male yes yes yes 9.7
## 1553 no no male yes yes yes 6.6
## 1554 no no male yes yes yes 12.3
## 1555 no no male yes yes yes 6.9
## 1556 no no male yes yes yes 7.2
## 1557 no no male yes yes yes 11.4
## 1558 no no male yes yes yes 6.2
## 1559 no no male yes yes yes 8.9
## 1560 no no male yes yes yes 8.9
## 1561 no no male yes yes yes 9.0
## 1562 no no male yes yes yes 15.0
## 1563 no no male yes yes yes 15.0
## 1564 no no male yes yes yes 6.3
## 1565 no no male yes yes yes 8.9
## 1566 no no male yes yes yes 8.8
## 1567 no no male yes yes yes 5.7
## 1568 no no male yes yes yes 7.2
## 1569 no no male yes yes yes 5.1
## 1570 no no male yes yes yes 8.7
## 1571 no no male yes yes yes 6.0
## 1572 no no male yes yes yes 5.8
## 1573 no no male yes yes yes 8.8
## 1574 no no male yes yes yes 10.3
## 1575 no no male yes yes yes 5.4
## 1576 no no male yes yes yes 7.2
## 1577 no no male yes yes yes 6.3
## 1578 no no male yes yes yes 6.8
## 1579 no no male yes yes yes 8.4
## 1580 no no male yes yes yes 8.2
## 1581 no no male yes yes yes 4.3
## 1582 no no male yes yes yes 4.3
## 1583 no no male yes yes yes 5.4
## 1584 no no male yes yes yes 5.8
## 1585 no no male yes yes yes 12.4
## 1586 no no male yes yes yes 5.9
## 1587 no no male yes yes yes 5.3
## 1588 no no male yes yes yes 10.1
## 1589 no no male yes yes yes 4.0
## 1590 no no male yes yes yes 11.5
## 1591 no no male yes yes yes 8.9
## 1592 no no male yes yes yes 9.0
## 1593 no no male yes yes yes 8.0
## 1594 no no male yes yes yes 5.1
## 1595 no no male yes yes yes 8.8
## 1596 no no male yes yes yes 9.5
## 1597 no no male yes yes yes 7.5
## 1598 no no male yes yes yes 3.9
## 1599 no no male yes yes yes 6.7
## 1600 no no male yes yes yes 11.8
## 1601 no no male yes yes yes 6.7
## 1602 no no male yes yes yes 4.1
## 1603 no no male yes yes yes 5.4
## 1604 no no male yes yes yes 10.5
## 1605 no no male yes yes yes 11.8
## 1606 no no male yes yes yes 5.7
## 1607 no no male yes yes yes 5.3
## 1608 no no male yes yes yes 9.4
## 1609 no no male yes yes yes 10.2
## 1610 no no male yes yes yes 9.1
## 1611 no no male yes yes yes 7.7
## 1612 no no male yes yes yes 8.0
## 1613 no no male yes yes yes 8.2
## 1614 no no male yes yes yes 7.4
## 1615 no no male yes yes yes 9.7
## 1616 no no male yes yes yes 10.5
## 1617 no no male yes yes yes 8.2
## 1618 no no male yes yes yes 11.1
## 1619 no no male yes yes yes 12.4
## 1620 no no male yes yes yes 9.0
## 1621 no no male yes yes yes 8.2
## 1622 no no male yes yes yes 6.0
## 1623 no no male yes yes yes 6.9
## 1624 no no male yes yes yes 12.3
## 1625 no no male yes yes yes 11.9
## 1626 no no male yes yes yes 5.6
## 1627 no no male yes yes yes 6.9
## 1628 no no male yes yes yes 11.8
## 1629 no no male yes yes yes 10.2
## 1630 no no male yes yes yes 10.4
## 1631 no no male yes yes yes 5.7
## 1632 no no male yes yes yes 13.0
## 1633 no no male yes yes yes 8.7
## 1634 no no male yes yes yes 10.5
## 1635 no no male yes yes yes 12.2
## 1636 no no male yes yes yes 14.4
## 1637 no no male yes yes yes 9.2
## 1638 no no male yes yes yes 3.9
## 1639 no no male yes yes yes 5.8
## 1640 no no male yes yes yes 8.1
## 1641 no no male yes yes yes 7.1
## 1642 no no male yes yes yes 8.2
## 1643 no no male yes yes yes 6.6
## 1644 no no male yes yes yes 12.1
## 1645 no no male yes yes yes 8.6
## 1646 no no male yes yes yes 7.4
## 1647 no no male yes yes yes 5.7
## 1648 no no male yes yes yes 5.9
## 1649 no no male yes yes yes 8.2
## 1650 no no male yes yes yes 7.3
## 1651 no no male yes yes yes 6.0
## 1652 no no male yes yes yes 5.8
## 1653 no no male yes yes yes 5.2
## 1654 no no male yes yes yes 11.8
## 1655 no no male yes yes yes 9.0
## 1656 no no male yes yes yes 7.0
## 1657 no no male yes yes yes 8.9
## 1658 no no male yes yes yes 7.8
## 1659 no no male yes yes yes 5.5
## 1660 no no male yes yes yes 6.3
## 1661 no no male yes yes yes 6.7
## 1662 no no male yes yes yes 9.0
## 1663 no no male yes yes yes 5.6
## 1664 no no male yes yes yes 9.3
## 1665 no no male yes yes yes 6.1
## 1666 no no male yes yes yes 14.3
## 1667 no no male yes yes yes 6.0
## 1668 no no male yes yes yes 9.0
## 1669 no no male yes yes yes 6.1
## 1670 no no male yes yes yes 7.4
## 1671 no no male yes yes yes 12.3
## 1672 no no male yes yes yes 7.0
## 1673 no no male yes yes yes 3.2
## 1674 no no male yes yes yes 6.0
## 1675 no no male yes yes yes 3.8
## 1676 no no male yes yes yes 7.0
## 1677 no no male yes yes yes 5.3
## 1678 no no male yes yes yes 9.0
## 1679 no no male yes yes yes 7.5
## 1680 no no male yes yes yes 9.3
## 1681 no no male yes yes yes 7.2
## 1682 no no male yes yes yes 8.0
## 1683 no no male yes yes yes 9.7
## 1684 no no male yes yes yes 7.4
## 1685 no no male yes yes yes 7.0
## 1686 no no male yes yes yes 10.3
## 1687 no no male yes yes yes 5.0
## 1688 no no male yes yes yes 8.1
## 1689 no no male yes yes yes 7.1
## 1690 no no male yes yes yes 8.8
## 1691 no no male yes yes yes 11.5
## 1692 no no male yes yes yes 11.7
## 1693 no no male yes yes yes 12.3
## 1694 no no male yes yes yes 5.4
## 1695 no no male yes yes yes 8.7
## 1696 no no male yes yes yes 11.8
## 1697 no no male yes yes yes 14.3
## 1698 no no male yes yes yes 3.6
## 1699 no no male yes yes yes 7.5
## 1700 no no male yes yes yes 5.6
## 1701 no no male yes yes yes 7.3
## 1702 no no male yes yes yes 10.0
## 1703 no no male yes yes yes 3.5
## 1704 no no male yes yes yes 5.8
## 1705 no no male yes yes yes 9.0
## 1706 no no male yes yes yes 6.5
## 1707 no no male yes yes yes 7.2
## 1708 no no male yes yes yes 8.5
## 1709 no no male yes yes yes 8.9
## 1710 no no male yes yes yes 8.0
## 1711 no no male yes yes yes 5.1
## 1712 no no male yes yes yes 10.3
## 1713 no no male yes yes yes 12.6
## 1714 no no male yes yes yes 14.3
## 1715 no no male yes yes yes 7.9
## 1716 no no male yes yes yes 8.4
## 1717 no no male yes yes yes 6.3
## 1718 no no male yes yes yes 11.9
## 1719 no no male yes yes yes 11.2
## 1720 no no male yes yes yes 11.8
## 1721 no no male yes yes yes 6.0
## 1722 no no male yes yes yes 7.2
## 1723 no no male yes yes yes 7.3
## 1724 no no male yes yes yes 4.1
## 1725 no no male yes yes yes 7.8
## 1726 no no male yes yes yes 6.7
## 1727 no no male yes yes yes 7.5
## 1728 no no male yes yes yes 9.7
## 1729 no no male yes yes yes 8.0
## 1730 no no male yes yes yes 5.7
## 1731 no no male yes yes yes 4.7
## 1732 no no male yes yes yes 5.2
## 1733 no no male yes yes yes 6.0
## 1734 no no male yes yes yes 10.1
## 1735 no no male yes yes yes 9.2
## 1736 no no male yes yes yes 9.0
## 1737 no no male yes yes yes 5.7
## 1738 no no male yes yes yes 6.7
## 1739 no no male yes yes yes 7.8
## 1740 no no male yes yes yes 7.2
## 1741 no no male yes yes yes 7.8
## 1742 no no male yes yes yes 7.4
## 1743 no no male yes yes yes 8.7
## 1744 no no male yes yes yes 5.1
## 1745 no no male yes yes yes 8.0
## 1746 no no male yes yes yes 6.3
## 1747 no no male yes yes yes 12.3
## 1748 no no male yes yes yes 7.6
## 1749 no no male yes yes yes 5.9
## 1750 no no male yes yes yes 7.2
## 1751 no no male yes yes yes 14.4
## 1752 no no male yes yes yes 5.5
## 1753 no no male yes yes yes 3.6
## 1754 no no male yes yes yes 8.5
## 1755 no no male yes yes yes 8.1
## 1756 no no male yes yes yes 9.9
## 1757 no no male yes yes yes 6.8
## 1758 no no male yes yes yes 10.0
## 1759 no no male yes yes yes 8.2
## 1760 no no male yes yes yes 12.6
## 1761 no no male yes yes yes 8.5
## 1762 no no male yes yes yes 8.3
## 1763 no no male yes yes yes 4.8
## 1764 no no male yes yes yes 5.7
## 1765 no no male yes yes yes 6.6
## 1766 no no male yes yes yes 7.2
## 1767 no no male yes yes yes 5.8
## 1768 no no male yes yes yes 8.9
## 1769 no no male yes yes yes 9.0
## 1770 no no male yes yes yes 7.5
## 1771 no no male yes yes yes 8.6
## 1772 no no male yes yes yes 6.0
## 1773 no no male yes yes yes 3.7
## 1774 no no male yes yes yes 4.9
## 1775 no no male yes yes yes 11.5
## 1776 no no male yes yes yes 9.9
## 1777 no no male yes yes yes 6.9
## 1778 no no male yes yes yes 5.4
## 1779 no no male yes yes yes 9.4
## 1780 no no male yes yes yes 5.9
## 1781 no no male yes yes yes 6.0
## 1782 no no male yes yes yes 8.0
## 1783 no no male yes yes yes 5.8
## 1784 no no male yes yes yes 7.0
## 1785 no no male yes yes yes 10.3
## 1786 no no male yes yes yes 5.5
## 1787 no no male yes yes yes 7.6
## 1788 no no male yes yes yes 8.2
## 1789 no no male yes yes yes 5.4
## 1790 no no male yes yes yes 11.5
## 1791 no no male yes yes yes 13.0
## 1792 no no male yes yes yes 9.1
## 1793 no no male yes yes yes 9.4
## 1794 no no male yes yes yes 3.8
## 1795 no no male yes yes yes 10.1
## 1796 no no male yes yes yes 6.0
## 1797 no no male yes yes yes 12.6
## 1798 no no male yes yes yes 6.2
## 1799 no no male yes yes yes 14.4
## 1800 no no male yes yes yes 7.5
## 1801 no no male yes yes yes 8.9
## 1802 no no male yes yes yes 9.1
## 1803 no no male yes yes yes 9.9
## 1804 no no male yes yes yes 4.3
## 1805 no no male yes yes yes 6.1
## 1806 no no male yes yes yes 7.0
## 1807 no no male yes yes yes 3.9
## 1808 no no male yes yes yes 6.7
## 1809 no no male yes yes yes 8.2
## 1810 no no male yes yes yes 18.0
## 1811 no no male yes yes yes 5.5
## 1812 no no male yes yes yes 9.7
## 1813 no no male yes yes yes 15.0
## 1814 no no male yes yes yes 7.8
## 1815 no no male yes yes yes 9.1
## 1816 no no male yes yes yes 10.5
## 1817 no no male yes yes yes 8.9
## 1818 no no male yes yes yes 7.2
## 1819 no no male yes yes yes 10.5
## 1820 no no male yes yes yes 9.9
## 1821 no no male yes yes yes 7.5
## 1822 no no male yes yes yes 8.0
## 1823 no no male yes yes yes 4.3
## 1824 no no male yes yes yes 6.5
## 1825 no no male yes yes yes 6.1
## 1826 no no male yes yes yes 5.6
## 1827 no no male yes yes yes 8.9
## 1828 no no male yes yes yes 12.3
## 1829 no no male yes yes yes 8.1
## 1830 no no male yes yes yes 5.4
## 1831 no no male yes yes yes 9.8
## 1832 no no male yes yes yes 8.6
## 1833 no no male yes yes yes 5.4
## 1834 no no male yes yes yes 6.9
## 1835 no no male yes yes yes 4.3
## 1836 no no male yes yes yes 4.2
## 1837 no no male yes yes yes 5.4
## 1838 no no male yes yes yes 5.1
## 1839 no no male yes yes yes 9.0
## 1840 no no male yes yes yes 5.3
## 1841 no no male yes yes yes 8.0
## 1842 no no male yes yes yes 8.1
## 1843 no no male yes yes yes 4.4
## 1844 no no male yes yes yes 5.2
## 1845 no no male yes yes yes 7.1
## 1846 no no male yes yes yes 5.6
## 1847 no no male yes yes yes 7.0
## 1848 no no male yes yes yes 5.4
## 1849 no no male yes yes yes 14.3
## 1850 no no male yes yes yes 8.0
## 1851 no no male yes yes yes 7.2
## 1852 no no male yes yes yes 6.7
## 1853 no yes female no no yes 11.0
## 1854 no yes female no no yes 5.3
## 1855 no yes female no no yes 7.2
## 1856 no yes female no no yes 7.2
## 1857 no yes female no no yes 5.4
## 1858 no yes female no no yes 4.8
## 1859 no yes female no no yes 4.2
## 1860 no yes female no no yes 7.5
## 1861 no yes female no no yes 8.2
## 1862 no yes female no no yes 9.7
## 1863 no yes female no no yes 7.3
## 1864 no yes female no no yes 5.8
## 1865 no yes female no no yes 5.6
## 1866 no yes female no no yes 6.8
## 1867 no yes female no no yes 9.2
## 1868 no yes female no no yes 6.2
## 1869 no yes female no no yes 6.9
## 1870 no yes female no no yes 5.9
## 1871 no yes female no no yes 5.0
## 1872 no yes female no no yes 11.4
## 1873 no yes female no no yes 6.2
## 1874 no yes female no no yes 8.9
## 1875 no yes female no no yes 6.6
## 1876 no yes female no no yes 10.0
## 1877 no yes female no no yes 6.0
## 1878 no yes female no no yes 9.1
## 1879 no yes female no no yes 5.8
## 1880 no yes female no no yes 6.3
## 1881 no yes female no no yes 7.8
## 1882 no yes female no no yes 4.8
## 1883 no yes female no no yes 5.7
## 1884 no yes female no no yes 5.4
## 1885 no yes female no no yes 10.2
## 1886 no yes female no yes no 3.5
## 1887 no yes female no yes no 5.4
## 1888 no yes female no yes no 7.7
## 1889 no yes female no yes no 7.3
## 1890 no yes female no yes no 6.9
## 1891 no yes female yes no no 6.3
## 1892 no yes female yes no no 9.1
## 1893 no yes female yes no no 3.5
## 1894 no yes female yes no no 7.1
## 1895 no yes female yes no no 3.1
## 1896 no yes female yes no no 5.0
## 1897 no yes female yes no no 5.5
## 1898 no yes female yes no no 9.7
## 1899 no yes female yes no no 5.3
## 1900 no yes female yes no no 8.4
## 1901 no yes female yes yes yes 5.4
## 1902 no yes female yes yes yes 7.3
## 1903 no yes female yes yes yes 7.0
## 1904 no yes female yes yes yes 4.6
## 1905 no yes female yes yes yes 10.1
## 1906 no yes female yes yes yes 11.6
## 1907 no yes female yes yes yes 5.6
## 1908 no yes female yes yes yes 10.0
## 1909 no yes female yes yes yes 6.0
## 1910 no yes female yes yes yes 7.0
## 1911 no yes female yes yes yes 11.8
## 1912 no yes female yes yes yes 9.4
## 1913 no yes female yes yes yes 3.2
## 1914 no yes female yes yes yes 8.4
## 1915 no yes female yes yes yes 8.1
## 1916 no yes female yes yes yes 9.1
## 1917 no yes female yes yes yes 14.6
## 1918 no yes female yes yes yes 11.5
## 1919 no yes female yes yes yes 9.4
## 1920 no yes female yes yes yes 6.4
## 1921 no yes female yes yes yes 10.2
## 1922 no yes female yes yes yes 5.2
## 1923 no yes female yes yes yes 5.2
## 1924 no yes female yes yes yes 8.0
## 1925 no yes female yes yes yes 7.0
## 1926 no yes female yes yes yes 7.3
## 1927 no yes female yes yes yes 5.7
## 1928 no yes female yes yes yes 7.2
## 1929 no yes female yes yes yes 11.0
## 1930 no yes male no no no 8.4
## 1931 no yes male no no no 6.7
## 1932 no yes male no no no 5.8
## 1933 no yes male no no no 9.3
## 1934 no yes male no no no 3.7
## 1935 no yes male no no no 3.5
## 1936 no yes male no no no 8.9
## 1937 no yes male no no no 7.1
## 1938 no yes male no no no 9.0
## 1939 no yes male no no no 3.9
## 1940 no yes male no no no 5.9
## 1941 no yes male no no no 6.4
## 1942 no yes male no no no 11.5
## 1943 no yes male no no no 12.3
## 1944 no yes male no no no 4.9
## 1945 no yes male no no no 6.8
## 1946 no yes male no no no 8.5
## 1947 no yes male no no no 7.8
## 1948 no yes male no no no 6.1
## 1949 no yes male no no no 6.9
## 1950 no yes male no no no 6.6
## 1951 no yes male no no no 9.7
## 1952 no yes male no no no 7.2
## 1953 no yes male no no no 6.7
## 1954 no yes male no no no 6.4
## 1955 no yes male no no no 5.1
## 1956 no yes male no no no 4.3
## 1957 no yes male no no no 3.8
## 1958 no yes male no no no 8.6
## 1959 no yes male no no no 4.3
## 1960 no yes male no no no 8.1
## 1961 no yes male no no no 5.8
## 1962 no yes male no no no 11.1
## 1963 no yes male no no no 5.7
## 1964 no yes male no no no 6.7
## 1965 no yes male no no no 7.5
## 1966 no yes male no no no 6.9
## 1967 no yes male no no no 6.3
## 1968 no yes male no no no 5.8
## 1969 no yes male no no no 6.1
## 1970 no yes male no no no 9.2
## 1971 no yes male no no no 6.3
## 1972 no yes male no no no 7.7
## 1973 no yes male no no no 8.0
## 1974 no yes male no no no 6.3
## 1975 no yes male no no no 5.3
## 1976 no yes male no no no 5.0
## 1977 no yes male no no no 7.1
## 1978 no yes male no no no 5.1
## 1979 no yes male no no no 7.8
## 1980 no yes male no no no 5.3
## 1981 no yes male no no no 7.3
## 1982 no yes male no no no 8.1
## 1983 no yes male no no no 8.5
## 1984 no yes male no no no 7.4
## 1985 no yes male no no no 6.6
## 1986 no yes male no no no 6.3
## 1987 no yes male no no no 5.6
## 1988 no yes male no no no 9.7
## 1989 no yes male no no no 6.3
## 1990 no yes male no no no 6.4
## 1991 no yes male no no no 7.7
## 1992 no yes male no no no 5.3
## 1993 no yes male no no no 11.7
## 1994 no yes male no no no 6.9
## 1995 no yes male no no no 10.0
## 1996 no yes male no no no 5.0
## 1997 no yes male no no no 4.9
## 1998 no yes male no no no 5.6
## 1999 no yes male no no no 7.5
## 2000 no yes male no no no 3.9
## 2001 no yes male no no no 5.8
## 2002 no yes male no no no 6.6
## 2003 no yes male no no no 5.5
## 2004 no yes male no no no 5.4
## 2005 no yes male no no no 6.9
## 2006 no yes male no yes yes 9.7
## 2007 no yes male no yes yes 5.1
## 2008 no yes male no yes yes 7.5
## 2009 no yes male no yes yes 4.4
## 2010 no yes male no yes yes 6.9
## 2011 no yes male no yes yes 6.6
## 2012 no yes male no yes yes 7.3
## 2013 no yes male no yes yes 8.7
## 2014 no yes male no yes yes 5.8
## 2015 no yes male no yes yes 14.2
## 2016 no yes male no yes yes 5.0
## 2017 no yes male no yes yes 6.5
## 2018 no yes male yes no yes 5.8
## 2019 no yes male yes no yes 7.2
## 2020 no yes male yes no yes 9.1
## 2021 no yes male yes no yes 5.8
## 2022 no yes male yes no yes 6.0
## 2023 no yes male yes no yes 7.3
## 2024 no yes male yes no yes 7.2
## 2025 no yes male yes no yes 9.0
## 2026 no yes male yes no yes 14.3
## 2027 no yes male yes no yes 5.2
## 2028 no yes male yes no yes 9.5
## 2029 no yes male yes no yes 7.5
## 2030 no yes male yes no yes 7.2
## 2031 no yes male yes no yes 8.2
## 2032 no yes male yes no yes 7.2
## 2033 no yes male yes no yes 5.5
## 2034 no yes male yes no yes 5.7
## 2035 no yes male yes no yes 8.0
## 2036 no yes male yes no yes 13.0
## 2037 no yes male yes no yes 5.6
## 2038 no yes male yes no yes 4.3
## 2039 no yes male yes no yes 5.4
## 2040 no yes male yes no yes 5.6
## 2041 no yes male yes no yes 6.6
## 2042 no yes male yes no yes 6.7
## 2043 no yes male yes no yes 4.8
## 2044 no yes male yes no yes 7.3
## 2045 no yes male yes no yes 6.4
## 2046 no yes male yes no yes 4.5
## 2047 no yes male yes no yes 7.5
## 2048 no yes male yes no yes 7.7
## 2049 no yes male yes no yes 6.3
## 2050 no yes male yes no yes 10.8
## 2051 no yes male yes no yes 6.7
## 2052 no yes male yes no yes 8.0
## 2053 no yes male yes no yes 3.3
## 2054 no yes male yes no yes 5.8
## 2055 no yes male yes no yes 8.9
## 2056 no yes male yes no yes 12.0
## 2057 no yes male yes no yes 6.5
## 2058 no yes male yes no yes 9.7
## 2059 no yes male yes no yes 6.3
## 2060 no yes male yes no yes 8.6
## 2061 no yes male yes no yes 6.4
## 2062 no yes male yes no yes 5.9
## 2063 no yes male yes no yes 12.3
## 2064 no yes male yes no yes 4.8
## 2065 no yes male yes no yes 14.3
## 2066 no yes male yes no yes 11.5
## 2067 no yes male yes no yes 8.4
## 2068 no yes male yes no yes 9.1
## 2069 no yes male yes no yes 4.8
## 2070 no yes male yes no yes 5.1
## 2071 no yes male yes no yes 8.1
## 2072 no yes male yes no yes 8.8
## 2073 no yes male yes no yes 5.7
## 2074 no yes male yes no yes 5.8
## 2075 no yes male yes no yes 6.3
## 2076 no yes male yes no yes 9.1
## 2077 no yes male yes no yes 6.2
## 2078 no yes male yes no yes 9.1
## 2079 no yes male yes no yes 10.8
## 2080 no yes male yes no yes 7.2
## 2081 no yes male yes no yes 5.6
## 2082 no yes male yes no yes 6.1
## 2083 no yes male yes no yes 5.9
## 2084 no yes male yes no yes 6.1
## 2085 no yes male yes no yes 7.2
## 2086 no yes male yes no yes 6.4
## 2087 no yes male yes no yes 4.5
## 2088 no yes male yes no yes 5.9
## 2089 no yes male yes no yes 8.1
## 2090 no yes male yes no yes 11.0
## 2091 no yes male yes no yes 3.5
## 2092 no yes male yes no yes 4.3
## 2093 no yes male yes no yes 7.0
## 2094 no yes male yes no yes 5.9
## 2095 no yes male yes no yes 9.0
## 2096 no yes male yes no yes 11.4
## 2097 no yes male yes no yes 3.8
## 2098 no yes male yes no yes 7.3
## 2099 no yes male yes no yes 7.5
## 2100 no yes male yes no yes 5.5
## 2101 no yes male yes no yes 11.9
## 2102 no yes male yes yes no 8.3
## 2103 no yes male yes yes no 5.2
## 2104 no yes male yes yes no 6.7
## 2105 no yes male yes yes no 8.2
## 2106 no yes male yes yes no 10.8
## 2107 no yes male yes yes no 5.7
## 2108 no yes male yes yes no 9.7
## 2109 no yes male yes yes no 6.5
## 2110 no yes male yes yes no 5.4
## 2111 no yes male yes yes no 8.5
## 2112 no yes male yes yes no 9.7
## 2113 no yes male yes yes no 5.3
## 2114 no yes male yes yes no 8.6
## 2115 no yes male yes yes no 6.0
## 2116 no yes male yes yes no 5.4
## 2117 no yes male yes yes no 5.7
## 2118 no yes male yes yes no 4.9
## 2119 no yes male yes yes no 5.4
## 2120 no yes male yes yes no 10.1
## 2121 no yes male yes yes no 5.8
## 2122 no yes male yes yes no 11.2
## 2123 no yes male yes yes no 5.6
## 2124 no yes male yes yes no 8.9
## 2125 no yes male yes yes no 5.5
## 2126 no yes male yes yes no 7.0
## 2127 no yes male yes yes no 8.6
## 2128 no yes male yes yes no 8.0
## 2129 no yes male yes yes no 6.4
## 2130 no yes male yes yes no 7.0
## 2131 no yes male yes yes no 12.1
## 2132 no yes male yes yes no 7.4
## 2133 no yes male yes yes no 5.7
## 2134 no yes male yes yes no 6.4
## 2135 no yes male yes yes no 6.3
## 2136 no yes male yes yes no 7.7
## 2137 no yes male yes yes no 5.7
## 2138 no yes male yes yes no 4.8
## 2139 no yes male yes yes no 6.1
## 2140 no yes male yes yes no 8.8
## 2141 no yes male yes yes no 4.3
## 2142 no yes male yes yes no 4.3
## 2143 no yes male yes yes no 10.1
## 2144 no yes male yes yes no 6.9
## 2145 no yes male yes yes no 5.3
## 2146 no yes male yes yes no 5.0
## 2147 no yes male yes yes no 4.0
## 2148 no yes male yes yes no 5.7
## 2149 no yes male yes yes no 7.1
## 2150 no yes male yes yes no 7.3
## 2151 no yes male yes yes no 6.5
## 2152 no yes male yes yes no 6.2
## 2153 no yes male yes yes no 4.1
## 2154 no yes male yes yes no 4.9
## 2155 no yes male yes yes no 9.2
## 2156 no yes male yes yes no 7.7
## 2157 no yes male yes yes no 8.0
## 2158 no yes male yes yes no 8.5
## 2159 no yes male yes yes no 7.1
## 2160 no yes male yes yes no 5.5
## 2161 no yes male yes yes no 11.0
## 2162 no yes male yes yes no 5.7
## 2163 no yes male yes yes no 10.0
## 2164 no yes male yes yes no 6.1
## 2165 no yes male yes yes no 7.8
## 2166 no yes male yes yes no 9.5
## 2167 no yes male yes yes no 5.3
## 2168 no yes male yes yes no 4.2
## 2169 no yes male yes yes no 9.0
## 2170 no yes male yes yes no 5.3
## 2171 no yes male yes yes no 8.9
## 2172 no yes male yes yes no 7.4
## 2173 no yes male yes yes no 9.7
## 2174 no yes male yes yes no 5.1
## 2175 no yes male yes yes no 5.8
## 2176 no yes male yes yes no 14.6
## 2177 no yes male yes yes no 4.2
## 2178 no yes male yes yes no 4.9
## 2179 no yes male yes yes no 6.5
## 2180 no yes male yes yes no 4.4
## 2181 no yes male yes yes no 6.2
## 2182 no yes male yes yes no 5.7
## 2183 no yes male yes yes no 6.0
## 2184 no yes male yes yes no 6.2
## 2185 no yes male yes yes no 10.3
## 2186 no yes male yes yes no 8.6
## 2187 no yes male yes yes no 8.0
## 2188 no yes male yes yes no 6.5
## 2189 no yes male yes yes no 6.2
## 2190 no yes male yes yes no 4.9
## 2191 no yes male yes yes no 12.6
## 2192 no yes male yes yes no 3.8
## 2193 no yes male yes yes no 7.2
## 2194 no yes male yes yes no 5.3
## 2195 no yes male yes yes no 9.0
## 2196 no yes male yes yes no 10.0
## 2197 no yes male yes yes no 6.9
## 2198 no yes male yes yes no 4.1
## 2199 no yes male yes yes no 7.5
## 2200 no yes male yes yes no 11.4
## 2201 no yes male yes yes no 13.0
## 2202 no yes male yes yes no 8.2
## 2203 no yes male yes yes no 9.8
## 2204 no yes male yes yes no 4.3
## 2205 no yes male yes yes no 10.3
## 2206 yes no female no no yes 11.1
## 2207 yes no female no no yes 14.3
## 2208 yes no female no no yes 9.5
## 2209 yes no female no no yes 4.8
## 2210 yes no female no no yes 7.2
## 2211 yes no female no no yes 4.1
## 2212 yes no female no no yes 5.3
## 2213 yes no female no no yes 9.9
## 2214 yes no female no no yes 4.5
## 2215 yes no female no no yes 7.5
## 2216 yes no female no no yes 5.9
## 2217 yes no female no no yes 4.1
## 2218 yes no female no no yes 6.9
## 2219 yes no female no no yes 6.9
## 2220 yes no female no no yes 6.7
## 2221 yes no female no no yes 9.5
## 2222 yes no female no no yes 11.6
## 2223 yes no female no no yes 5.8
## 2224 yes no female no no yes 9.7
## 2225 yes no female no no yes 3.6
## 2226 yes no female no no yes 5.7
## 2227 yes no female no no yes 9.3
## 2228 yes no female no no yes 10.8
## 2229 yes no female no no yes 4.8
## 2230 yes no female no no yes 9.7
## 2231 yes no female no no yes 5.8
## 2232 yes no female no no yes 6.3
## 2233 yes no female no no yes 5.2
## 2234 yes no female no no yes 5.3
## 2235 yes no female no no yes 5.7
## 2236 yes no female no no yes 5.0
## 2237 yes no female no no yes 7.2
## 2238 yes no female no no yes 5.8
## 2239 yes no female no no yes 6.2
## 2240 yes no female no no yes 6.8
## 2241 yes no female no no yes 9.7
## 2242 yes no female no no yes 11.4
## 2243 yes no female no no yes 8.6
## 2244 yes no female no no yes 3.5
## 2245 yes no female no no yes 11.7
## 2246 yes no female no no yes 7.2
## 2247 yes no female no no yes 7.2
## 2248 yes no female no no yes 7.2
## 2249 yes no female no no yes 5.7
## 2250 yes no female no no yes 10.3
## 2251 yes no female no no yes 4.0
## 2252 yes no female no no yes 9.4
## 2253 yes no female no no yes 5.7
## 2254 yes no female no no yes 6.1
## 2255 yes no female no yes no 5.4
## 2256 yes no female no yes no 7.8
## 2257 yes no female no yes no 12.6
## 2258 yes no female no yes no 10.2
## 2259 yes no female no yes no 3.9
## 2260 yes no female no yes no 5.6
## 2261 yes no female no yes no 5.4
## 2262 yes no female no yes no 5.4
## 2263 yes no female no yes no 5.6
## 2264 yes no female no yes no 11.8
## 2265 yes no female no yes no 5.3
## 2266 yes no female no yes no 5.3
## 2267 yes no female no yes no 8.4
## 2268 yes no female no yes no 6.4
## 2269 yes no female no yes no 6.3
## 2270 yes no female no yes no 7.5
## 2271 yes no female no yes no 8.5
## 2272 yes no female no yes no 8.6
## 2273 yes no female no yes no 5.6
## 2274 yes no female no yes no 5.2
## 2275 yes no female no yes no 5.7
## 2276 yes no female yes no no 6.7
## 2277 yes no female yes no no 7.5
## 2278 yes no female yes no no 11.5
## 2279 yes no female yes no no 6.4
## 2280 yes no female yes no no 5.6
## 2281 yes no female yes yes yes 3.5
## 2282 yes no female yes yes yes 8.9
## 2283 yes no female yes yes yes 6.6
## 2284 yes no female yes yes yes 6.7
## 2285 yes no female yes yes yes 11.8
## 2286 yes no female yes yes yes 5.9
## 2287 yes no female yes yes yes 7.1
## 2288 yes no female yes yes yes 7.8
## 2289 yes no female yes yes yes 3.5
## 2290 yes no female yes yes yes 7.8
## 2291 yes no female yes yes yes 5.6
## 2292 yes no female yes yes yes 9.7
## 2293 yes no female yes yes yes 8.1
## 2294 yes no female yes yes yes 12.6
## 2295 yes no female yes yes yes 3.6
## 2296 yes no female yes yes yes 8.2
## 2297 yes no female yes yes yes 5.4
## 2298 yes no female yes yes yes 5.8
## 2299 yes no female yes yes yes 8.6
## 2300 yes no female yes yes yes 5.2
## 2301 yes no female yes yes yes 7.0
## 2302 yes no female yes yes yes 10.3
## 2303 yes no female yes yes yes 5.3
## 2304 yes no female yes yes yes 5.9
## 2305 yes no female yes yes yes 8.6
## 2306 yes no female yes yes yes 5.8
## 2307 yes no female yes yes yes 5.4
## 2308 yes no female yes yes yes 5.6
## 2309 yes no female yes yes yes 6.2
## 2310 yes no female yes yes yes 5.7
## 2311 yes no female yes yes yes 10.1
## 2312 yes no female yes yes yes 11.1
## 2313 yes no female yes yes yes 7.8
## 2314 yes no female yes yes yes 5.8
## 2315 yes no female yes yes yes 11.9
## 2316 yes no female yes yes yes 3.9
## 2317 yes no female yes yes yes 4.8
## 2318 yes no female yes yes yes 4.1
## 2319 yes no female yes yes yes 7.4
## 2320 yes no female yes yes yes 11.9
## 2321 yes no female yes yes yes 5.9
## 2322 yes no female yes yes yes 5.8
## 2323 yes no female yes yes yes 6.3
## 2324 yes no female yes yes yes 10.4
## 2325 yes no female yes yes yes 6.6
## 2326 yes no female yes yes yes 6.6
## 2327 yes no female yes yes yes 9.0
## 2328 yes no female yes yes yes 9.1
## 2329 yes no male no no no 5.4
## 2330 yes no male no no no 4.8
## 2331 yes no male no no no 5.6
## 2332 yes no male no no no 6.3
## 2333 yes no male no no no 4.6
## 2334 yes no male no no no 11.7
## 2335 yes no male no no no 12.6
## 2336 yes no male no no no 8.1
## 2337 yes no male no no no 5.8
## 2338 yes no male no no no 6.3
## 2339 yes no male no no no 6.9
## 2340 yes no male no no no 6.7
## 2341 yes no male no no no 3.5
## 2342 yes no male no no no 5.5
## 2343 yes no male no no no 7.2
## 2344 yes no male no no no 7.1
## 2345 yes no male no no no 8.0
## 2346 yes no male no no no 4.0
## 2347 yes no male no no no 7.2
## 2348 yes no male no no no 6.5
## 2349 yes no male no no no 7.5
## 2350 yes no male no no no 6.3
## 2351 yes no male no no no 6.3
## 2352 yes no male no no no 8.1
## 2353 yes no male no no no 6.3
## 2354 yes no male no no no 6.5
## 2355 yes no male no no no 7.2
## 2356 yes no male no no no 5.7
## 2357 yes no male no no no 8.6
## 2358 yes no male no no no 6.0
## 2359 yes no male no no no 7.0
## 2360 yes no male no no no 7.0
## 2361 yes no male no no no 4.5
## 2362 yes no male no no no 7.3
## 2363 yes no male no no no 5.0
## 2364 yes no male no no no 9.0
## 2365 yes no male no no no 3.5
## 2366 yes no male no no no 5.5
## 2367 yes no male no no no 6.8
## 2368 yes no male no no no 8.5
## 2369 yes no male no no no 7.2
## 2370 yes no male no no no 5.5
## 2371 yes no male no no no 4.1
## 2372 yes no male no no no 8.2
## 2373 yes no male no no no 6.3
## 2374 yes no male no no no 7.2
## 2375 yes no male no no no 7.9
## 2376 yes no male no no no 6.5
## 2377 yes no male no no no 3.8
## 2378 yes no male no no no 6.2
## 2379 yes no male no no no 7.5
## 2380 yes no male no no no 7.2
## 2381 yes no male no no no 9.4
## 2382 yes no male no yes yes 6.7
## 2383 yes no male no yes yes 6.9
## 2384 yes no male no yes yes 13.1
## 2385 yes no male no yes yes 11.5
## 2386 yes no male no yes yes 7.2
## 2387 yes no male no yes yes 10.4
## 2388 yes no male no yes yes 4.7
## 2389 yes no male no yes yes 5.7
## 2390 yes no male no yes yes 13.1
## 2391 yes no male no yes yes 5.6
## 2392 yes no male no yes yes 10.8
## 2393 yes no male no yes yes 10.4
## 2394 yes no male yes no yes 5.7
## 2395 yes no male yes no yes 5.0
## 2396 yes no male yes no yes 4.0
## 2397 yes no male yes no yes 10.8
## 2398 yes no male yes no yes 7.7
## 2399 yes no male yes no yes 5.6
## 2400 yes no male yes no yes 6.6
## 2401 yes no male yes no yes 6.5
## 2402 yes no male yes no yes 3.8
## 2403 yes no male yes no yes 10.8
## 2404 yes no male yes no yes 14.7
## 2405 yes no male yes no yes 6.3
## 2406 yes no male yes no yes 10.2
## 2407 yes no male yes no yes 8.1
## 2408 yes no male yes no yes 7.2
## 2409 yes no male yes no yes 6.3
## 2410 yes no male yes no yes 4.1
## 2411 yes no male yes no yes 9.1
## 2412 yes no male yes no yes 5.3
## 2413 yes no male yes no yes 6.2
## 2414 yes no male yes no yes 8.9
## 2415 yes no male yes no yes 7.0
## 2416 yes no male yes no yes 2.8
## 2417 yes no male yes no yes 12.6
## 2418 yes no male yes no yes 13.7
## 2419 yes no male yes no yes 10.0
## 2420 yes no male yes no yes 8.6
## 2421 yes no male yes no yes 8.0
## 2422 yes no male yes no yes 5.4
## 2423 yes no male yes no yes 5.8
## 2424 yes no male yes no yes 7.0
## 2425 yes no male yes no yes 5.4
## 2426 yes no male yes no yes 8.0
## 2427 yes no male yes no yes 7.2
## 2428 yes no male yes no yes 10.3
## 2429 yes no male yes no yes 6.8
## 2430 yes no male yes no yes 12.4
## 2431 yes no male yes no yes 4.9
## 2432 yes no male yes no yes 5.3
## 2433 yes no male yes yes no 7.2
## 2434 yes no male yes yes no 9.0
## 2435 yes no male yes yes no 3.2
## 2436 yes no male yes yes no 4.5
## 2437 yes no male yes yes no 5.1
## 2438 yes no male yes yes no 6.7
## 2439 yes no male yes yes no 6.5
## 2440 yes no male yes yes no 4.2
## 2441 yes no male yes yes no 5.5
## 2442 yes no male yes yes no 3.2
## 2443 yes no male yes yes no 10.0
## 2444 yes no male yes yes no 8.0
## 2445 yes no male yes yes no 7.8
## 2446 yes no male yes yes no 7.2
## 2447 yes no male yes yes no 6.5
## 2448 yes no male yes yes no 7.8
## 2449 yes no male yes yes no 7.9
## 2450 yes no male yes yes no 12.4
## 2451 yes no male yes yes no 4.2
## 2452 yes no male yes yes no 10.3
## 2453 yes no male yes yes no 10.2
## 2454 yes no male yes yes no 8.4
## 2455 yes no male yes yes no 5.1
## 2456 yes no male yes yes no 9.0
## 2457 yes no male yes yes no 6.7
## 2458 yes no male yes yes no 5.1
## 2459 yes no male yes yes no 8.8
## 2460 yes no male yes yes no 7.7
## 2461 yes no male yes yes no 7.0
## 2462 yes no male yes yes no 3.6
## 2463 yes no male yes yes no 2.8
## 2464 yes no male yes yes no 6.9
## 2465 yes no male yes yes no 7.5
## 2466 yes no male yes yes no 9.2
## 2467 yes no male yes yes no 7.9
## 2468 yes no male yes yes no 8.1
## 2469 yes no male yes yes no 10.3
## 2470 yes no male yes yes no 7.7
## 2471 yes no male yes yes no 8.4
## 2472 yes no male yes yes no 8.8
## 2473 yes no male yes yes no 8.6
## 2474 yes yes female no no no 6.5
## 2475 yes yes female no no no 6.5
## 2476 yes yes female no no no 6.0
## 2477 yes yes female no no no 5.8
## 2478 yes yes female no no no 5.9
## 2479 yes yes female no yes yes 9.1
## 2480 yes yes female no yes yes 7.5
## 2481 yes yes female no yes yes 9.0
## 2482 yes yes female no yes yes 14.6
## 2483 yes yes female no yes yes 4.3
## 2484 yes yes female no yes yes 12.0
## 2485 yes yes female no yes yes 5.9
## 2486 yes yes female no yes yes 10.3
## 2487 yes yes female no yes yes 11.5
## 2488 yes yes female no yes yes 7.4
## 2489 yes yes female yes no yes 5.8
## 2490 yes yes female yes no yes 8.2
## 2491 yes yes female yes yes no 7.6
## 2492 yes yes female yes yes no 5.8
## 2493 yes yes male no no yes 7.3
## 2494 yes yes male no no yes 4.5
## 2495 yes yes male no no yes 9.9
## 2496 yes yes male no no yes 6.6
## 2497 yes yes male no no yes 4.7
## 2498 yes yes male no no yes 8.1
## 2499 yes yes male no no yes 7.4
## 2500 yes yes male no no yes 11.8
## 2501 yes yes male no no yes 9.4
## 2502 yes yes male no no yes 7.3
## 2503 yes yes male no no yes 8.1
## 2504 yes yes male no no yes 4.1
## 2505 yes yes male no no yes 5.9
## 2506 yes yes male no no yes 9.4
## 2507 yes yes male no no yes 8.9
## 2508 yes yes male no no yes 9.7
## 2509 yes yes male no no yes 5.5
## 2510 yes yes male no no yes 7.5
## 2511 yes yes male no no yes 6.8
## 2512 yes yes male no no yes 12.4
## 2513 yes yes male no no yes 7.2
## 2514 yes yes male no no yes 11.4
## 2515 yes yes male no no yes 12.4
## 2516 yes yes male no no yes 7.3
## 2517 yes yes male no no yes 14.6
## 2518 yes yes male no no yes 9.1
## 2519 yes yes male no no yes 5.8
## 2520 yes yes male no yes no 8.1
## 2521 yes yes male yes no no 5.1
## 2522 yes yes male yes no no 11.1
## 2523 yes yes male yes no no 6.2
## 2524 yes yes male yes no no 5.8
## 2525 yes yes male yes no no 5.4
## 2526 yes yes male yes yes yes 4.7
## 2527 yes yes male yes yes yes 7.2
## 2528 yes yes male yes yes yes 5.7
## 2529 yes yes male yes yes yes 6.5
## 2530 yes yes male yes yes yes 5.8
## 2531 yes yes male yes yes yes 4.4
## 2532 yes yes male yes yes yes 10.1
## 2533 yes yes male yes yes yes 6.4
## 2534 yes yes male yes yes yes 11.7
## 2535 yes yes male yes yes yes 4.5
## 2536 yes yes male yes yes yes 8.9
## 2537 yes yes male yes yes yes 8.2
## 2538 yes yes male yes yes yes 7.1
## 2539 yes yes male yes yes yes 7.8
## 2540 yes yes male yes yes yes 5.4
## 2541 yes yes male yes yes yes 10.1
## 2542 yes yes male yes yes yes 11.2
## 2543 yes yes male yes yes yes 7.8
## 2544 yes yes male yes yes yes 7.3
## 2545 yes yes male yes yes yes 7.5
## 2546 yes yes male yes yes yes 12.4
## 2547 yes yes male yes yes yes 9.7
## 2548 yes yes male yes yes yes 8.0
## 2549 yes yes male yes yes yes 9.4
## 2550 yes yes male yes yes yes 6.4
## 2551 yes yes male yes yes yes 8.0
## 2552 yes yes male yes yes yes 5.2
## 2553 yes yes male yes yes yes 9.8
## 2554 yes yes male yes yes yes 6.7
## 2555 yes yes male yes yes yes 7.2#Extract and display all unique rows from "FFD_benefits".
FFD_benefits_unique <- unique(FFD_benefits[,1:7])
FFD_benefits_unique## nwhite school12 sex married dkids ui stateur
## 1 no no female no no no 5.0
## 2 no no female no no no 5.8
## 3 no no female no no no 4.9
## 5 no no female no no no 5.3
## 6 no no female no no no 3.6
## 7 no no female no no no 10.3
## 8 no no female no no no 8.4
## 9 no no female no no no 3.7
## 10 no no female no no no 8.0
## 11 no no female no no no 6.3
## 12 no no female no no no 10.2
## 14 no no female no no no 5.1
## 15 no no female no no no 9.4
## 17 no no female no no no 4.5
## 18 no no female no no no 6.2
## 19 no no female no no no 7.3
## 20 no no female no no no 4.7
## 22 no no female no no no 7.8
## 23 no no female no no no 6.9
## 25 no no female no no no 4.3
## 27 no no female no no no 12.6
## 29 no no female no no no 9.0
## 31 no no female no no no 9.7
## 32 no no female no no no 3.1
## 33 no no female no no no 6.0
## 34 no no female no no no 3.5
## 35 no no female no no no 7.6
## 36 no no female no no no 8.1
## 37 no no female no no no 4.1
## 39 no no female no no no 4.8
## 40 no no female no no no 5.9
## 41 no no female no no no 10.0
## 42 no no female no no no 6.8
## 43 no no female no no no 8.9
## 45 no no female no no no 10.8
## 46 no no female no no no 6.7
## 47 no no female no no no 11.5
## 49 no no female no no no 15.0
## 50 no no female no no no 6.4
## 52 no no female no no no 11.6
## 53 no no female no no no 12.1
## 55 no no female no no no 9.2
## 56 no no female no no no 3.9
## 57 no no female no no no 7.2
## 60 no no female no no no 8.6
## 64 no no female no no no 7.5
## 71 no no female no no no 4.2
## 73 no no female no no no 6.6
## 74 no no female no no no 5.4
## 75 no no female no no no 8.8
## 76 no no female no yes yes 5.0
## 77 no no female no yes yes 4.9
## 78 no no female no yes yes 6.5
## 79 no no female no yes yes 5.6
## 80 no no female no yes yes 14.6
## 81 no no female no yes yes 7.1
## 82 no no female no yes yes 8.0
## 83 no no female no yes yes 6.3
## 84 no no female no yes yes 6.0
## 85 no no female no yes yes 9.9
## 86 no no female no yes yes 7.2
## 88 no no female no yes yes 6.1
## 89 no no female no yes yes 9.7
## 90 no no female no yes yes 8.5
## 91 no no female no yes yes 12.2
## 92 no no female no yes yes 5.7
## 93 no no female no yes yes 5.5
## 94 no no female no yes yes 9.1
## 95 no no female no yes yes 9.2
## 97 no no female no yes yes 7.0
## 98 no no female no yes yes 3.3
## 99 no no female no yes yes 7.8
## 106 no no female no yes yes 5.2
## 107 no no female no yes yes 11.1
## 108 no no female no yes yes 11.9
## 109 no no female no yes yes 14.3
## 112 no no female no yes yes 6.6
## 113 no no female no yes yes 11.6
## 115 no no female no yes yes 9.4
## 116 no no female no yes yes 11.7
## 118 no no female no yes yes 6.7
## 119 no no female no yes yes 8.9
## 120 no no female no yes yes 11.2
## 121 no no female no yes yes 4.3
## 123 no no female no yes yes 11.4
## 127 no no female no yes yes 6.8
## 132 no no female no yes yes 8.4
## 135 no no female no yes yes 5.8
## 136 no no female no yes yes 7.3
## 137 no no female no yes yes 4.0
## 139 no no female yes no yes 4.5
## 140 no no female yes no yes 7.5
## 141 no no female yes no yes 5.8
## 142 no no female yes no yes 8.9
## 144 no no female yes no yes 5.6
## 145 no no female yes no yes 5.3
## 146 no no female yes no yes 7.1
## 147 no no female yes no yes 12.2
## 148 no no female yes no yes 3.8
## 149 no no female yes no yes 9.3
## 151 no no female yes no yes 8.6
## 153 no no female yes no yes 6.2
## 154 no no female yes no yes 4.1
## 155 no no female yes no yes 4.9
## 158 no no female yes no yes 8.0
## 160 no no female yes no yes 8.2
## 162 no no female yes no yes 6.0
## 164 no no female yes no yes 6.1
## 165 no no female yes no yes 5.7
## 167 no no female yes no yes 8.3
## 168 no no female yes no yes 8.5
## 171 no no female yes no yes 8.7
## 172 no no female yes no yes 6.7
## 175 no no female yes no yes 9.0
## 177 no no female yes no yes 4.2
## 180 no no female yes no yes 12.3
## 184 no no female yes no yes 4.3
## 186 no no female yes no yes 12.4
## 187 no no female yes no yes 6.5
## 188 no no female yes no yes 3.6
## 191 no no female yes no yes 3.3
## 192 no no female yes no yes 6.4
## 196 no no female yes no yes 6.9
## 197 no no female yes no yes 6.3
## 198 no no female yes no yes 9.7
## 201 no no female yes no yes 5.2
## 205 no no female yes no yes 7.7
## 206 no no female yes no yes 7.4
## 207 no no female yes no yes 9.2
## 210 no no female yes no yes 11.8
## 211 no no female yes no yes 5.5
## 212 no no female yes no yes 9.4
## 220 no no female yes no yes 10.1
## 226 no no female yes no yes 5.0
## 227 no no female yes no yes 6.6
## 229 no no female yes no yes 5.1
## 232 no no female yes no yes 7.8
## 235 no no female yes no yes 7.2
## 236 no no female yes no yes 14.2
## 237 no no female yes no yes 9.1
## 245 no no female yes no yes 5.4
## 246 no no female yes no yes 9.8
## 250 no no female yes no yes 11.7
## 251 no no female yes no yes 4.0
## 257 no no female yes no yes 8.8
## 262 no no female yes no yes 4.8
## 263 no no female yes no yes 3.7
## 264 no no female yes no yes 10.5
## 271 no no female yes no yes 7.0
## 274 no no female yes no yes 11.1
## 287 no no female yes no yes 7.9
## 288 no no female yes no yes 5.9
## 293 no no female yes no yes 11.9
## 294 no no female yes no yes 10.8
## 295 no no female yes no yes 9.9
## 296 no no female yes yes no 7.3
## 297 no no female yes yes no 5.2
## 298 no no female yes yes no 11.8
## 299 no no female yes yes no 5.4
## 300 no no female yes yes no 11.4
## 301 no no female yes yes no 8.4
## 302 no no female yes yes no 4.5
## 303 no no female yes yes no 5.3
## 304 no no female yes yes no 5.0
## 305 no no female yes yes no 7.0
## 306 no no female yes yes no 7.8
## 307 no no female yes yes no 8.8
## 308 no no female yes yes no 6.4
## 310 no no female yes yes no 3.5
## 311 no no female yes yes no 9.4
## 312 no no female yes yes no 8.9
## 313 no no female yes yes no 9.0
## 315 no no female yes yes no 5.1
## 316 no no female yes yes no 6.3
## 317 no no female yes yes no 5.5
## 318 no no female yes yes no 6.7
## 322 no no female yes yes no 5.9
## 324 no no female yes yes no 5.6
## 327 no no female yes yes no 9.8
## 329 no no female yes yes no 12.2
## 330 no no female yes yes no 7.9
## 331 no no female yes yes no 6.2
## 334 no no female yes yes no 5.8
## 335 no no female yes yes no 4.6
## 340 no no female yes yes no 9.2
## 342 no no female yes yes no 6.9
## 343 no no female yes yes no 8.6
## 344 no no female yes yes no 7.6
## 345 no no female yes yes no 6.6
## 346 no no female yes yes no 10.3
## 348 no no female yes yes no 8.0
## 350 no no female yes yes no 4.3
## 351 no no female yes yes no 12.4
## 353 no no female yes yes no 6.8
## 354 no no female yes yes no 14.6
## 355 no no female yes yes no 11.2
## 356 no no female yes yes no 9.7
## 358 no no female yes yes no 6.0
## 360 no no female yes yes no 7.5
## 364 no no female yes yes no 3.2
## 365 no no female yes yes no 9.9
## 369 no no female yes yes no 11.7
## 370 no no male no no yes 6.2
## 371 no no male no no yes 9.7
## 372 no no male no no yes 8.0
## 373 no no male no no yes 6.6
## 374 no no male no no yes 3.9
## 376 no no male no no yes 11.2
## 377 no no male no no yes 6.8
## 378 no no male no no yes 6.0
## 379 no no male no no yes 5.0
## 381 no no male no no yes 5.7
## 382 no no male no no yes 4.5
## 383 no no male no no yes 4.3
## 384 no no male no no yes 10.1
## 385 no no male no no yes 9.0
## 386 no no male no no yes 5.3
## 387 no no male no no yes 14.2
## 388 no no male no no yes 8.1
## 389 no no male no no yes 7.1
## 390 no no male no no yes 11.7
## 391 no no male no no yes 7.4
## 393 no no male no no yes 11.9
## 395 no no male no no yes 7.7
## 396 no no male no no yes 7.2
## 397 no no male no no yes 9.1
## 398 no no male no no yes 7.5
## 402 no no male no no yes 3.7
## 403 no no male no no yes 10.0
## 404 no no male no no yes 5.4
## 405 no no male no no yes 12.1
## 407 no no male no no yes 10.9
## 408 no no male no no yes 10.8
## 409 no no male no no yes 10.3
## 411 no no male no no yes 7.3
## 412 no no male no no yes 9.2
## 416 no no male no no yes 7.8
## 418 no no male no no yes 3.5
## 420 no no male no no yes 5.8
## 421 no no male no no yes 10.4
## 422 no no male no no yes 4.0
## 423 no no male no no yes 11.4
## 425 no no male no no yes 6.7
## 427 no no male no no yes 6.9
## 429 no no male no no yes 11.8
## 430 no no male no no yes 15.0
## 432 no no male no no yes 8.5
## 433 no no male no no yes 10.5
## 434 no no male no no yes 8.6
## 438 no no male no no yes 8.8
## 441 no no male no no yes 11.5
## 445 no no male no no yes 8.9
## 448 no no male no no yes 4.4
## 451 no no male no no yes 14.3
## 454 no no male no no yes 6.4
## 455 no no male no no yes 5.5
## 456 no no male no no yes 5.2
## 458 no no male no no yes 13.1
## 459 no no male no no yes 3.2
## 460 no no male no no yes 9.4
## 462 no no male no no yes 13.7
## 465 no no male no no yes 6.3
## 467 no no male no no yes 2.5
## 468 no no male no no yes 5.6
## 471 no no male no no yes 9.5
## 473 no no male no no yes 7.0
## 478 no no male no no yes 14.6
## 483 no no male no no yes 9.9
## 485 no no male no no yes 12.3
## 493 no no male no no yes 4.8
## 494 no no male no no yes 5.9
## 498 no no male no no yes 11.0
## 499 no no male no no yes 3.6
## 501 no no male no no yes 5.1
## 510 no no male no no yes 11.1
## 526 no no male no no yes 4.2
## 529 no no male no no yes 12.4
## 530 no no male no no yes 3.8
## 531 no no male no no yes 8.2
## 542 no no male no no yes 6.5
## 547 no no male no no yes 8.7
## 550 no no male no no yes 4.6
## 551 no no male no no yes 18.0
## 558 no no male no no yes 11.6
## 563 no no male no no yes 13.0
## 580 no no male no no yes 7.6
## 588 no no male no no yes 4.9
## 623 no no male no no yes 7.9
## 668 no no male no no yes 8.4
## 670 no no male no no yes 6.1
## 685 no no male no no yes 10.2
## 739 no no male no no yes 4.1
## 744 no no male no no yes 3.3
## 754 no no male no no yes 12.2
## 770 no no male no no yes 2.6
## 791 no no male no no yes 2.7
## 798 no no male no no yes 14.4
## 804 no no male no no yes 4.7
## 808 no no male no yes no 11.4
## 809 no no male no yes no 8.4
## 810 no no male no yes no 3.8
## 811 no no male no yes no 6.6
## 812 no no male no yes no 9.1
## 813 no no male no yes no 3.9
## 814 no no male no yes no 7.1
## 815 no no male no yes no 9.0
## 817 no no male no yes no 6.2
## 818 no no male no yes no 7.6
## 819 no no male no yes no 11.8
## 820 no no male no yes no 7.5
## 821 no no male no yes no 5.1
## 823 no no male no yes no 6.0
## 825 no no male no yes no 5.7
## 826 no no male no yes no 4.0
## 827 no no male no yes no 6.3
## 828 no no male no yes no 9.3
## 830 no no male no yes no 14.6
## 831 no no male no yes no 8.8
## 832 no no male no yes no 7.2
## 833 no no male no yes no 7.9
## 834 no no male no yes no 9.7
## 835 no no male no yes no 4.9
## 836 no no male no yes no 9.9
## 837 no no male no yes no 6.8
## 841 no no male no yes no 7.3
## 844 no no male no yes no 10.1
## 845 no no male no yes no 5.4
## 848 no no male no yes no 6.1
## 849 no no male no yes no 10.5
## 850 no no male no yes no 5.8
## 852 no no male no yes no 8.0
## 853 no no male no yes no 4.3
## 854 no no male no yes no 6.9
## 855 no no male no yes no 14.2
## 858 no no male no yes no 5.6
## 860 no no male no yes no 12.0
## 861 no no male yes no no 6.7
## 862 no no male yes no no 5.6
## 863 no no male yes no no 5.1
## 864 no no male yes no no 5.5
## 866 no no male yes no no 9.0
## 867 no no male yes no no 9.7
## 868 no no male yes no no 9.4
## 869 no no male yes no no 3.8
## 870 no no male yes no no 5.9
## 871 no no male yes no no 8.9
## 872 no no male yes no no 6.1
## 873 no no male yes no no 6.8
## 874 no no male yes no no 9.1
## 875 no no male yes no no 7.2
## 879 no no male yes no no 4.0
## 880 no no male yes no no 5.0
## 881 no no male yes no no 5.4
## 884 no no male yes no no 5.7
## 886 no no male yes no no 7.7
## 887 no no male yes no no 3.6
## 888 no no male yes no no 4.5
## 889 no no male yes no no 6.4
## 891 no no male yes no no 6.6
## 894 no no male yes no no 12.2
## 895 no no male yes no no 6.2
## 896 no no male yes no no 6.3
## 897 no no male yes no no 6.5
## 898 no no male yes no no 12.3
## 900 no no male yes no no 9.2
## 901 no no male yes no no 8.0
## 903 no no male yes no no 4.1
## 905 no no male yes no no 4.6
## 906 no no male yes no no 7.3
## 907 no no male yes no no 4.9
## 909 no no male yes no no 11.7
## 910 no no male yes no no 10.2
## 911 no no male yes no no 6.0
## 914 no no male yes no no 10.0
## 915 no no male yes no no 6.9
## 917 no no male yes no no 10.8
## 918 no no male yes no no 7.0
## 919 no no male yes no no 8.4
## 920 no no male yes no no 5.2
## 925 no no male yes no no 9.8
## 932 no no male yes no no 5.3
## 933 no no male yes no no 11.5
## 937 no no male yes no no 8.5
## 942 no no male yes no no 3.7
## 944 no no male yes no no 13.0
## 950 no no male yes no no 3.9
## 955 no no male yes no no 8.6
## 971 no no male yes no no 4.2
## 976 no no male yes no no 5.8
## 977 no no male yes no no 4.3
## 978 no no male yes no no 7.8
## 983 no no male yes no no 3.5
## 986 no no male yes no no 3.1
## 989 no no male yes no no 2.8
## 990 no no male yes no no 7.1
## 998 no no male yes no no 10.1
## 1000 no no male yes no no 11.8
## 1003 no no male yes no no 8.8
## 1006 no no male yes no no 2.7
## 1011 no no male yes no no 9.3
## 1013 no no male yes no no 7.6
## 1015 no no male yes no no 2.5
## 1016 no no male yes no no 3.4
## 1022 no no male yes no no 7.5
## 1032 no no male yes yes yes 5.8
## 1033 no no male yes yes yes 7.5
## 1034 no no male yes yes yes 5.2
## 1035 no no male yes yes yes 12.2
## 1036 no no male yes yes yes 9.1
## 1037 no no male yes yes yes 11.5
## 1038 no no male yes yes yes 10.3
## 1039 no no male yes yes yes 7.7
## 1040 no no male yes yes yes 7.1
## 1041 no no male yes yes yes 6.0
## 1042 no no male yes yes yes 8.9
## 1043 no no male yes yes yes 9.4
## 1044 no no male yes yes yes 6.9
## 1046 no no male yes yes yes 6.1
## 1047 no no male yes yes yes 6.6
## 1049 no no male yes yes yes 14.3
## 1050 no no male yes yes yes 11.8
## 1051 no no male yes yes yes 3.8
## 1052 no no male yes yes yes 9.9
## 1053 no no male yes yes yes 3.7
## 1056 no no male yes yes yes 6.4
## 1060 no no male yes yes yes 7.4
## 1061 no no male yes yes yes 6.2
## 1062 no no male yes yes yes 13.0
## 1064 no no male yes yes yes 5.0
## 1065 no no male yes yes yes 14.2
## 1066 no no male yes yes yes 11.7
## 1069 no no male yes yes yes 9.0
## 1070 no no male yes yes yes 4.1
## 1072 no no male yes yes yes 7.8
## 1073 no no male yes yes yes 9.2
## 1075 no no male yes yes yes 3.2
## 1076 no no male yes yes yes 9.5
## 1077 no no male yes yes yes 5.4
## 1079 no no male yes yes yes 7.2
## 1080 no no male yes yes yes 13.1
## 1081 no no male yes yes yes 8.5
## 1085 no no male yes yes yes 8.2
## 1088 no no male yes yes yes 5.5
## 1089 no no male yes yes yes 8.0
## 1090 no no male yes yes yes 6.5
## 1091 no no male yes yes yes 7.6
## 1092 no no male yes yes yes 6.7
## 1093 no no male yes yes yes 8.7
## 1094 no no male yes yes yes 5.9
## 1095 no no male yes yes yes 10.8
## 1098 no no male yes yes yes 10.9
## 1102 no no male yes yes yes 8.8
## 1104 no no male yes yes yes 8.6
## 1106 no no male yes yes yes 5.6
## 1107 no no male yes yes yes 5.7
## 1109 no no male yes yes yes 12.4
## 1113 no no male yes yes yes 11.2
## 1114 no no male yes yes yes 14.4
## 1118 no no male yes yes yes 4.0
## 1122 no no male yes yes yes 3.0
## 1135 no no male yes yes yes 4.5
## 1140 no no male yes yes yes 11.6
## 1141 no no male yes yes yes 9.7
## 1150 no no male yes yes yes 6.3
## 1156 no no male yes yes yes 10.0
## 1157 no no male yes yes yes 4.2
## 1166 no no male yes yes yes 11.0
## 1169 no no male yes yes yes 4.9
## 1173 no no male yes yes yes 3.9
## 1174 no no male yes yes yes 4.6
## 1176 no no male yes yes yes 7.0
## 1180 no no male yes yes yes 9.3
## 1181 no no male yes yes yes 4.8
## 1182 no no male yes yes yes 12.9
## 1206 no no male yes yes yes 3.1
## 1215 no no male yes yes yes 12.1
## 1221 no no male yes yes yes 4.4
## 1227 no no male yes yes yes 6.8
## 1233 no no male yes yes yes 5.1
## 1234 no no male yes yes yes 14.6
## 1238 no no male yes yes yes 3.5
## 1240 no no male yes yes yes 11.4
## 1248 no no male yes yes yes 12.6
## 1269 no no male yes yes yes 4.3
## 1275 no no male yes yes yes 15.0
## 1279 no no male yes yes yes 10.1
## 1282 no no male yes yes yes 2.7
## 1306 no no male yes yes yes 5.3
## 1336 no no male yes yes yes 7.3
## 1344 no no male yes yes yes 8.1
## 1345 no no male yes yes yes 11.1
## 1349 no no male yes yes yes 10.2
## 1365 no no male yes yes yes 12.3
## 1366 no no male yes yes yes 8.4
## 1370 no no male yes yes yes 18.0
## 1452 no no male yes yes yes 4.7
## 1472 no no male yes yes yes 12.0
## 1483 no no male yes yes yes 7.9
## 1487 no no male yes yes yes 10.5
## 1524 no no male yes yes yes 9.8
## 1625 no no male yes yes yes 11.9
## 1630 no no male yes yes yes 10.4
## 1698 no no male yes yes yes 3.6
## 1762 no no male yes yes yes 8.3
## 1853 no yes female no no yes 11.0
## 1854 no yes female no no yes 5.3
## 1855 no yes female no no yes 7.2
## 1857 no yes female no no yes 5.4
## 1858 no yes female no no yes 4.8
## 1859 no yes female no no yes 4.2
## 1860 no yes female no no yes 7.5
## 1861 no yes female no no yes 8.2
## 1862 no yes female no no yes 9.7
## 1863 no yes female no no yes 7.3
## 1864 no yes female no no yes 5.8
## 1865 no yes female no no yes 5.6
## 1866 no yes female no no yes 6.8
## 1867 no yes female no no yes 9.2
## 1868 no yes female no no yes 6.2
## 1869 no yes female no no yes 6.9
## 1870 no yes female no no yes 5.9
## 1871 no yes female no no yes 5.0
## 1872 no yes female no no yes 11.4
## 1874 no yes female no no yes 8.9
## 1875 no yes female no no yes 6.6
## 1876 no yes female no no yes 10.0
## 1877 no yes female no no yes 6.0
## 1878 no yes female no no yes 9.1
## 1880 no yes female no no yes 6.3
## 1881 no yes female no no yes 7.8
## 1883 no yes female no no yes 5.7
## 1885 no yes female no no yes 10.2
## 1886 no yes female no yes no 3.5
## 1887 no yes female no yes no 5.4
## 1888 no yes female no yes no 7.7
## 1889 no yes female no yes no 7.3
## 1890 no yes female no yes no 6.9
## 1891 no yes female yes no no 6.3
## 1892 no yes female yes no no 9.1
## 1893 no yes female yes no no 3.5
## 1894 no yes female yes no no 7.1
## 1895 no yes female yes no no 3.1
## 1896 no yes female yes no no 5.0
## 1897 no yes female yes no no 5.5
## 1898 no yes female yes no no 9.7
## 1899 no yes female yes no no 5.3
## 1900 no yes female yes no no 8.4
## 1901 no yes female yes yes yes 5.4
## 1902 no yes female yes yes yes 7.3
## 1903 no yes female yes yes yes 7.0
## 1904 no yes female yes yes yes 4.6
## 1905 no yes female yes yes yes 10.1
## 1906 no yes female yes yes yes 11.6
## 1907 no yes female yes yes yes 5.6
## 1908 no yes female yes yes yes 10.0
## 1909 no yes female yes yes yes 6.0
## 1911 no yes female yes yes yes 11.8
## 1912 no yes female yes yes yes 9.4
## 1913 no yes female yes yes yes 3.2
## 1914 no yes female yes yes yes 8.4
## 1915 no yes female yes yes yes 8.1
## 1916 no yes female yes yes yes 9.1
## 1917 no yes female yes yes yes 14.6
## 1918 no yes female yes yes yes 11.5
## 1920 no yes female yes yes yes 6.4
## 1921 no yes female yes yes yes 10.2
## 1922 no yes female yes yes yes 5.2
## 1924 no yes female yes yes yes 8.0
## 1927 no yes female yes yes yes 5.7
## 1928 no yes female yes yes yes 7.2
## 1929 no yes female yes yes yes 11.0
## 1930 no yes male no no no 8.4
## 1931 no yes male no no no 6.7
## 1932 no yes male no no no 5.8
## 1933 no yes male no no no 9.3
## 1934 no yes male no no no 3.7
## 1935 no yes male no no no 3.5
## 1936 no yes male no no no 8.9
## 1937 no yes male no no no 7.1
## 1938 no yes male no no no 9.0
## 1939 no yes male no no no 3.9
## 1940 no yes male no no no 5.9
## 1941 no yes male no no no 6.4
## 1942 no yes male no no no 11.5
## 1943 no yes male no no no 12.3
## 1944 no yes male no no no 4.9
## 1945 no yes male no no no 6.8
## 1946 no yes male no no no 8.5
## 1947 no yes male no no no 7.8
## 1948 no yes male no no no 6.1
## 1949 no yes male no no no 6.9
## 1950 no yes male no no no 6.6
## 1951 no yes male no no no 9.7
## 1952 no yes male no no no 7.2
## 1955 no yes male no no no 5.1
## 1956 no yes male no no no 4.3
## 1957 no yes male no no no 3.8
## 1958 no yes male no no no 8.6
## 1960 no yes male no no no 8.1
## 1962 no yes male no no no 11.1
## 1963 no yes male no no no 5.7
## 1965 no yes male no no no 7.5
## 1967 no yes male no no no 6.3
## 1970 no yes male no no no 9.2
## 1972 no yes male no no no 7.7
## 1973 no yes male no no no 8.0
## 1975 no yes male no no no 5.3
## 1976 no yes male no no no 5.0
## 1981 no yes male no no no 7.3
## 1984 no yes male no no no 7.4
## 1987 no yes male no no no 5.6
## 1993 no yes male no no no 11.7
## 1995 no yes male no no no 10.0
## 2003 no yes male no no no 5.5
## 2004 no yes male no no no 5.4
## 2006 no yes male no yes yes 9.7
## 2007 no yes male no yes yes 5.1
## 2008 no yes male no yes yes 7.5
## 2009 no yes male no yes yes 4.4
## 2010 no yes male no yes yes 6.9
## 2011 no yes male no yes yes 6.6
## 2012 no yes male no yes yes 7.3
## 2013 no yes male no yes yes 8.7
## 2014 no yes male no yes yes 5.8
## 2015 no yes male no yes yes 14.2
## 2016 no yes male no yes yes 5.0
## 2017 no yes male no yes yes 6.5
## 2018 no yes male yes no yes 5.8
## 2019 no yes male yes no yes 7.2
## 2020 no yes male yes no yes 9.1
## 2022 no yes male yes no yes 6.0
## 2023 no yes male yes no yes 7.3
## 2025 no yes male yes no yes 9.0
## 2026 no yes male yes no yes 14.3
## 2027 no yes male yes no yes 5.2
## 2028 no yes male yes no yes 9.5
## 2029 no yes male yes no yes 7.5
## 2031 no yes male yes no yes 8.2
## 2033 no yes male yes no yes 5.5
## 2034 no yes male yes no yes 5.7
## 2035 no yes male yes no yes 8.0
## 2036 no yes male yes no yes 13.0
## 2037 no yes male yes no yes 5.6
## 2038 no yes male yes no yes 4.3
## 2039 no yes male yes no yes 5.4
## 2041 no yes male yes no yes 6.6
## 2042 no yes male yes no yes 6.7
## 2043 no yes male yes no yes 4.8
## 2045 no yes male yes no yes 6.4
## 2046 no yes male yes no yes 4.5
## 2048 no yes male yes no yes 7.7
## 2049 no yes male yes no yes 6.3
## 2050 no yes male yes no yes 10.8
## 2053 no yes male yes no yes 3.3
## 2055 no yes male yes no yes 8.9
## 2056 no yes male yes no yes 12.0
## 2057 no yes male yes no yes 6.5
## 2058 no yes male yes no yes 9.7
## 2060 no yes male yes no yes 8.6
## 2062 no yes male yes no yes 5.9
## 2063 no yes male yes no yes 12.3
## 2066 no yes male yes no yes 11.5
## 2067 no yes male yes no yes 8.4
## 2070 no yes male yes no yes 5.1
## 2071 no yes male yes no yes 8.1
## 2072 no yes male yes no yes 8.8
## 2077 no yes male yes no yes 6.2
## 2082 no yes male yes no yes 6.1
## 2090 no yes male yes no yes 11.0
## 2091 no yes male yes no yes 3.5
## 2093 no yes male yes no yes 7.0
## 2096 no yes male yes no yes 11.4
## 2097 no yes male yes no yes 3.8
## 2101 no yes male yes no yes 11.9
## 2102 no yes male yes yes no 8.3
## 2103 no yes male yes yes no 5.2
## 2104 no yes male yes yes no 6.7
## 2105 no yes male yes yes no 8.2
## 2106 no yes male yes yes no 10.8
## 2107 no yes male yes yes no 5.7
## 2108 no yes male yes yes no 9.7
## 2109 no yes male yes yes no 6.5
## 2110 no yes male yes yes no 5.4
## 2111 no yes male yes yes no 8.5
## 2113 no yes male yes yes no 5.3
## 2114 no yes male yes yes no 8.6
## 2115 no yes male yes yes no 6.0
## 2118 no yes male yes yes no 4.9
## 2120 no yes male yes yes no 10.1
## 2121 no yes male yes yes no 5.8
## 2122 no yes male yes yes no 11.2
## 2123 no yes male yes yes no 5.6
## 2124 no yes male yes yes no 8.9
## 2125 no yes male yes yes no 5.5
## 2126 no yes male yes yes no 7.0
## 2128 no yes male yes yes no 8.0
## 2129 no yes male yes yes no 6.4
## 2131 no yes male yes yes no 12.1
## 2132 no yes male yes yes no 7.4
## 2135 no yes male yes yes no 6.3
## 2136 no yes male yes yes no 7.7
## 2138 no yes male yes yes no 4.8
## 2139 no yes male yes yes no 6.1
## 2140 no yes male yes yes no 8.8
## 2141 no yes male yes yes no 4.3
## 2144 no yes male yes yes no 6.9
## 2146 no yes male yes yes no 5.0
## 2147 no yes male yes yes no 4.0
## 2149 no yes male yes yes no 7.1
## 2150 no yes male yes yes no 7.3
## 2152 no yes male yes yes no 6.2
## 2153 no yes male yes yes no 4.1
## 2155 no yes male yes yes no 9.2
## 2161 no yes male yes yes no 11.0
## 2163 no yes male yes yes no 10.0
## 2165 no yes male yes yes no 7.8
## 2166 no yes male yes yes no 9.5
## 2168 no yes male yes yes no 4.2
## 2169 no yes male yes yes no 9.0
## 2174 no yes male yes yes no 5.1
## 2176 no yes male yes yes no 14.6
## 2180 no yes male yes yes no 4.4
## 2185 no yes male yes yes no 10.3
## 2191 no yes male yes yes no 12.6
## 2192 no yes male yes yes no 3.8
## 2193 no yes male yes yes no 7.2
## 2199 no yes male yes yes no 7.5
## 2200 no yes male yes yes no 11.4
## 2201 no yes male yes yes no 13.0
## 2203 no yes male yes yes no 9.8
## 2206 yes no female no no yes 11.1
## 2207 yes no female no no yes 14.3
## 2208 yes no female no no yes 9.5
## 2209 yes no female no no yes 4.8
## 2210 yes no female no no yes 7.2
## 2211 yes no female no no yes 4.1
## 2212 yes no female no no yes 5.3
## 2213 yes no female no no yes 9.9
## 2214 yes no female no no yes 4.5
## 2215 yes no female no no yes 7.5
## 2216 yes no female no no yes 5.9
## 2218 yes no female no no yes 6.9
## 2220 yes no female no no yes 6.7
## 2222 yes no female no no yes 11.6
## 2223 yes no female no no yes 5.8
## 2224 yes no female no no yes 9.7
## 2225 yes no female no no yes 3.6
## 2226 yes no female no no yes 5.7
## 2227 yes no female no no yes 9.3
## 2228 yes no female no no yes 10.8
## 2232 yes no female no no yes 6.3
## 2233 yes no female no no yes 5.2
## 2236 yes no female no no yes 5.0
## 2239 yes no female no no yes 6.2
## 2240 yes no female no no yes 6.8
## 2242 yes no female no no yes 11.4
## 2243 yes no female no no yes 8.6
## 2244 yes no female no no yes 3.5
## 2245 yes no female no no yes 11.7
## 2250 yes no female no no yes 10.3
## 2251 yes no female no no yes 4.0
## 2252 yes no female no no yes 9.4
## 2254 yes no female no no yes 6.1
## 2255 yes no female no yes no 5.4
## 2256 yes no female no yes no 7.8
## 2257 yes no female no yes no 12.6
## 2258 yes no female no yes no 10.2
## 2259 yes no female no yes no 3.9
## 2260 yes no female no yes no 5.6
## 2264 yes no female no yes no 11.8
## 2265 yes no female no yes no 5.3
## 2267 yes no female no yes no 8.4
## 2268 yes no female no yes no 6.4
## 2269 yes no female no yes no 6.3
## 2270 yes no female no yes no 7.5
## 2271 yes no female no yes no 8.5
## 2272 yes no female no yes no 8.6
## 2274 yes no female no yes no 5.2
## 2275 yes no female no yes no 5.7
## 2276 yes no female yes no no 6.7
## 2277 yes no female yes no no 7.5
## 2278 yes no female yes no no 11.5
## 2279 yes no female yes no no 6.4
## 2280 yes no female yes no no 5.6
## 2281 yes no female yes yes yes 3.5
## 2282 yes no female yes yes yes 8.9
## 2283 yes no female yes yes yes 6.6
## 2284 yes no female yes yes yes 6.7
## 2285 yes no female yes yes yes 11.8
## 2286 yes no female yes yes yes 5.9
## 2287 yes no female yes yes yes 7.1
## 2288 yes no female yes yes yes 7.8
## 2291 yes no female yes yes yes 5.6
## 2292 yes no female yes yes yes 9.7
## 2293 yes no female yes yes yes 8.1
## 2294 yes no female yes yes yes 12.6
## 2295 yes no female yes yes yes 3.6
## 2296 yes no female yes yes yes 8.2
## 2297 yes no female yes yes yes 5.4
## 2298 yes no female yes yes yes 5.8
## 2299 yes no female yes yes yes 8.6
## 2300 yes no female yes yes yes 5.2
## 2301 yes no female yes yes yes 7.0
## 2302 yes no female yes yes yes 10.3
## 2303 yes no female yes yes yes 5.3
## 2309 yes no female yes yes yes 6.2
## 2310 yes no female yes yes yes 5.7
## 2311 yes no female yes yes yes 10.1
## 2312 yes no female yes yes yes 11.1
## 2315 yes no female yes yes yes 11.9
## 2316 yes no female yes yes yes 3.9
## 2317 yes no female yes yes yes 4.8
## 2318 yes no female yes yes yes 4.1
## 2319 yes no female yes yes yes 7.4
## 2323 yes no female yes yes yes 6.3
## 2324 yes no female yes yes yes 10.4
## 2327 yes no female yes yes yes 9.0
## 2328 yes no female yes yes yes 9.1
## 2329 yes no male no no no 5.4
## 2330 yes no male no no no 4.8
## 2331 yes no male no no no 5.6
## 2332 yes no male no no no 6.3
## 2333 yes no male no no no 4.6
## 2334 yes no male no no no 11.7
## 2335 yes no male no no no 12.6
## 2336 yes no male no no no 8.1
## 2337 yes no male no no no 5.8
## 2339 yes no male no no no 6.9
## 2340 yes no male no no no 6.7
## 2341 yes no male no no no 3.5
## 2342 yes no male no no no 5.5
## 2343 yes no male no no no 7.2
## 2344 yes no male no no no 7.1
## 2345 yes no male no no no 8.0
## 2346 yes no male no no no 4.0
## 2348 yes no male no no no 6.5
## 2349 yes no male no no no 7.5
## 2356 yes no male no no no 5.7
## 2357 yes no male no no no 8.6
## 2358 yes no male no no no 6.0
## 2359 yes no male no no no 7.0
## 2361 yes no male no no no 4.5
## 2362 yes no male no no no 7.3
## 2363 yes no male no no no 5.0
## 2364 yes no male no no no 9.0
## 2367 yes no male no no no 6.8
## 2368 yes no male no no no 8.5
## 2371 yes no male no no no 4.1
## 2372 yes no male no no no 8.2
## 2375 yes no male no no no 7.9
## 2377 yes no male no no no 3.8
## 2378 yes no male no no no 6.2
## 2381 yes no male no no no 9.4
## 2382 yes no male no yes yes 6.7
## 2383 yes no male no yes yes 6.9
## 2384 yes no male no yes yes 13.1
## 2385 yes no male no yes yes 11.5
## 2386 yes no male no yes yes 7.2
## 2387 yes no male no yes yes 10.4
## 2388 yes no male no yes yes 4.7
## 2389 yes no male no yes yes 5.7
## 2391 yes no male no yes yes 5.6
## 2392 yes no male no yes yes 10.8
## 2394 yes no male yes no yes 5.7
## 2395 yes no male yes no yes 5.0
## 2396 yes no male yes no yes 4.0
## 2397 yes no male yes no yes 10.8
## 2398 yes no male yes no yes 7.7
## 2399 yes no male yes no yes 5.6
## 2400 yes no male yes no yes 6.6
## 2401 yes no male yes no yes 6.5
## 2402 yes no male yes no yes 3.8
## 2404 yes no male yes no yes 14.7
## 2405 yes no male yes no yes 6.3
## 2406 yes no male yes no yes 10.2
## 2407 yes no male yes no yes 8.1
## 2408 yes no male yes no yes 7.2
## 2410 yes no male yes no yes 4.1
## 2411 yes no male yes no yes 9.1
## 2412 yes no male yes no yes 5.3
## 2413 yes no male yes no yes 6.2
## 2414 yes no male yes no yes 8.9
## 2415 yes no male yes no yes 7.0
## 2416 yes no male yes no yes 2.8
## 2417 yes no male yes no yes 12.6
## 2418 yes no male yes no yes 13.7
## 2419 yes no male yes no yes 10.0
## 2420 yes no male yes no yes 8.6
## 2421 yes no male yes no yes 8.0
## 2422 yes no male yes no yes 5.4
## 2423 yes no male yes no yes 5.8
## 2428 yes no male yes no yes 10.3
## 2429 yes no male yes no yes 6.8
## 2430 yes no male yes no yes 12.4
## 2431 yes no male yes no yes 4.9
## 2433 yes no male yes yes no 7.2
## 2434 yes no male yes yes no 9.0
## 2435 yes no male yes yes no 3.2
## 2436 yes no male yes yes no 4.5
## 2437 yes no male yes yes no 5.1
## 2438 yes no male yes yes no 6.7
## 2439 yes no male yes yes no 6.5
## 2440 yes no male yes yes no 4.2
## 2441 yes no male yes yes no 5.5
## 2443 yes no male yes yes no 10.0
## 2444 yes no male yes yes no 8.0
## 2445 yes no male yes yes no 7.8
## 2449 yes no male yes yes no 7.9
## 2450 yes no male yes yes no 12.4
## 2452 yes no male yes yes no 10.3
## 2453 yes no male yes yes no 10.2
## 2454 yes no male yes yes no 8.4
## 2459 yes no male yes yes no 8.8
## 2460 yes no male yes yes no 7.7
## 2461 yes no male yes yes no 7.0
## 2462 yes no male yes yes no 3.6
## 2463 yes no male yes yes no 2.8
## 2464 yes no male yes yes no 6.9
## 2465 yes no male yes yes no 7.5
## 2466 yes no male yes yes no 9.2
## 2468 yes no male yes yes no 8.1
## 2473 yes no male yes yes no 8.6
## 2474 yes yes female no no no 6.5
## 2476 yes yes female no no no 6.0
## 2477 yes yes female no no no 5.8
## 2478 yes yes female no no no 5.9
## 2479 yes yes female no yes yes 9.1
## 2480 yes yes female no yes yes 7.5
## 2481 yes yes female no yes yes 9.0
## 2482 yes yes female no yes yes 14.6
## 2483 yes yes female no yes yes 4.3
## 2484 yes yes female no yes yes 12.0
## 2485 yes yes female no yes yes 5.9
## 2486 yes yes female no yes yes 10.3
## 2487 yes yes female no yes yes 11.5
## 2488 yes yes female no yes yes 7.4
## 2489 yes yes female yes no yes 5.8
## 2490 yes yes female yes no yes 8.2
## 2491 yes yes female yes yes no 7.6
## 2492 yes yes female yes yes no 5.8
## 2493 yes yes male no no yes 7.3
## 2494 yes yes male no no yes 4.5
## 2495 yes yes male no no yes 9.9
## 2496 yes yes male no no yes 6.6
## 2497 yes yes male no no yes 4.7
## 2498 yes yes male no no yes 8.1
## 2499 yes yes male no no yes 7.4
## 2500 yes yes male no no yes 11.8
## 2501 yes yes male no no yes 9.4
## 2504 yes yes male no no yes 4.1
## 2505 yes yes male no no yes 5.9
## 2507 yes yes male no no yes 8.9
## 2508 yes yes male no no yes 9.7
## 2509 yes yes male no no yes 5.5
## 2510 yes yes male no no yes 7.5
## 2511 yes yes male no no yes 6.8
## 2512 yes yes male no no yes 12.4
## 2513 yes yes male no no yes 7.2
## 2514 yes yes male no no yes 11.4
## 2517 yes yes male no no yes 14.6
## 2518 yes yes male no no yes 9.1
## 2519 yes yes male no no yes 5.8
## 2520 yes yes male no yes no 8.1
## 2521 yes yes male yes no no 5.1
## 2522 yes yes male yes no no 11.1
## 2523 yes yes male yes no no 6.2
## 2524 yes yes male yes no no 5.8
## 2525 yes yes male yes no no 5.4
## 2526 yes yes male yes yes yes 4.7
## 2527 yes yes male yes yes yes 7.2
## 2528 yes yes male yes yes yes 5.7
## 2529 yes yes male yes yes yes 6.5
## 2530 yes yes male yes yes yes 5.8
## 2531 yes yes male yes yes yes 4.4
## 2532 yes yes male yes yes yes 10.1
## 2533 yes yes male yes yes yes 6.4
## 2534 yes yes male yes yes yes 11.7
## 2535 yes yes male yes yes yes 4.5
## 2536 yes yes male yes yes yes 8.9
## 2537 yes yes male yes yes yes 8.2
## 2538 yes yes male yes yes yes 7.1
## 2539 yes yes male yes yes yes 7.8
## 2540 yes yes male yes yes yes 5.4
## 2542 yes yes male yes yes yes 11.2
## 2544 yes yes male yes yes yes 7.3
## 2545 yes yes male yes yes yes 7.5
## 2546 yes yes male yes yes yes 12.4
## 2547 yes yes male yes yes yes 9.7
## 2548 yes yes male yes yes yes 8.0
## 2549 yes yes male yes yes yes 9.4
## 2552 yes yes male yes yes yes 5.2
## 2553 yes yes male yes yes yes 9.8
## 2554 yes yes male yes yes yes 6.7#Since there are multiple values of 'stateur' that correspond to the 32 unique rows of the design matrix "FrDesign", take a sample of 32 observations from "FFD_benefits_unique" and display the resulting dataframe "FFD_final".
FFD_index = sample(1:nrow(FFD_benefits_unique),32,replace=FALSE)
FFD_final <- FFD_benefits_unique[FFD_index,]
FFD_final## nwhite school12 sex married dkids ui stateur
## 455 no no male no no yes 5.5
## 1181 no no male yes yes yes 4.8
## 918 no no male yes no no 7.0
## 411 no no male no no yes 7.3
## 2026 no yes male yes no yes 14.3
## 84 no no female no yes yes 6.0
## 2431 yes no male yes no yes 4.9
## 52 no no female no no no 11.6
## 1993 no yes male no no no 11.7
## 2199 no yes male yes yes no 7.5
## 2070 no yes male yes no yes 5.1
## 257 no no female yes no yes 8.8
## 5 no no female no no no 5.3
## 1948 no yes male no no no 6.1
## 1076 no no male yes yes yes 9.5
## 1888 no yes female no yes no 7.7
## 2312 yes no female yes yes yes 11.1
## 237 no no female yes no yes 9.1
## 2208 yes no female no no yes 9.5
## 43 no no female no no no 8.9
## 1898 no yes female yes no no 9.7
## 1859 no yes female no no yes 4.2
## 41 no no female no no no 10.0
## 167 no no female yes no yes 8.3
## 210 no no female yes no yes 11.8
## 529 no no male no no yes 12.4
## 2463 yes no male yes yes no 2.8
## 74 no no female no no no 5.4
## 306 no no female yes yes no 7.8
## 1075 no no male yes yes yes 3.2
## 2473 yes no male yes yes no 8.6
## 2423 yes no male yes no yes 5.8#Display the summary statistics of "FFD_final".
summary(FFD_final)## nwhite school12 sex married dkids ui stateur
## yes: 6 yes: 8 male :16 yes:18 yes:10 yes:18 Min. : 2.80
## no :26 no :24 female:16 no :14 no :22 no :14 1st Qu.: 5.47
## Median : 7.75
## Mean : 7.87
## 3rd Qu.: 9.55
## Max. :14.30#Display the names found in "FFD_final".
names(FFD_final)## [1] "nwhite" "school12" "sex" "married" "dkids" "ui"
## [7] "stateur"#Display the structure of "FFD_final".
str(FFD_final)## 'data.frame': 32 obs. of 7 variables:
## $ nwhite : Factor w/ 2 levels "yes","no": 2 2 2 2 2 2 1 2 2 2 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "yes" "no"
## .. .. ..$ : NULL
## $ school12: Factor w/ 2 levels "yes","no": 2 2 2 2 1 2 2 2 1 1 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "yes" "no"
## .. .. ..$ : NULL
## $ sex : Factor w/ 2 levels "male","female": 1 1 1 1 1 2 1 2 1 1 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "male" "female"
## .. .. ..$ : NULL
## $ married : Factor w/ 2 levels "yes","no": 2 1 1 2 1 2 1 2 2 1 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "yes" "no"
## .. .. ..$ : NULL
## $ dkids : Factor w/ 2 levels "yes","no": 2 1 2 2 2 1 2 2 2 1 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "yes" "no"
## .. .. ..$ : NULL
## $ ui : Factor w/ 2 levels "yes","no": 1 1 2 1 1 1 1 2 2 2 ...
## ..- attr(*, "contrasts")= num [1:2, 1] -1 1
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr "yes" "no"
## .. .. ..$ : NULL
## $ stateur : num 5.5 4.8 7 7.3 14.3 6 4.9 11.6 11.7 7.5 ...#Display the head and tail of "FFD_final".
head(FFD_final)## nwhite school12 sex married dkids ui stateur
## 455 no no male no no yes 5.5
## 1181 no no male yes yes yes 4.8
## 918 no no male yes no no 7.0
## 411 no no male no no yes 7.3
## 2026 no yes male yes no yes 14.3
## 84 no no female no yes yes 6.0tail(FFD_final)## nwhite school12 sex married dkids ui stateur
## 2463 yes no male yes yes no 2.8
## 74 no no female no no no 5.4
## 306 no no female yes yes no 7.8
## 1075 no no male yes yes yes 3.2
## 2473 yes no male yes yes no 8.6
## 2423 yes no male yes no yes 5.8#Display the levels of the 6 factors being considered within "FFD_final".
levels(FFD_final$nwhite)## [1] "yes" "no"levels(FFD_final$school12)## [1] "yes" "no"levels(FFD_final$sex)## [1] "male" "female"levels(FFD_final$married)## [1] "yes" "no"levels(FFD_final$dkids)## [1] "yes" "no"levels(FFD_final$ui)## [1] "yes" "no"#Create and display results of ANOVA model generated using "FFD_final" while still maintaining a "design"" class designation.
model_resp <- add.response(FrDesign,FFD_final$stateur)
anova(lm(model_resp))## Analysis of Variance Table
##
## Response: FFD_final.stateur
## Df Sum Sq Mean Sq F value Pr(>F)
## nwhite 1 25.7 25.74 2.35 0.16
## school12 1 0.8 0.81 0.07 0.79
## sex 1 2.3 2.26 0.21 0.66
## married 1 0.3 0.26 0.02 0.88
## dkids 1 21.0 20.96 1.91 0.20
## ui 1 0.3 0.34 0.03 0.86
## nwhite:school12 1 5.2 5.20 0.47 0.51
## nwhite:sex 1 13.1 13.13 1.20 0.30
## nwhite:married 1 0.2 0.17 0.02 0.90
## nwhite:dkids 1 1.0 1.02 0.09 0.77
## nwhite:ui 1 15.8 15.82 1.44 0.26
## school12:sex 1 10.0 10.01 0.91 0.36
## school12:married 1 15.3 15.26 1.39 0.27
## school12:dkids 1 8.5 8.51 0.78 0.40
## school12:ui 1 1.2 1.24 0.11 0.74
## sex:married 1 5.4 5.36 0.49 0.50
## sex:dkids 1 0.6 0.63 0.06 0.81
## sex:ui 1 2.7 2.70 0.25 0.63
## married:dkids 1 7.9 7.90 0.72 0.42
## married:ui 1 1.5 1.49 0.14 0.72
## dkids:ui 1 2.7 2.70 0.25 0.63
## Residuals 10 109.5 10.95#Generate main effects plot and interaction effects plot for "model_FFD_final".
par(mfrow=c(1,1))
plot(model_resp, cex = 1.2, cex.lab = 1.2, cex.axis = 1.2, main = "Main effects plot for model_resp", cex.main = 2)
MEPlot(model_resp, abbrev = 5, cex.xax = 1.6, cex.main = 2, main = "Main Effects Plot for 'model_resp'")
IAPlot(model_resp, abbrev = 5, show.alias = TRUE, lwd = 2, cex = 2, cex.xax = 1.2, cex.lab = 1.5)
Upon carrying out this fractional factorial design [2^(6-1)] and observing the main effects plots (two different versions of the same plot) that were generated for this design, it appears that ‘nwhite’ and ‘dkids’ have the largest effect on the state unemployment rate. Furthermore, upon generating an interaction effects plot for this design, it appears that the interactions of ‘nwhite:married’, ‘nwhite:dkids’, and ‘nwhite:ui’ have the largest effect on the state unemployment rate. However, upon observing the p-values that correspond to the factors contained within the ANOVA model of this fractional factorial design, it’s clear that we would fail to reject the null hypothesis of our experiment (since all of the p-values are > 0.05), leading us to believe that the variation that is observed in the mean values of the state unemployment rate cannot be explained by any of the six factors being considered in this analysis (or by any interaction of those six factors) and, as such, is likely caused solely by randomization. It’s important to note, however, that this fractional factorial design only takes into account a very small portion of the large dataset “benefits”. Since there are multiple values of ‘stateur’ that correspond to the 32 unique rows of the design matrix “FrDesign” (namely, the 2,555 observations contained within “FFD_benefits”), and since only a sample of 32 observations were taken from “FFD_benefits_unique” to generate this fractional factorial design, it’s likely that the data included in this design was not sufficient enough to properly determine the statistical significance of each of the six factors with relation to the determination of whether or not the variation that is observed in the response variable (which corresponds to ‘stateur’ in this analysis) can be explained by the variation existent in any of the six factor-treatments of the experiment (which correspond to ‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’).
Estimation (of Parameters)
In estimating the different parameters of the experiment, summary statistics were determined for the relevant data in the dataset pertaining to the state unemployment rate contained in “Benefits” (which includes both the average state unemployment rate values for all of the states contained within the dataset and the standard deviation of those average state unemployment rates) and the data pertaining to the six different factors that are considered in this analysis (which includes both the quantities of individuals who are categorized as falling under one of the two different levels that exist for each respective factor [‘nwhite’, ‘school12’, ‘sex’, ‘married’, ‘dkids’, and ‘ui’] and the standard deviation of those distributed quantities).
Tables of Parameter Values
#Display summary statistics of benefits$stateur.
summary(benefits$stateur)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.20 5.70 7.20 7.51 9.00 18.00#Display standard deviation of benefits$stateur.
sd(benefits$stateur, na.rm = FALSE)## [1] 2.501#Display summary statistics of benefits$nwhite.
summary(benefits$nwhite)## no yes
## 4159 718#Display standard deviation of benefits$nwhite.
sd(benefits$nwhite, na.rm = FALSE)## [1] 0.3544#Display summary statistics of benefits$school12.
summary(benefits$school12)## no yes
## 3950 927#Display standard deviation of benefits$school12.
sd(benefits$school12, na.rm = FALSE)## [1] 0.3924#Display summary statistics of benefits$sex.
summary(benefits$sex)## female male
## 1150 3727#Display standard deviation of benefits$sex.
sd(benefits$sex, na.rm = FALSE)## [1] 0.4245#Display summary statistics of benefits$married.
summary(benefits$married)## no yes
## 1791 3086#Display standard deviation of benefits$married.
sd(benefits$married, na.rm = FALSE)## [1] 0.4821#Display summary statistics of benefits$dkids.
summary(benefits$dkids)## no yes
## 2508 2369#Display standard deviation of benefits$dkids.
sd(benefits$dkids, na.rm = FALSE)## [1] 0.4998#Display summary statistics of benefits$ui.
summary(benefits$ui)## no yes
## 1542 3335#Display standard deviation of benefits$ui.
sd(benefits$ui, na.rm = FALSE)## [1] 0.465Diagnostics/Model Adequacy Checking
In verifying the results of this experiment, it’s important to ensure that the dataset itself meets all of the assumptions that correlate with the design approach that was carried out. In this way, we want to make sure that our dataset exhibits normality. Until we know that our dataset does, in fact, exhibit normality, we cannot yet say with confidence that our results are significant and representative of a properly carried-out modeling approach. In verifying our dataset for normality, we can both create a Normal Quantile-Quantile (QQ) Plot of our data and perform a Shapiro-Wilk Test of Normality on our data.
#Create a Normal Q-Q Plot for the state unemployment rate.
qqnorm(benefits[,"stateur"], main = "Normal Q-Q Plot of the State Unemployment Rate")
qqline(benefits[,"stateur"])
#Create a Normal Q-Q Plot of the residuals of the ANOVA model "model_stateur".
qqnorm(residuals(model_stateur), main = "Normal Q-Q Plot of Residuals of 'model_stateur'")
qqline(residuals(model_stateur))
Shapiro-Wilk Test of Normality Results
#Perform Shapiro-Wilk Test of Normality on the state unemployment rate (normality is assummed if p > 0.1).
shapiro.test(benefits[,"stateur"])##
## Shapiro-Wilk normality test
##
## data: benefits[, "stateur"]
## W = 0.9602, p-value < 2.2e-16Upon both constructing Normal Q-Q Plots and performing a Shapiro-Wilk Test of Normality on the data in this analysis, it’s likely that we cannot readily assume that our data exhibits normality, since the resulting p-value of the Shapiro-Wilk Test of Normality for “benefits[,“stateur”]” was found to be < 0.1 at its value of < 2.2e-16 and since all of the constructed Normal Q-Q Plots (and their respective “tails”, especially) did not seem to display a trend of data that aligned closely with the Normal Q-Q Line.
In further attempting to verify the validity of our original ANOVA model’s results, we can generate a “quality of fit” model that plots residual error against the fitted model that was developed in our original analysis of variance (ANOVA).
#Create a "Quality of Fit Model" that plots the residuals of "model_stateur" against its fitted model.
par(mfrow=c(1,1))
plot(fitted(model_stateur),residuals(model_stateur), main = "Quality of Fit of 'model_stateur'")
Because the resulting plot does not appear to be scatted and clumped around zero, the ANOVA model that was developed does not particularly suggest good fit under this “model adequacy checking” criteria. Thus, we cannot confidently rely on both the modeling approach that we carried out and the dataset that we analyzed in justifying the significance of our results.
4. Contingencies to the Experimental Design/Analysis if Modeling Assumptions Failed
Since our modeling assumptions of data normality and factor independence seemingly failed in our analysis, we can err on the side of caution by performing the nonparametric Kruskal-Wallis rank sum test to back up our original results (which will help us to decide whether the population distributions are identical without necessarily exhibiting a normal distribution).
Kruskal-Wallis Rank Sum Test Results
#Perform Kruskal-Wallis Rank Sum Test on 'stateur' within the "Benefits" dataset for each of the six factors that this analysis considers (identical populations is assummed if p > 0.05).
kruskal.test(benefits[,"stateur"],benefits$nwhite)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$nwhite
## Kruskal-Wallis chi-squared = 0.01, df = 1, p-value = 0.9203kruskal.test(benefits[,"stateur"],benefits$school12)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$school12
## Kruskal-Wallis chi-squared = 0.0317, df = 1, p-value = 0.8587kruskal.test(benefits[,"stateur"],benefits$sex)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$sex
## Kruskal-Wallis chi-squared = 6.239, df = 1, p-value = 0.0125kruskal.test(benefits[,"stateur"],benefits$married)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$married
## Kruskal-Wallis chi-squared = 1.692, df = 1, p-value = 0.1933kruskal.test(benefits[,"stateur"],benefits$dkids)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$dkids
## Kruskal-Wallis chi-squared = 19.29, df = 1, p-value = 1.122e-05kruskal.test(benefits[,"stateur"],benefits$ui)##
## Kruskal-Wallis rank sum test
##
## data: benefits[, "stateur"] and benefits$ui
## Kruskal-Wallis chi-squared = 68.7, df = 1, p-value < 2.2e-16Since the p-values for the resulting Kruskal-Wallis rank sum test that considers the factors ‘sex’, ‘dkids’, and ‘ui’ against the response variable ‘stateur’ are less than 0.05, we can assume that the mean values of the state unemployment rate compared to the factors ‘sex’, ‘dkids’, and ‘ui’, respectively, are comparatively nonidentical populations. Therefore, this result suggests that we would reject the null hypothesis of our main experiment for the factors ‘sex’, ‘dkids’, and ‘ui’, which would lead us to infer that the differences in mean values of the state unemployment rate for each of the corresponding factors ‘sex’, ‘dkids’, and ‘ui’ being considered in this dataset is caused by something other than randomization, leading us to believe that the variation that is observed in the mean values of the state unemployment rate can be explained by the variation existent in the factors ‘sex’, ‘dkids’, and ‘ui’ being considered in this analysis. Alternately, this result also suggests that we would fail to reject the null hypothesis of our main experiment for the factors ‘nwhite’, ‘school12’, and ‘married’, which would lead us to infer that the differences in mean values of the state unemployment rate for each of the corresponding factors ‘nwhite’, ‘school12’, and ‘married’ being considered in this dataset is solely caused by randomization, leading us to believe that the variation that is observed in the mean values of the state unemployment rate cannot be explained by the variation existent in the factors ‘nwhite’, ‘school12’, and ‘married’ being considered in this analysis. Furthermore, in addition to treating our data in such a way that uses a nonparametric analysis upon any realization that normality cannot be assumed, transformations such as the “Box-Cox Power Transformation” certainly could have been performed on the data to make it approximately normal. However, these transformations would not be necessary for this analysis, since the nonparametric significance results that we generated by using the Kruskal-Wallis rank sums test were suitable in giving us confidence in the results of our analysis.
5. References to the literature
[1] McCall, B.P. (1995) “The impact of unemployment insurance benefit levels on recipiency”, Journal of Business and Economic Statistics, 13, 189-198.
6. Appendices
A summary of, or pointer to, the raw data
complete and documented R code
This data frame contains a cross-section of information from 1972 pertaining to the unemployment rates of blue collar workers in the United States, collected for the research corresponding to the article entitled “The impact of unemployment insurance benefit levels on recipiency” (McCall, B.P. 1995) [1]. [http://www.stats4stem.org/r-benefits-data.html]. This data frame, which is called ‘Benefits’, has been conveniently packaged for R users in the R Library ‘Ecdat’.