Sesame Street
Chase Rosendale, Lei Wang, Ryan Williams
September 8, 2017
Project Description
The Children’s Television Workshop is interested in finding whether Sesame Street is effective at improving children between 3-5 years old in their knowledge of letters, numbers, and forms. The data of interest that was collected includes information on the test children’s age, sex, and population site. Each child took a pretest and a post-test for their knowledge of letters, numbers, and forms.
The children were chosen from five different populations of interest: - Three to five year old disadvantaged children from inner city areas in various parts of the country - Four year old advantaged suburban children - Advantaged rural children - Disadvantaged rural children - Disadvantaged Spanish-speaking children
Research Questions
- Question 1: Is Sesame Street effective in improving children’s knowledge of letters, numbers and forms? Does encouragement to watch and setting affect the amount of improvement?
- Question 2: How does selection site (the populations of interest) influence the improvement in the knowledge of letters, numbers and forms?
- Question 3: What factors are effective in predicting the improvement in the scores of letters, numbers and forms?
Statisical Questions
- Question 1: Is the improvement in letters, numbers, and forms influenced by the variable regular, the variable indicating whether the children watch Sesame Street on a regular basis?
- Question 2: Does the encouragement to watch Sesame Street along with setting(watching at school or watching at home) affect the amount of improvement?
- Question 3: Is there a significant difference between the improvement scores for letters, number, and forms for each population of interest?
- Question 4: What is the best model to predict the improvement in the categories: letters, numbers, and forms.
Variables of Interest
There were 14 variables of interest that were collected in the study. These variables included the explanatory variables: site, age, sex, view category, setting, and viewing encouraged. The pretest and post-test scores for letters, numbers, and forms were used to create the three response variables; numbers improvement, letters improvement, and form improvement. These variables were calculated using the difference of the post-test and the pretest divided by the maximum score.
| Variable | Description | Type | Levels | |
|---|---|---|---|---|
| 1 | Site | Populations of Interest, listed in Appendix | Nominal | 5 Levels, each level is a different population of interest |
| 2 | Sex | Male 1, Female 2 | Dichotomous | 2 Levels |
| 3 | Age | Age in months | Numerical Discrete | Ranges from 34-69 |
| 4 | Viewing Category | Viewing categories from rarely watched to watched more than 5 times a week | Ordinal | Ranges from 1 to 4 |
| 5 | Setting | Setting in which Sesame Street was viewed | Dichotomous | 2 levels: Home 1, School 2 |
| 6 | Viewing Encouraged | Whether children were encouraged to watch | Dichotomous | 2 Levels: Encouraged 1, Not 2 |
| 7 | Pretest Letters | Pretest on knowledge of letters | Numerical Discrete | Ranges from 0-58 |
| 8 | Pretest Numbers | Pretest on knowledge of numbers | Numerical Discrete | Ranges from 0-54 |
| 9 | Pretest Forms | Pretest on knowledge of forms | Numerical Discrete | Ranges from 0-20 |
| 10 | Posttest Letters | Posttest knowledge of letters | Numerical Discrete | Ranges from 0-58 |
| 11 | Posttest Numbers | Posttest knowledge of numbers | Numerical Discrete | Ranges from 0-54 |
| 12 | Posttest Forms | Posttest knowledge of forms | Numerical Discrete | Ranges from 0-20 |
| 13 | Numbers Improvement | Improvement in numbers as a proportion of the maximum score | Numerical Continuous | Ranges from -1 to 1 |
| 14 | Letters Improvement | Improvement in letters as a proportion of the maximum score | Numerical Continuous | Ranges from -1 to 1 |
| 15 | Forms Improvement | Improvement in forms as a proportion of the maximum score | Numerical Continuous | Ranges from -1 to 1 |
Preface
This report was created using RMarkdown with a Slidy Presentation Output
Requirements to reproduce this report independantly
require(car)
require(ISwR)
require(dplyr)
require(leaps)
require(ggplot2)
require(gdata)
data1 <- read.csv("E:/OneDrive/STAT 470/Sesame_Street_Case_Study_files/sesame.csv", header = TRUE)
attach(data1)Exploratory Data Analysis(EDA)
- Check for Missing Data or Data Entry Mistakes
- Check the factors towards the viewcat for any “weirdness”
- Check the difference between the post and pre variables and the viewcat to see how the improvement in scores would look
- Check assumptions (L.I.N.E.) before moving forward
Check for Missing Data
- Using is.na() in R, we confirmed there was no missing data entries
Graphs of Post Scores to Viewing Categories
Graph of POSTLET to VIEWCAT
let <- ggplot(data2, aes(x=factor(viewcat), y=postlet))
let + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of POSTFORM to VIEWCAT
form <- ggplot(data2, aes(x=factor(viewcat), y=postform))
form + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of POSTNUMB to VIEWCAT
numb <- ggplot(data2, aes(x=factor(viewcat), y=postnumb))
numb + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Summary of Previous Graphs
- We can see that based on the three different response variables (numbers, forms, letters), there are very different spreads in the data.
- If you only looked at the box-plots (and the means in turn) you would only see that the more often the children watched Sesame Street, the higher post-scores they received.
- However, by looking at the spread of the data, we can see that although generally that may hold true, there is much to be said about how much the post-scores vary even inside the same viewing categories
- We also wanted to check if the relationship held true for how often they watched and the difference between the Pre and Post scores for our response variables
Graphs of Improvements from Pre to Post Scores
Graph of DIFFLET to VIEWCAT
difflet <- postlet - prelet #Creating new variable for difference between post and pre scores
dlet <- ggplot(data2, aes(x=factor(viewcat), y=difflet))
dlet + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of DIFFFORM to VIEWCAT
diffform <- postform - preform #Creating new variable for difference between post and pre scores
dform <- ggplot(data2, aes(x=factor(viewcat), y=diffform))
dform + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of DIFFNUMB to VIEWCAT
diffnumb <- postnumb - prenumb #Creating new variable for difference between post and pre scores
dnumb <- ggplot(data2, aes(x=factor(viewcat), y=diffnumb))
dnumb + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Summary of Previous Graphs
- It seems as though by plotting based on the difference between the post and pre scores (plotting the improvement) the spread we saw in the previous graphs has went away
- This might mean that by using the improvement in the scores, we’ll eliminate some of that variation within the post-scores
- We will keep this in mind when selecting a model
Improvement Summaries
| Variable | N | Mean | Standard.Deviation | Minimum | Maximum | |
|---|---|---|---|---|---|---|
| 1 | Letter Improvement | 240 | 0.18628 | 0.19255 | -0.37931 | 0.7069 |
| 2 | Number Improvement | 240 | 0.16667 | 0.17954 | -0.64815 | 0.61111 |
| 3 | Forms Improvement | 240 | 0.1906 | 0.18732 | -0.5 | 0.85 |
Assumptions for this Data
Linearity:
- Cannot see a need to transform the data (see alternate plots in Appendix)
plot(prenumb,diffnumb)
plot(preform,diffform)
plot(prelet, difflet)
Independance
- We will assume that the children in the study were independent of one another
Normality:
Equal Variance
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.602861 Df = 1 p = 0.2054982## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.127897 Df = 1 p = 0.2882244## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.03792127 Df = 1 p = 0.8456013## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085- All values are within an acceptable range
Statistical Analysis
- We ran multiple step functions to eliminate any insignificant factors
- We will pick the model with the lowest AIC (or highest correlation) to the data
Questions 1 and 2:
Testing A Model for Improvement In Factors
testmodel <- lm(diffform ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffformmodel <- lm(diffform ~ factor(viewcat), data = data2)testmodel <- lm(difflet ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffletmodel <- lm(difflet ~ factor(site) + factor(viewcat) + viewenc +
agecat, data = data2)testmodel <- lm(diffnumb ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffnumbmodel <- lm(diffnumb ~ factor(viewcat), data = data2)Question 3:
- In order to test whether there is significance based on the population, the improvement scores were compared to the site numbers, using one of the sites as a baseline. Depending on the baseline, there were different sites marked as significant. Because of this, we can conclude that at least one site is significantly different from the other sites, so this factor is significant.
Question 4:
- In order to find the best final model, the regression equations with predictors that produced the lowest AIC (Akaike information criterion, lower = better) were selected.
Testing A Model for Post Factors
testmodel <- lm(postnumb ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the modeltestmodel <- lm(postform ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the modeltestmodel <- lm(postlet ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the modelAlternate Models
These are some of the other models we tried
modelform10 <- lm(diffform ~ factor(site), data = data2)
modellet10 <- lm(difflet ~ factor(site), data = data2)
modelnumb11 <- lm(postnumb ~ log(prenumb) + factor(viewcat), data = data2)
modelform11 <- lm(postform ~ log(preform) + factor(viewcat), data = data2)
modellet11 <- lm(postlet ~ log(prelet) + factor(viewcat), data = data2)Decision on Models
- The final models for each improvement score were determined by the models chosen by the lowest AIC score, while also ensuring that the test variables such as watching regularly, setting, and population of interest are in the final model. The following regression formulas for each improvement score is listed below.
modelnumb <- lm(diffnumb ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)
modelform <- lm(diffform ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)
modellet <- lm(difflet ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)Checking for Influential Data Points in Our Models
We will use Cook’s Distance to find any influential points in our models
Cook’s Distance for Postnumb Model
cookdis <- cooks.distance(modelnumb) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postnumb Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Cook’s Distance for Postform Model
cookdis <- cooks.distance(modelform) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postform Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Cook’s Distance for Postlet Model
cookdis <- cooks.distance(modellet) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postnumb Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Check to see if removing Influential Points improves model
Original R-Squared Values (Model Correlation to Data, Higher is Better)
## [1] 0.2392241## [1] 0.3572446## [1] 0.4020194New R-Squared Values with influentials removed
## [1] 0.2502526## [1] 0.4154165## [1] 0.4563963As you can see, with the influentials removed, the models have a better correlation to the data, this being true, we will continue to report the models with both the influenctials removed and not removed.
Regression Plots of our Models (Outliers removed, see Appendix for Regression with Outliers)
Post Numbers Regression Model
Post Forms Regression Model
Post Letters Regression Model
Considerations
- First, the data for the populations of interest may have some overlap. One of the categories for population of interest, Spanish speaking disadvantaged, may overlap with the other disadvantaged categories.
- Another consideration is that the relationship between the pre test scores and the improvement scores may not be linear. With a lower starting score, there is more room for improvement.
- The subjective nature of the data collection is also a concern. The self-reporting nature of the viewing encouraged and how often the children viewed Sesame Street will have variation from parent to parent.
- It is also important to note that some pretest scores predict a rise in the improvement, while others predict a smaller improvement score.
Appendix (Extra Regression Plots, Outliers included w/ ggplot code showing)
ggplot function
x <- 1:nrow(data2)
ggplotRegression <- function (fit) {
ggplot(fit$model, aes_string(x, y = names(fit$model)[1])) +
geom_point() +
stat_smooth(method = "lm", col = "red") +
labs(title = "Regression Plot")
}
#Here we've created a function that plots the
#model results to the risk values so we can see if we can improve our
#model in any way as well as use this function for future models
#We can apply our model to this functionPost Numbers Regression Model (outliers included)
ggplotRegression(modelnumb) 
Post Forms Regression Model (outliers included)
ggplotRegression(modelform)
Post Letters Regression Model (outliers included)
ggplotRegression(modellet)
Appendix (Extra Plots)
plot(log(prelet) ~ postlet)
plot(log(preform) ~ log(postform))
plot(log(prenumb) ~ postnumb)
Appendix (Extra Code)
Letter Improvement:
> sitemodellet<-lm(difflet~factor(site),data=sesame_data_NOut)
> summary(sitemodellet)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.20125 0.02223 9.051 < 2e-16 ***
factor(site)2 0.12953 0.03159 4.100 5.77e-05 ***
factor(site)3 -0.08085 0.03078 -2.627 0.00922 **
factor(site)4 -0.07769 0.03379 -2.299 0.02241 *
factor(site)5 -0.03459 0.04478 -0.772 0.44067
Site 2,3,4 are significantly different from Site 1 when considering no other factors.
Number Improvement:
> sitemodelnum<-lm(diffnum~factor(site),data=sesame_data_NOut)
> summary(sitemodelnum)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.186195 0.021247 8.763 4.77e-16 ***
factor(site)2 0.040828 0.030187 1.353 0.1776
factor(site)3 -0.021072 0.029415 -0.716 0.4745
factor(site)4 -0.061857 0.032290 -1.916 0.0567 .
factor(site)5 0.001048 0.042788 0.024 0.9805
No significance
Form Improvement:
> sitemodelform<-lm(diffform~factor(site),data=sesame_data_NOut)
> summary(sitemodelform)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.20125 0.02223 9.051 < 2e-16 ***
factor(site)2 0.12953 0.03159 4.100 5.77e-05 ***
factor(site)3 -0.08085 0.03078 -2.627 0.00922 **
factor(site)4 -0.07769 0.03379 -2.299 0.02241 *
factor(site)5 -0.03459 0.04478 -0.772 0.44067
Site 2,3,4 are significantly different from Site 1 when considering no other factors.
Full Model Selection:
Number Improvement:
Lowest AIC:
diffnum ~ factor(site) + factor(viewcat) + age + sex + viewenc + setting
Form Improvement:
diffform ~ factor(site) + factor(viewcat) + age + sex + viewenc + setting
Letter Improvement:
difflet ~ factor(site) + factor(viewcat) + age + sex + viewenc + setting
model<-lm(diffform~factor(site)+sex+age+factor(viewcat)+setting+viewenc,data=sesame_data_NOut)
step<- stepAIC(model,diection="both")
fullmodel_num<-lm(diffnum~factor(site)+factor(viewcat)+ age +sex +viewenc + setting, data= sesame_data_NOut)
> step<- stepAIC(fullmodel_num,diection="both")
Checking for significance of Regular:
> regularnum<-lm(diffnum~regular,data=sesame_data)
> summary(regularnum)
Call:
lm(formula = diffnum ~ regular, data = sesame_data)
Residuals:
Min 1Q Median 3Q Max
-45.478 -5.814 0.407 6.407 22.522
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.593 1.279 3.591 0.000399 ***
regular 5.886 1.453 4.052 6.88e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.397 on 238 degrees of freedom
Multiple R-squared: 0.06454, Adjusted R-squared: 0.06061
F-statistic: 16.42 on 1 and 238 DF, p-value: 6.876e-05
> regularlet<-lm(difflet~regular,data=sesame_data)
> summary(regularlet)
Call:
lm(formula = difflet ~ regular, data = sesame_data)
Residuals:
Min 1Q Median 3Q Max
-35.220 -7.220 -1.481 5.584 27.780
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.481 1.394 1.780 0.0764 .
regular 10.739 1.584 6.781 9.37e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10.25 on 238 degrees of freedom
Multiple R-squared: 0.1619, Adjusted R-squared: 0.1584
F-statistic: 45.98 on 1 and 238 DF, p-value: 9.366e-11
> regularform<-lm(diffform~regular,data=sesame_data)
> summary(regularform)
Call:
lm(formula = diffform ~ regular, data = sesame_data)
Residuals:
Min 1Q Median 3Q Max
-14.1129 -2.1129 -0.1129 2.2222 12.8871
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.7778 0.5052 5.499 9.85e-08 ***
regular 1.3351 0.5738 2.327 0.0208 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.712 on 238 degrees of freedom
Multiple R-squared: 0.02224, Adjusted R-squared: 0.01813
F-statistic: 5.413 on 1 and 238 DF, p-value: 0.02083
Checking for setting/viewenc
> settingnum<-lm(diffnum~setting+viewenc,data=sesame_data)
> settinglet<-lm(difflet~setting+viewenc,data=sesame_data)
> settingform<-lm(diffform~setting+viewenc,data=sesame_data)
Num: neither significant.
Let: viewenc is significant
Form: Neither significant
Checking for Site significance: Use different sites for the baseline.
> sitenum<-lm(diffnum~factor(site),data=sesame_data)
> sitelet<-lm(difflet~factor(site),data=sesame_data)
> siteform<-lm(diffform~factor(site),data=sesame_data)
> sitenum<-lm(diffnum~factor(site,levels=c(3,2,1,4,5)),data=sesame_data)
Finding the final model:
Number Improvement:
>final_model_num<-lm(diffnum~factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform,data=sesame_data)
> step(final_model_num)
Letter Improvement:
final_model_let<-lm(difflet~factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform,data=sesame_data)
step(final_model_let)
Form Improvement:
final_model_form<-lm(diffform~factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform,data=sesame_data)
> step(final_model_form)
>num_final<-lm(diffnum~factor(site)+age+viewenc+regular+setting+prenumb+preform,data=sesame_data)
> summary(num_final)Raw Data
data1## id site sex age viewcat setting viewenc prebody prelet preform
## 1 1 1 1 66 1 2 1 16 23 12
## 2 2 1 2 67 3 2 1 30 26 9
## 3 3 1 1 56 3 2 2 22 14 9
## 4 4 1 1 49 1 2 2 23 11 10
## 5 5 1 1 69 4 2 2 32 47 15
## 6 6 1 2 54 3 2 2 29 26 10
## 7 7 1 2 47 3 2 2 23 12 11
## 8 8 1 1 51 2 2 1 32 48 19
## 9 9 1 1 69 4 2 1 27 44 18
## 10 10 1 2 53 3 2 1 30 38 17
## 11 11 1 2 58 2 2 2 25 48 14
## 12 12 1 2 58 4 2 2 21 25 13
## 13 13 1 2 49 1 2 2 28 8 9
## 14 14 1 1 64 2 2 1 26 11 15
## 15 15 1 2 58 2 2 1 23 15 9
## 16 16 1 1 49 3 2 1 25 12 17
## 17 17 1 1 57 2 2 1 25 15 13
## 18 18 1 1 45 4 2 1 16 12 8
## 19 19 1 1 45 3 2 1 25 16 12
## 20 20 1 1 60 3 2 2 19 19 8
## 21 21 1 2 65 4 2 1 29 24 14
## 22 22 1 1 44 4 1 1 25 15 17
## 23 23 1 2 38 3 1 1 20 9 2
## 24 24 1 1 35 4 1 1 11 6 8
## 25 25 1 2 42 2 1 1 15 7 8
## 26 26 1 2 50 2 1 1 26 14 10
## 27 27 1 1 61 4 2 2 28 42 16
## 28 28 1 2 34 4 1 1 17 13 7
## 29 29 1 1 60 3 1 2 23 13 9
## 30 30 1 2 39 2 1 1 11 5 5
## 31 31 1 1 39 3 1 1 24 4 11
## 32 32 1 2 41 2 1 1 24 8 3
## 33 33 1 2 55 3 1 1 31 15 17
## 34 34 1 2 42 3 1 1 23 11 7
## 35 35 1 1 50 4 1 1 18 17 12
## 36 36 1 1 58 2 1 1 13 12 6
## 37 37 1 2 59 3 1 2 27 7 13
## 38 38 1 2 36 1 1 2 11 12 9
## 39 39 1 1 51 2 1 1 32 16 16
## 40 40 1 1 51 2 1 1 31 18 13
## 41 41 1 1 48 3 1 1 13 14 8
## 42 42 1 1 43 2 1 1 17 13 14
## 43 43 1 2 35 3 1 2 23 12 8
## 44 44 1 2 36 1 1 2 11 2 6
## 45 45 1 2 39 2 1 2 20 18 6
## 46 46 1 1 45 4 1 2 14 13 9
## 47 47 1 1 58 3 1 2 30 38 15
## 48 48 1 2 38 3 1 1 13 10 7
## 49 49 1 2 57 4 1 1 26 15 11
## 50 50 1 1 49 3 1 2 26 35 10
## 51 51 1 1 55 1 2 2 24 11 10
## 52 52 1 2 44 4 2 2 25 39 18
## 53 53 1 1 56 1 2 2 13 11 6
## 54 54 1 2 48 2 2 2 17 11 9
## 55 55 1 1 50 2 2 2 16 10 8
## 56 56 1 1 52 1 2 2 16 15 6
## 57 57 1 2 51 2 2 1 24 14 10
## 58 58 1 2 58 1 2 2 25 17 17
## 59 59 1 2 48 3 2 2 13 10 10
## 60 60 1 1 54 4 2 2 16 13 10
## 61 61 2 1 52 4 2 2 20 35 15
## 62 62 2 2 48 1 2 2 20 12 11
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