Getting Familiar with Categorical Data in R
Luoxi Hao
2020-01-20
Homework #1 is worth 100 points and each question is worth 6.5 points each.
Submission Instructions: save the .HTML file as ‘Familiar_ Categorical_Data_Assignmentyourlastname.HTML’ and upload the HTML file to the assignment entitled ‘Getting Familiar with Categorical Data in R’ on Canvas on or before Tuesday November 12, 2019 by 11:59p.m. EST. No late assignments are accepted.
- #2.1 p.p. 60-61
Run the code chunk below.
library(vcd)## Loading required package: gridlibrary(grid)
library(gnm)
library(vcdExtra)
ds <- datasets(package = c("vcd", "vcdExtra"))
str(ds, vec.len=2)## 'data.frame': 76 obs. of 5 variables:
## $ Package: chr "vcd" "vcd" ...
## $ Item : chr "Arthritis" "Baseball" ...
## $ class : chr "data.frame" "data.frame" ...
## $ dim : chr "84x5" "322x25" ...
## $ Title : chr "Arthritis Treatment Data" "Baseball Data" ...View(ds)
View(UCBAdmissions)
str(UCBAdmissions)## 'table' num [1:2, 1:2, 1:6] 512 313 89 19 353 207 17 8 120 205 ...
## - attr(*, "dimnames")=List of 3
## ..$ Admit : chr [1:2] "Admitted" "Rejected"
## ..$ Gender: chr [1:2] "Male" "Female"
## ..$ Dept : chr [1:6] "A" "B" "C" "D" ...- How many data sets are there altogether? How many are there in each package?
nrow(ds)## [1] 76table(ds$Package)##
## vcd vcdExtra
## 33 43- Make a tabular display of the frequencies by Package and class.
table(ds$Package, ds$class)##
## array data.frame matrix table
## vcd 1 17 0 15
## vcdExtra 3 24 1 15- Choose one or two data sets from this list, and examine their help files (e.g., help(Arthritis) or ?Arthritis). You can use, e.g., example(Arthritis) to run the R code for a given example.
?Arthritis## starting httpd help server ... doneexample("Arthritis")##
## Arthrt> data("Arthritis")
##
## Arthrt> art <- xtabs(~ Treatment + Improved, data = Arthritis, subset = Sex == "Female")
##
## Arthrt> art
## Improved
## Treatment None Some Marked
## Placebo 19 7 6
## Treated 6 5 16
##
## Arthrt> mosaic(art, gp = shading_Friendly)
##
## Arthrt> mosaic(art, gp = shading_max)
?Trucks
example("Trucks")##
## Trucks> library(MASS)
##
## Trucks> data("Trucks")
##
## Trucks> tab <- xtabs(Freq ~ period + collision + light + parked, data = Trucks)
##
## Trucks> loglm(~ (collision + period) * parked * light, data = tab)
## Call:
## loglm(formula = ~(collision + period) * parked * light, data = tab)
##
## Statistics:
## X^2 df P(> X^2)
## Likelihood Ratio 6.853404 6 0.3346175
## Pearson 6.972248 6 0.3234213
##
## Trucks> doubledecker(collision ~ parked + light + period, data = tab)
##
## Trucks> cotabplot(tab, panel = cotab_coindep)
- p. 61 #2.3
- Find the total number of cases contained in this table.
summary(UCBAdmissions)## Number of cases in table: 4526
## Number of factors: 3
## Test for independence of all factors:
## Chisq = 2000.3, df = 16, p-value = 0- For each department, find the total number of applicants.
colSums(UCBAdmissions, na.rm = TRUE)## Dept
## Gender A B C D E F
## Male 825 560 325 417 191 373
## Female 108 25 593 375 393 341- For each department, find the overall proportion of applicants who were admitted.
prop.table(UCBAdmissions)## , , Dept = A
##
## Gender
## Admit Male Female
## Admitted 0.113124171 0.019664163
## Rejected 0.069155988 0.004197967
##
## , , Dept = B
##
## Gender
## Admit Male Female
## Admitted 0.077993814 0.003756076
## Rejected 0.045735749 0.001767565
##
## , , Dept = C
##
## Gender
## Admit Male Female
## Admitted 0.026513478 0.044631021
## Rejected 0.045293858 0.086389748
##
## , , Dept = D
##
## Gender
## Admit Male Female
## Admitted 0.030490499 0.028943880
## Rejected 0.061643836 0.053910738
##
## , , Dept = E
##
## Gender
## Admit Male Female
## Admitted 0.011710119 0.020768891
## Rejected 0.030490499 0.066062749
##
## , , Dept = F
##
## Gender
## Admit Male Female
## Admitted 0.004860804 0.005302696
## Rejected 0.077551922 0.070039770- Construct a tabular display of department (rows) and gender (columns), showing the proportion of applicants in each cell who were admitted relative to the total applicants in that cell.
ftable(prop.table(UCBAdmissions, c(3,2)))## Dept A B C D E F
## Admit Gender
## Admitted Male 0.62060606 0.63035714 0.36923077 0.33093525 0.27748691 0.05898123
## Female 0.82407407 0.68000000 0.34064081 0.34933333 0.23918575 0.07038123
## Rejected Male 0.37939394 0.36964286 0.63076923 0.66906475 0.72251309 0.94101877
## Female 0.17592593 0.32000000 0.65935919 0.65066667 0.76081425 0.92961877- p. 61 #2.4 a, c, e
- Find the total number of cases represented in this table.
data("DanishWelfare")
summary(DanishWelfare)## Freq Alcohol Income Status Urban
## Min. : 0.00 <1 :60 0-50 :45 Widow :60 Copenhagen :36
## 1st Qu.: 3.00 1-2:60 50-100 :45 Married :60 SubCopenhagen:36
## Median : 12.00 >2 :60 100-150:45 Unmarried:60 LargeCity :36
## Mean : 28.58 >150 :45 City :36
## 3rd Qu.: 35.25 Country :36
## Max. :255.00sum(DanishWelfare$Freq)## [1] 5144- Convert this data frame to table form, DanishWelfare.tab, a 4-way array containing the frequencies with appropriate variable names and level names.
DanishWelfare.tab <- xtabs(Freq ~., data = DanishWelfare)
summary(DanishWelfare.tab)## Call: xtabs(formula = Freq ~ ., data = DanishWelfare)
## Number of cases in table: 5144
## Number of factors: 4
## Test for independence of all factors:
## Chisq = 1733.5, df = 168, p-value = 7.514e-258
## Chi-squared approximation may be incorrectstr(DanishWelfare.tab)## 'xtabs' num [1:3, 1:4, 1:3, 1:5] 1 3 2 8 1 3 2 5 2 42 ...
## - attr(*, "dimnames")=List of 4
## ..$ Alcohol: chr [1:3] "<1" "1-2" ">2"
## ..$ Income : chr [1:4] "0-50" "50-100" "100-150" ">150"
## ..$ Status : chr [1:3] "Widow" "Married" "Unmarried"
## ..$ Urban : chr [1:5] "Copenhagen" "SubCopenhagen" "LargeCity" "City" ...
## - attr(*, "call")= language xtabs(formula = Freq ~ ., data = DanishWelfare)- Use structable () or ftable () to produce a pleasing flattened display of the frequencies in the 4-way table. Choose the variables used as row and column variables to make it easier to compare levels of Alcohol across the other factors.
ftable(xtabs(Freq ~., data = DanishWelfare))## Urban Copenhagen SubCopenhagen LargeCity City Country
## Alcohol Income Status
## <1 0-50 Widow 1 4 1 8 6
## Married 14 8 41 100 175
## Unmarried 6 1 2 6 9
## 50-100 Widow 8 2 7 14 5
## Married 42 51 62 234 255
## Unmarried 7 5 9 20 27
## 100-150 Widow 2 3 1 5 2
## Married 21 30 23 87 77
## Unmarried 3 2 1 12 4
## >150 Widow 42 29 17 95 46
## Married 24 30 50 167 232
## Unmarried 33 24 15 64 68
## 1-2 0-50 Widow 3 0 1 4 2
## Married 15 7 15 25 48
## Unmarried 2 3 9 9 7
## 50-100 Widow 1 1 3 8 4
## Married 39 59 68 172 143
## Unmarried 12 3 11 20 23
## 100-150 Widow 5 4 1 9 4
## Married 32 68 43 128 86
## Unmarried 6 10 5 21 15
## >150 Widow 26 34 14 48 24
## Married 43 76 70 198 136
## Unmarried 36 23 48 89 64
## >2 0-50 Widow 2 0 2 1 0
## Married 1 2 2 7 7
## Unmarried 3 0 1 5 1
## 50-100 Widow 3 0 2 1 3
## Married 14 21 14 38 35
## Unmarried 2 0 3 12 13
## 100-150 Widow 2 1 1 1 0
## Married 20 31 10 36 21
## Unmarried 0 2 3 9 7
## >150 Widow 21 13 5 20 8
## Married 23 47 21 53 36
## Unmarried 38 20 13 39 26- p. 62 #2.5 a, b, c
#code from text
data("UKSoccer", package = "vcd")
ftable(UKSoccer)## Away 0 1 2 3 4
## Home
## 0 27 29 10 8 2
## 1 59 53 14 12 4
## 2 28 32 14 12 4
## 3 19 14 7 4 1
## 4 7 8 10 2 0- Verify that the total number of games represented in this table is 380.
sum(UKSoccer)## [1] 380- Find the marginal total of the number of goals scored by each of the home and away teams.
margin.table(UKSoccer,1)## Home
## 0 1 2 3 4
## 76 142 90 45 27margin.table(UKSoccer,2)## Away
## 0 1 2 3 4
## 140 136 55 38 11- Express each of the marginal totals as proportions.
prop.table(margin.table(UKSoccer, 1))## Home
## 0 1 2 3 4
## 0.20000000 0.37368421 0.23684211 0.11842105 0.07105263prop.table(margin.table(UKSoccer, 2))## Away
## 0 1 2 3 4
## 0.36842105 0.35789474 0.14473684 0.10000000 0.02894737- Run the code below and notice there is a data frame entitled SpaceShuttle. Using the R help, read about the details of this data frame. That is, familiarize yourself with the context and understand the meaning of the different rows.
library(vcd)
library(vcdExtra)
ds <- datasets(package = c("vcd", "vcdExtra"))
str(ds)## 'data.frame': 76 obs. of 5 variables:
## $ Package: chr "vcd" "vcd" "vcd" "vcd" ...
## $ Item : chr "Arthritis" "Baseball" "BrokenMarriage" "Bundesliga" ...
## $ class : chr "data.frame" "data.frame" "data.frame" "data.frame" ...
## $ dim : chr "84x5" "322x25" "20x4" "14018x7" ...
## $ Title : chr "Arthritis Treatment Data" "Baseball Data" "Broken Marriage Data" "Ergebnisse der Fussball-Bundesliga" ...View(ds)
?SpaceShuttle
summary(SpaceShuttle)## FlightNumber Temperature Pressure Fail nFailures
## 1 : 1 Min. :53.00 Min. : 50.0 no :16 Min. :0.0000
## 2 : 1 1st Qu.:67.00 1st Qu.: 50.0 yes : 7 1st Qu.:0.0000
## 3 : 1 Median :70.00 Median :200.0 NA's: 1 Median :0.0000
## 4 : 1 Mean :70.00 Mean :141.7 Mean :0.3913
## 41B : 1 3rd Qu.:75.25 3rd Qu.:200.0 3rd Qu.:1.0000
## 41C : 1 Max. :81.00 Max. :200.0 Max. :2.0000
## (Other):18 NA's :1
## Damage
## Min. : 0.000
## 1st Qu.: 0.000
## Median : 0.000
## Mean : 1.609
## 3rd Qu.: 4.000
## Max. :11.000
## NA's :1- Using the structable() function, create a “flat” table that has the Damage Index on the columns and whether the O-ring failed and how many failures on the rows.
structable(Damage ~ Fail + nFailures, data = SpaceShuttle)## Damage 0 2 4 11
## Fail nFailures
## no 0 15 0 1 0
## 1 0 0 0 0
## 2 0 0 0 0
## yes 0 0 0 0 0
## 1 0 1 4 0
## 2 0 0 1 1- Construct the same formatted table that you did in part a, but now use the xtabs() and ftable() functions.
xtabs(Damage ~ Fail + nFailures, data = SpaceShuttle)## nFailures
## Fail 0 1 2
## no 4 0 0
## yes 0 18 15ftable(Damage ~ Fail + nFailures, data = SpaceShuttle)## Damage 0 2 4 11
## Fail nFailures
## no 0 15 0 1 0
## 1 0 0 0 0
## 2 0 0 0 0
## yes 0 0 0 0 0
## 1 0 1 4 0
## 2 0 0 1 1