Familiar_ Categorical_Data_Assignment_Zhu
Xinyi Zhu
2022-11-10
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 Wednesday November 13, 2019 by 11:59p.m. EST. No late assignments are accepted.
- #2.1 p.p. 60-61
Run the code chunk below.
library(vcd)## Warning: package 'vcd' was built under R version 4.1.2## Loading required package: gridlibrary(grid)
library(gnm)## Warning: package 'gnm' was built under R version 4.1.2library(vcdExtra)## Warning: package 'vcdExtra' was built under R version 4.1.2ds <- 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] 76ds_1=datasets(package = "vcd")
nrow(ds_1)## [1] 33ds_2=datasets(package = "vcdExtra")
nrow(ds_2)## [1] 43- Make a tabular display of the frequencies by Package and class.
table(ds$Package,ds$class)##
## array data.frame table
## vcd 1 17 15
## vcdExtra 4 24 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.
help(Baseball)
example(Baseball)##
## Basbll> data("Baseball")help(Butterfly)
example(Butterfly)##
## Bttrfl> data("Butterfly")
##
## Bttrfl> Ord_plot(Butterfly)
- p. 61 #2.3
- Find the total number of cases contained in this table.
sum(UCBAdmissions)## [1] 4526- For each department, find the total number of applicants.
margin.table(UCBAdmissions,3)## Dept
## A B C D E F
## 933 585 918 792 584 714- For each department, find the overall proportion of applicants who were admitted.
UCBA=as.data.frame(UCBAdmissions)
Overall=xtabs(Freq~Dept+Admit,data = UCBA)
prop.table(Overall,1)## Admit
## Dept Admitted Rejected
## A 0.64415863 0.35584137
## B 0.63247863 0.36752137
## C 0.35076253 0.64923747
## D 0.33964646 0.66035354
## E 0.25171233 0.74828767
## F 0.06442577 0.93557423- 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.
UCBA2=xtabs(Freq~Dept+Gender+Admit,data=UCBA)
prop.table(UCBA2,1)## , , Admit = Admitted
##
## Gender
## Dept Male Female
## A 0.54876742 0.09539121
## B 0.60341880 0.02905983
## C 0.13071895 0.22004357
## D 0.17424242 0.16540404
## E 0.09075342 0.16095890
## F 0.03081232 0.03361345
##
## , , Admit = Rejected
##
## Gender
## Dept Male Female
## A 0.33547696 0.02036442
## B 0.35384615 0.01367521
## C 0.22331155 0.42592593
## D 0.35227273 0.30808081
## E 0.23630137 0.51198630
## F 0.49159664 0.44397759- p. 61 #2.4 a, c, e
- Find the total number of cases represented in this table.
sum(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=structable(Freq~Urban+Status+Income+Alcohol,data = DanishWelfare)
DanishWelfare.tab## Status Widow Married Unmarried
## Alcohol <1 1-2 >2 <1 1-2 >2 <1 1-2 >2
## Urban Income
## Copenhagen 0-50 1 3 2 14 15 1 6 2 3
## 50-100 8 1 3 42 39 14 7 12 2
## 100-150 2 5 2 21 32 20 3 6 0
## >150 42 26 21 24 43 23 33 36 38
## SubCopenhagen 0-50 4 0 0 8 7 2 1 3 0
## 50-100 2 1 0 51 59 21 5 3 0
## 100-150 3 4 1 30 68 31 2 10 2
## >150 29 34 13 30 76 47 24 23 20
## LargeCity 0-50 1 1 2 41 15 2 2 9 1
## 50-100 7 3 2 62 68 14 9 11 3
## 100-150 1 1 1 23 43 10 1 5 3
## >150 17 14 5 50 70 21 15 48 13
## City 0-50 8 4 1 100 25 7 6 9 5
## 50-100 14 8 1 234 172 38 20 20 12
## 100-150 5 9 1 87 128 36 12 21 9
## >150 95 48 20 167 198 53 64 89 39
## Country 0-50 6 2 0 175 48 7 9 7 1
## 50-100 5 4 3 255 143 35 27 23 13
## 100-150 2 4 0 77 86 21 4 15 7
## >150 46 24 8 232 136 36 68 64 26- 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)
head(ds)## Package Item class dim
## 1 vcd Arthritis data.frame 84x5
## 2 vcd Baseball data.frame 322x25
## 3 vcd BrokenMarriage data.frame 20x4
## 4 vcd Bundesliga data.frame 14018x7
## 5 vcd Bundestag2005 table 16x5
## 6 vcd Butterfly table 24
## Title
## 1 Arthritis Treatment Data
## 2 Baseball Data
## 3 Broken Marriage Data
## 4 Ergebnisse der Fussball-Bundesliga
## 5 Votes in German Bundestag Election 2005
## 6 Butterfly Species in Malaya- 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.
DamageTable=structable(Damage~Fail+nFailures,data=SpaceShuttle)
DamageTable## 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.
ftable(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