Include your answers in this document in the sections below the rubric.

Rubric

Answer the questions with the two data examples.


Admissions rates

# read the data
adm <- read.csv("ADA1_WS_12_SimpSchoolMajors.csv")
adm$Acceptance <- relevel(adm$Acceptance, "Success")
str(adm)
## 'data.frame':    560 obs. of  3 variables:
##  $ Gender    : Factor w/ 2 levels "Female","Male": 1 2 1 1 2 1 2 1 1 1 ...
##  $ Acceptance: Factor w/ 2 levels "Success","Failure": 2 1 2 2 2 1 2 2 1 2 ...
##  $ School    : Factor w/ 2 levels "Art","Business": 2 1 2 2 2 2 2 2 1 2 ...
head(adm)
##   Gender Acceptance   School
## 1 Female    Failure Business
## 2   Male    Success      Art
## 3 Female    Failure Business
## 4 Female    Failure Business
## 5   Male    Failure Business
## 6 Female    Success Business
tail(adm)
##     Gender Acceptance   School
## 555   Male    Failure      Art
## 556   Male    Success      Art
## 557 Female    Success      Art
## 558 Female    Failure Business
## 559 Female    Success Business
## 560   Male    Success Business

Admission rates by gender

##           Gender
## Acceptance Female Male
##    Success     88  198
##    Failure    112  162
##           Gender
## Acceptance Female Male
##    Success   0.44 0.55
##    Failure   0.56 0.45
## Joining by: Acceptance, Gender

  1. (2 p) Interpret the table and associated plot.

For example, “The proportion of Females is XX, which is XX higher/lower than Males.”

Admission rates by gender, for each School

## [1] "Art"
##           Gender
## Acceptance Female Male
##    Success     64  180
##    Failure     16   60
##           Gender
## Acceptance Female Male
##    Success   0.80 0.75
##    Failure   0.20 0.25
## [1] "Business"
##           Gender
## Acceptance Female Male
##    Success     24   18
##    Failure     96  102
##           Gender
## Acceptance Female Male
##    Success   0.20 0.15
##    Failure   0.80 0.85
## Joining by: Acceptance, Gender, School

  1. (1 p) Interpret the table and assocated plot.

  2. (1 p) Compare the Acceptance by Gender (where schools were combined) to when Schools were treated separately. What do you observe?

  3. (1 p) Does this surprise you? Why?

  4. (1 p) What is the name of the “paradox” given to this data phenomenon?


Death penalty

Example 1 - Death Penalty

A 2-by-2-by-2 in from Agresti (1990) studied effects of racial characteristics on whether individuals convicted of homicide received the death penalty. The 326 subjects were defendants in homicide indictments in 20 Florida counties during 1976-1977. Is there an association between death penalty, defendant’s race and victim’s race? What kind of association? We can display this table in long format:

# read the data
penalty <- read.table(text="
Defendant Victim Death Freq
white     white  yes     19
white     white  no     132
white     black  yes      0
white     black  no       9
black     white  yes     11
black     white  no      52
black     black  yes      6
black     black  no      97
", header = TRUE)

penalty$Death <- relevel(penalty$Death, "yes")

str(penalty)
## 'data.frame':    8 obs. of  4 variables:
##  $ Defendant: Factor w/ 2 levels "black","white": 2 2 2 2 1 1 1 1
##  $ Victim   : Factor w/ 2 levels "black","white": 2 2 1 1 2 2 1 1
##  $ Death    : Factor w/ 2 levels "yes","no": 1 2 1 2 1 2 1 2
##  $ Freq     : int  19 132 0 9 11 52 6 97

Death penalty by Defendant race

##      Defendant
## Death black white
##   yes    17    19
##   no    149   141
##      Defendant
## Death     black     white
##   yes 0.1024096 0.1187500
##   no  0.8975904 0.8812500
## Joining by: Death, Defendant

  1. (2 p) Interpret the table and assocated plot.

Death penalty by Defendant race, by Victim’s race

## [1] "black"
##      Defendant
## Death black white
##   yes     6     0
##   no     97     9
##      Defendant
## Death      black      white
##   yes 0.05825243 0.00000000
##   no  0.94174757 1.00000000
## [1] "white"
##      Defendant
## Death black white
##   yes    11    19
##   no     52   132
##      Defendant
## Death     black     white
##   yes 0.1746032 0.1258278
##   no  0.8253968 0.8741722
## Joining by: Death, Defendant, Victim

  1. (1 p) Interpret the tables and assocated plot.

  2. (1 p) Compare the Death by Defendant (where victim’s race were combined) to when victim’s race were treated separately. What do you observe?