case1902: Death Penalty and Race

In Sleuth2: Data Sets from Ramsey and Schafer's "Statistical Sleuth (2nd Ed)"

Description

Lawyers collected data on convicted black murderers in the state of Georgia to see whether convicted black murderers whose victim was white were more likely to receive the death penalty than those whose victim was black, after accounting for aggravation level of the murder. They categorized murders into 6 progressively more serious types. Category 1 comprises barroom brawls, liquor-induced arguments lovers' quarrels, and similar crimes. Category 6 includes the most vicious, cruel, cold=blooded, unprovoked crimes.

Usage

case1902

Format

A data frame with 12 observations on the following 4 variables.

Aggravation

the aggravation level of the crime, a factor with levels "1", "2", "3", "4", "5" and "6"

Victim

a factor indicating race of murder victim, with levels "White" and "Black"

Death

number in the aggravation and victim category who received the death penalty

Nodeath

number in the aggravation and victim category who did not receive the death penalty

Source

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis (2nd ed), Duxbury.

References

Woodworth, G.C. (1989). Statistics and the Death Penalty, Stats 2: 9–12.

Examples

str(case1902)

# Add smidgeon to denominator because of zeros
empiricalodds <- with(case1902, Death/(Nodeath + .5))
plot(empiricalodds ~ as.numeric(Aggravation), case1902, log="y",
  pch=ifelse(Victim=="White", 21, 19),
  xlab="Aggravation Level of the Murder", ylab="Odds of Death Penalty")
legend(3.8,.02,legend=c("White Victim Murderers","Black Victim Murderers"),pch=c(21,19))

fitbig <- glm(cbind(Death,Nodeath) ~ Aggravation*Victim, case1902, family=binomial)
# No evidence of overdispersion; no statistically significant evidence
# of interactive effect 
anova(fitbig, test="Chisq") 
fitlinear <- glm(cbind(Death,Nodeath) ~ Aggravation + Victim, case1902, family=binomial)
summary(fitlinear)

# Mantel Haenszel Test, as an alternative
table1902   <- with(case1902, rbind(Death,Nodeath))
dim(table1902) <- c(2,2,6)
mantelhaen.test(table1902)

Example output

'data.frame':	12 obs. of  4 variables:
 $ Aggravation: Factor w/ 6 levels "1","2","3","4",..: 1 1 2 2 3 3 4 4 5 5 ...
 $ Victim     : Factor w/ 2 levels "White","Black": 1 2 1 2 1 2 1 2 1 2 ...
 $ Death      : num  2 1 2 1 6 2 9 2 9 4 ...
 $ Nodeath    : num  60 181 15 21 7 9 3 4 0 3 ...
Analysis of Deviance Table

Model: binomial, link: logit

Response: cbind(Death, Nodeath)

Terms added sequentially (first to last)


                   Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
NULL                                  11    212.284              
Aggravation         5  198.320         6     13.964 < 2.2e-16 ***
Victim              1   11.725         5      2.239 0.0006167 ***
Aggravation:Victim  5    2.239         0      0.000 0.8151731    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Call:
glm(formula = cbind(Death, Nodeath) ~ Aggravation + Victim, family = binomial, 
    data = case1902)

Deviance Residuals: 
       1         2         3         4         5         6         7         8  
 0.02705  -0.03705  -0.27695   0.46062  -0.22255   0.33222   0.02846  -0.03695  
       9        10        11        12  
 1.21437  -0.55797   0.00006   0.00007  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)    -3.4207     0.6144  -5.567 2.59e-08 ***
Aggravation2    1.6090     0.8506   1.892  0.05855 .  
Aggravation3    3.3902     0.7474   4.536 5.74e-06 ***
Aggravation4    4.5004     0.7858   5.727 1.02e-08 ***
Aggravation5    5.8814     0.9128   6.443 1.17e-10 ***
Aggravation6   26.2636  8772.8073   0.003  0.99761    
VictimBlack    -1.7409     0.5426  -3.208  0.00134 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 212.2838  on 11  degrees of freedom
Residual deviance:   2.2391  on  5  degrees of freedom
AIC: 38.105

Number of Fisher Scoring iterations: 19


	Mantel-Haenszel chi-squared test with continuity correction

data:  table1902
Mantel-Haenszel X-squared = 9.6983, df = 1, p-value = 0.001844
alternative hypothesis: true common odds ratio is not equal to 1
95 percent confidence interval:
  1.910687 15.789312
sample estimates:
common odds ratio 
          5.49258 

Sleuth2 documentation built on May 2, 2019, 7:01 a.m.