case0502: The Spock Conspiracy Trial

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

Description

In 1968, Dr. Benjamin Spock was tried in Boston on charges of conspiring to violate the Selective Service Act by encouraging young men to resist being drafted into military service for Vietnam. The defence in the case challenged the method of jury selection claiming that women were underrepresented. Boston juries are selected in three stages. First 300 names are selected at random from the City Directory, then a venire of 30 or more jurors is selected from the initial list of 300 and finally, an actual jury is selected from the venire in a nonrandom process allowing each side to exclude certain jurors. There was one woman on the venire and no women on the final list. The defence argued that the judge in the trial had a history of venires in which women were systematically underrepresented and compared the judge's recent venires with the venires of six other Boston area district judges.

Usage

case0502

Format

A data frame with 46 observations on the following 2 variables.

Percent

is the percent of women on the venire's of the Spock trial judge and 6 other Boston area judges

Judge

is a factor with levels "Spock's", "A", "B", "C", "D", "E" and "F"

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Zeisel, H. and Kalven, H. Jr. (1972). Parking Tickets and Missing Women: Statistics and the Law in Tanur, J.M. et al. (eds.) Statistics: A Guide to the Unknown, Holden-Day.

Examples

str(case0502)  
attach(case0502) 

# Make new factor level names (with sample sizes) for boxplots
myNames <- c("A (5)", "B (6)", "C (9)", "D (2)", "E (6)", "F (9)", "Spock's (9)")
  
boxplot(Percent ~ Judge, ylab = "Percent of Women on Judges' Venires",
  names = myNames, xlab = "Judge (and number of venires)",
  main = "Percent Women on Venires of 7 Massachusetts Judges") 
myAov1  <- aov(Percent ~ Judge)  
plot(myAov1, which=1)   # Residual plot
summary(myAov1) # Initial screening. Any evidence of judge differences? (yes)
   
## ANALYSIS 1. TWO-SAMPLE t-TEST (ASSUMING NON-SPOCK JUDGES HAVE A COMMON MEAN)
SpockOrOther <- factor(ifelse(Judge=="Spock's","Spock","Other"))                                   
aovFull      <- aov(Percent ~ Judge) 
aovReduced   <- aov(Percent ~ SpockOrOther) 
anova(aovReduced,aovFull) #Any evidence that 7 mean fits better than the 2 mean?       
t.test(Percent ~ SpockOrOther, var.equal=TRUE) # Evidence that 2 means differ?  

## ANALYSIS 2. COMPARE SPOCK MEAN TO AVERAGE OF OTHER MEANS 
  myAov3        <- aov(Percent ~ Judge - 1) 
  myContrast    <- rbind(c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6, - 1))
if(require(multcomp)){  # use multcomp library
  myComparison  <- glht(myAov3, linfct=myContrast) 
  summary(myComparison, test=adjusted("none"))   
  confint(myComparison) 
}

## BOXPLOTS FOR PRESENTATION   
boxplot(Percent ~ Judge,  ylab= "Percent of Women on Judges' Venires",
        names=myNames, xlab="Judge (and number of venires)",
        main= "Percent Women on Venires of 7 Massachusetts Judges",
        col="green", boxlwd=2,  medlwd=2,  whisklty=1,  whisklwd=2,
        staplewex=.2, staplelwd=2,  outlwd=2,  outpch=21, outbg="green",
        outcex=1.5)         
        
detach(case0502)  

Example output

'data.frame':	46 obs. of  2 variables:
 $ Percent: num  6.4 8.7 13.3 13.6 15 15.2 17.7 18.6 23.1 16.8 ...
 $ Judge  : Factor w/ 7 levels "A","B","C","D",..: 7 7 7 7 7 7 7 7 7 1 ...
            Df Sum Sq Mean Sq F value  Pr(>F)    
Judge        6   1927   321.2   6.718 6.1e-05 ***
Residuals   39   1864    47.8                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Analysis of Variance Table

Model 1: Percent ~ SpockOrOther
Model 2: Percent ~ Judge
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     44 2190.9                           
2     39 1864.5  5    326.46 1.3658 0.2582

	Two Sample t-test

data:  Percent by SpockOrOther
t = 5.6697, df = 44, p-value = 1.03e-06
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  9.584045 20.155294
sample estimates:
mean in group Other mean in group Spock 
           29.49189            14.62222 

Loading required package: multcomp
Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: 'TH.data'

The following object is masked from 'package:MASS':

    geyser


	 Simultaneous Confidence Intervals

Fit: aov(formula = Percent ~ Judge - 1)

Quantile = 2.0227
95% family-wise confidence level
 

Linear Hypotheses:
       Estimate lwr     upr    
1 == 0 14.9783   9.6348 20.3219

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.