Swain vs. Alabama: Seth's Answer

In 1965, the U.S. Supreme Court decided the case of Swain vs. Alabama. Swain, a black man, was convicted in Talladega County, Alabama, of raping a white woman. He was sentenced to death. The case was appealed to the Supreme Court on the grounds that there were no blacks on the jury; moreover, no black “within the memory of persons now living has ever served on any petition jury in any civil or criminal case tried in Talladega County, Alabama.” The Supreme Court denied the appeal, on the following grounds. As provided by Alabama law, the jury was selected from a panel of about 100 persons. There were 8 blacks on the panel. (They did not serve on the jury because they were “struck,” or removed, through a maneuver called peremptory challenges by the prosecution. Such challenges were until quite recently constitutionally protected.) The Supreme Court ruled that the presence of 8 blacks on the panel showed “The overall percentage disparity has been small and reflects no studied attempt to include or exclude a specified number of blacks.” At that time in Alabama, only men over the age of 21 were eligible for jury duty (times have changed!). There were 16,000 such men in Talladega County, and about 26% were black.

Do you agree with the Supreme Court? Was there bias in jury selection? How might you approach this question statistically?

What does it mean for an “overall percentage disparity” to be small? What would be a large disparity?

From a statistical perspective what does it mean for something to be large or small?

Could you express the results as a p-value? What hypothesis would you be testing?

#The population of eligible jurors was 16000
#26% were black
#How many white potential jurors were there in the county?
wPop <- 16000 * (1-.26)

#How many black potential jurors were there in the county?
bPop <- 16000 * .26

#make a "virtual" population
white <- rep(0, wPop)
black <- rep(1, bPop)
pop <- c(black, white)

#Select a jury panel
panel <- sample(pop, 100, replace=F)

#make nsim jury panels by randomly sampling from the population
nsim <- 1000000 #a million jury panels
panels <- matrix(nrow=nsim, ncol=1)
for (i in 1:nsim){
  panel <- sample(pop, 100)
  panels[i] <- sum(panel)
    }

options(scipen=100000) #supress scientifc notation
hist(panels, breaks=30, xlim=c(0,50), 
     main=paste("Histogram of the number of African Americans on", 
                nsim, "jury panels \n assuming unbiased jury pool selection", sep=" "))
abline(v=8, col="red", lwd=2) # draw a reference line at 8

sum(panels <= 8) #number of jury pools with 8 or fewer blacks

## [1] 5

Conclusion

paste("In our simulations of unbiased jury pool selection only ", sum(panels <= 8), " out of ", nsim, " jury pools (",(sum(panels <= 8)/nsim)*100 ," %) had 8 or fewer African Americans", sep="")

## [1] "In our simulations of unbiased jury pool selection only 5 out of 1000000 jury pools (0.0005 %) had 8 or fewer African Americans"