STA442/1008 Assignment 5

Quiz on Friday Oct. 16th in tutorial

This assignment is based upon Chapter 4. You are asked to read the chapter on your own; there will be no lecture on this material. It's not really so bad; the chapter is only 15 page long including a page of references.

The (non-random) sample here consists of prisoners in U.S. Jails (in Florida, I believe) who were convicted of first degree murder. The prisoners are either Black or White, the victims were either Black or White, and the prisoner either got the death penalty or not. If you are interested in more detail, the reference is American Sociological Review 1981, 46, 918-927. Of course you do not need to go to the library to do this assignment.

The data are available in the file deathpen.data. The variables are

  1. Race of Prisoner (1=White 2=Black)
  2. Race of Victim (1=White 2=Black)
  3. Death Penalty (1=Yes 2=No)

Please do the following.

  1. Examine all three 2-dimensional tables, and do chisquare tests. Just so you can check your work, for the table of prisoner's race by victim's race, I get a Phi coefficient of 0.5940. For each test you do, be able to answer questions like these.
    1. What is the value of the test statistic? The answer is a single number from the printout.
    2. What is the p-value? The answer is a single number from the printout.
    3. Do you reject the null hypothesis at the 0.05 level? Answer Yes or No.
    4. Are the results statistically significant at the 0.05 level? Answer Yes or No.
    5. In plain, non-technical language, what do you conclude, if anything?
  2. Test the association between Race of Prisoner and Death Penalty, controlling for Race of Victim. Give the value of the test statistic (a number), the degrees of freedom and the p-value. What, if anything, do you conclude about race and the death penalty? Just so you can check your work, I notice that when the victim was White, Black prisoners got the death penalty 17.46% of the time.
  3. Test the association between Race of Victim and Death Penalty, controlling for Race of Prisoner. Give the value of the test statistic (a number), the degrees of freedom and the p-value. What, if anything, do you conclude about race and the death penalty?
  4. What percent of White prisoners
    1. Got the death penalty when the victim was White?
    2. Got the death penalty when the victim was Black?
  5. Is the difference between percentages from the last question a statisitcally significant one? Answer Yes or No and give the p-value.
  6. In your opinion, is there a potential problem with measurement error in this study? Briefly discuss.

Note: SAS warns us about a cell with expected frequency less than 5. In fact, it's also less than one, but don't worry. That sub-table is contributing a small value to the chisquare statistic, not a large one, so it is not inflating Type I error -- and that's what we care about, mostly. So, please don't worry about the warning. No trap is being laid for you here.