Exercises 175agreed with “Sex is fun for me and my partner” on a four-point scale ranging from “never
or occasionally” to “almost always.” The data appear below:
Wife’s RatingHusband’s Fairly Very Almost
Rating Never Often Often Always TOTAL
Never 7 7 2 3 19
Fairly Often 2 8 3 7 20
Very Often 1 5 4 9 19
Almost Always 2 8 9 14 33
TOTAL 12 28 18 33 91
a. How would you go about analyzing these data? Remember that you want to know more
than just whether or not the two ratings are independent. Presumably you would like to
show that as one spouse’s ratings go up, so do the other’s, and vice versa.
b. Use both Pearson’s chi-square and the likelihood ratio chi-square.
c. What does Cramér’s Voffer?
d. What about odds ratios?
e. What about kappa?
f. Finally, what if you combined the Never and Fairly Often categories and the Very Often
and Almost Always categories? Would the results be clearer, and under what conditions
might this make sense?6.39 In the previous question we were concerned with whether husbands and wives rate their de-
gree of sexual fun congruently (i.e., to the same degree). But suppose that women have dif-
ferent cut points on an underlying scale of “fun.” For example, maybe women’s idea of
Fairly Often or Almost Always is higher than men’s. (Maybe men would rate “a couple of
times a month” as “Very Often” while women would rate “a couple of times a month” as
“Fairly Often.”) How would this affect your conclusions? Would it represent an underlying
incongruency between males and females?
6.40 Use SPSS or another statistical package to calculate Fisher’s Exact Test for the data in Exer-
cise 6.13. How does it compare to the probability associated with Pearson’s chi-square?
6.41 The following data come from Ramsey and Shafer (1996) but were originally collected in
conjunction with the trial of McClesky v. Zantin 1998. In that trial the defendant’s
lawyers tried to demonstrate that black defendants were more likely to receive the death
penalty if the victim was white than if the victim was black. They were attempting to
prove systematic discrimination in sentencing. The State of Georgia agreed with the basic
fact, but argued that the crimes against whites tended to be more serious crimes than those
committed against blacks, and thus the difference in sentencing was understandable. The
data are shown below. Were the statisticians on the defendant’s side correct in arguing that
sentencing appeared discriminatory? Test this hypothesis using the Mantel-Haenszel
procedure.