Cognitive-based therapy (CBT) and family-based therapy (FBT) aretwo different treatments for anorexia. In an experimental study,forty-six anorexic teenage girls were randomly assigned to twogroups. One group, consisting of n1 = 29 individuals, received CBT,and the other group, consisting of n2 = 17 individuals, receivedFBT. Weight of each individual is measured twice, once at thebeginning and once at the end of the study period. The variable ofinterest is the weight change, i.e. weight after therapy minusweight before therapy. The data collected from the two samples aregiven below.
cognitive = c(1.7, 0.7, -0.1, -0.7, -3.5, 14.9, 3.5,17.1, -7.6, 1.6, 11.7, 6.1,
1.1, -4.0, 20.9, -9.1, 2.1, -1.4, 1.4,-0.3, -3.7, -0.8, 2.4, 12.6, 1.9, 3.9,
0.1, 15.4, -0.7)
family = c(11.4, 11.0, 5.5, 9.4, 13.6,-2.9, -0.1, 7.4, 21.5, -5.3, -3.8, 13.4,
13.1, 9.0, 3.9, 5.7,10.7)
Note that a positive weight change (weight gain) is generallygood for anorexia patients. Let ?1 be the population mean weightchange in the CBT group, and ?2 the population mean weight changein the FBT group. The goal is to conduct statistical inference onthe difference ?1 ? ?2
-
4. Two-sample t-test relies on the assumption that the twosamples are either large enough (n1 ? 30 and n2 ? 30) or comingfrom normal distributions. In the context of this problem, neitherof the two samples is large enough.
(a) Check the normality assumption for both samples using thenormal quantile-quantile plot. Re- member that you can do this in Rusing the qqnorm command.
(b) Suppose one thinks that the normality assumption does nothold for this data set, hence does not trust the results providedin the two-sample t-test. Suggest a different hypothesis testingprocedure that does not rely on the normality assumption. (Note:You don’t have to carry out the test.
