samples, or dependent samples) and wish to perform a test on the difference between their
two means. In this case we want what is often called the matched-sample ttest.Treatment of Anorexia
Everitt, in Hand, et al., 1994, reported on family therapy as a treatment for anorexia. There
were 17 girls in this experiment, and they were weighed before and after treatment. The
weights of the girls, in pounds,^7 is given in Table 7.3. The row of difference scores was ob-
tained by subtracting the Before score from the After score, so that a negative difference
represents weight loss, and a positive difference represents a gain.
One of the first things we should probably do, although it takes us away from ttests for
a moment, is to plot the relationship between Before Treatment and After Treatment
weights, looking to see if there is, in fact, a relationship, and how linear that relationship is.
Such a plot is given in Figure 7.7. Notice that the relationship is basically linear, with a196 Chapter 7 Hypothesis Tests Applied to Means
(^7) Everitt reported that these weights were in kilograms, but if so he has a collection of anorexic young girls whose
mean weight is about 185 pounds, and that just doesn’t sound reasonable. The example is completely unaffected
by the units in which we record weight.
Table 7.3 Data from Everitt on weight gain
ID 1234 5 6 7 8 910
Before 83.8 83.3 86.0 82.5 86.7 79.6 76.9 94.2 73.4 80.5
After 95.2 94.3 91.5 91.9 100.3 76.7 76.8 101.6 94.9 75.2
Diff 11.4 11.0 5.5 9.4 13.6 2 2.9 2 0.1 7.4 21.5 5.3
ID 11 12 13 14 15 16 17 Mean St. Dev
Before 81.6 82.1 77.6 83.5 89.9 86.0 87.3 83.23 5.02
After 77.8 95.5 90.7 92.5 93.8 91.7 98.0 90.49 8.48
Diff 2 3.8 13.4 13.1 9.0 3.9 5.7 10.7 7.26 7.16
Weight before treatment (in pounds)
Weight after treatment (in pounds)
70 80 90 100
110
100
90
80
70
Figure 7.7 Relationship of weight before and after family therapy, for a group of
17 Anorexic girls
matched-sample
ttest