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StatXact Example 8
Comparison of Five Modes of Therapy for the Treatment of Depression
Exact and Asymptotic Kruskal-Wallis Tests Yield Different Conclusions!
This hypothetical example is adapted from an actual study of clinical depression reported on page 193 of the second edition of Nonparametric Statistics for the Behavioral Sciences by Siegel and Castellan (1988, McGraw Hill). Fifteen subjects with very severe symptoms of clinical depression were treated by one of five modes of therapy: psychotherapy, relaxation therapy, drug therapy, behavior therapy, or cognitive therapy. At the end of the treatment the subjects were scored for depression on the Beck Depression Inventory (BDI). The scores were collapsed into 5 categories: normal (score < 7), mild (7 < score < 14), moderate (14 < score < 21), severe (21 < score < 28), very severe (score > 28). The table below displays the frequency count of subjects, by mode of therapy and the depression category into which they fell at the end of the therapy session:
| Mode of Treatment |
Post-Treatment Depression Category |
Totals |
|
Normal |
Mild |
Moderate |
Severe |
Very Severe |
(N = 15) |
| Psychotherapy |
1 |
2 |
2 |
0 |
0 |
5 |
| Relaxation Therapy |
0 |
1 |
1 |
0 |
1 |
3 |
| Drug Therapy |
3 |
0 |
0 |
0 |
0 |
3 |
| Behavior Therapy |
0 |
1 |
1 |
0 |
0 |
2 |
| Cognitive Therapy |
0 |
0 |
0 |
1 |
1 |
2 |
| TOTALS |
4 |
4 |
4 |
1 |
2 |
15 |
Do these data demonstrate that the five modes of treatment differ in their efficacy? The proper test to answer this is the Kruskal-Wallis test whose output, as computed by StatXact, is displayed below:
Notice that the usual asymptotic Kruskal-Wallis p-value is 0.0507, suggesting that the five modes of treatment are not significantly different at the 5% level. However for a data set this small the asymptotic p-value is unreliable. The exact Kruskal-Wallis is computed by StatXact to be 0.0178 and strongly suggests that the five modes of therapy do indeed differ in their results.
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