More than Two Categories (1 of 3)

A skeptical view of psychotherapy can be summed up as follows: one third better, one third worse, one third the same. In other words, one third of the patients improve as a result of psychotherapy, one third get worse, and one third stay the same.

Consider a hypothetical study of 100 patients who underwent psychotherapy. Assume that 45 were classified as having improved, 30 as having gotten worse, and 25 as having stayed the same. Is this outcome significantly different from that expected under the one third better, one third worse, one third the same? The test is conducted by constructing a table similar to the one used to test the difference between p and π .

 Frequency Better 45 (33.333) Worse 25 (33.333) Same 30 (33.333) Total 100

The first column contains the three categories into which patients could be classified. The top line in each cell in the second column contains the number of patients in the category; the second line contains the number expected under the null hypothesis. These "expected" frequencies are computed by multiplying the total number of subjects (100) by the proportion expected to be in the category (0.33333).