Drury et al (Reference Drury, Birchwood and Cochrane2000) reported no significant difference in relapse rates, positive symptoms or insight between a cognitive therapy group and a recreational activities and support group of patients who had an acute episode of a non-affective psychosis. This 5-year outcome study assessed 34 out of an original cohort of 40 patients.

Working on the basis of small trials having a large type II error, the group size for each group can be estimated. If the anticipated mean response in one group is μ₁ and the standard deviation is σ, to show a significant result the mean relapse of one group can be estimated at 2 (μ₁) and the standard deviation can be estimated at 1.5 (σ). The estimated difference between the groups (δ) can be set at 0.5 (μ₂-μ₁). A formula to calculate the number (n) in each group (Reference PocockPocock, 1983: 127-128) can be used as follows:

\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\ n=\frac{2{\sigma}^{2}}{({\mu}_{1}-{\mu}_{2})^{2}}{\times}f({\alpha},{\beta})\ \] \end{document}

The α (type I error) is by convention set at 0.05, and the β (type II error) can be set at 0.2. The power of finding a true result (1 - β) will therefore be 0.8 or 80% and, by using a statistical table, f(α, β) is 7.9. Therefore, n can be calculated as

\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\ \frac{2{\times}1.5^{2}}{0.5^{2}}{\times}7.9=142\ \] \end{document}

patients in each group.

It would therefore take a very large sample to prove the null hypothesis in the above hypothetical estimate. In the study by Drury et al (Reference Drury, Birchwood and Cochrane2000), it would be misleading to extrapolate that there was no long-term benefit of using cognitive therapy in schizophrenia in terms of relapse. Larger studies are needed in this rapidly evolving area.