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Someone asked me by email about confidence intervals in complex research designs. This person had rejected the use of post hoc power calculations, and wanted instead to use confidence intervals to help answer the question about whether the sample size was adequate. In a simple setting, such as the comparison of a treatment group to a control group, the choice of confidence interval is obvious, but how would you handle complex research designs (more than two groups and/or repeated measurements over time).

For example, if you are comparing a low, medium, and high dose to a placebo, then three confidence intervals for the difference between each dose and placebo might be interesting. If there is no dose response pattern, then a confidence interval comparing the two extreme doses might be helpful because it places limits on the size of any possible dose response pattern.

If your repeated measures include a baseline, 6 month and 12 month measures, then a confidence interval for the short term change (6 month minus baseline) and an interval for the long term change (12 month minus baseline) might be useful. Combining the two scenarios together, perhaps you know there is a strong placebo response, so then you might want a confidence interval for the long term change score between each dose and the placebo.

If you end up with more than two or three confidence intervals, you might want to consider some sort of adjustment like Bonferroni.