USING COHEN TABLES TO DETERMINE THE MAXIMUM POWER ATTAINABLE IN 2-SAMPLE TESTS WHEN ONE SAMPLE IS LIMITED IN SIZE

Advantages of using equal sample sizes in 2 sample tests for means, correlations, and proportions are well known. However, in applied research there are frequently circumstances that limit the size of 1 of the 2 samples. This article draws attention to a simple method of determining, from Cohen's (1988) tables, the effects that this constraint (on the size of one sample) has on the maximum attainable power of these tests. These effects can be extremely serious in the case of small, medium, and even large effect sizes and clearly indicate that availability of a very large 2nd sample may not compensate for a constraint on the size of the 1st sample.