Issues in biomedical statistics: comparing means under normal distribution theory.

The test used most commonly in biomedical research to compare means when measurements have been made on a continuous scale is Student's t-test, followed closely by various forms of analysis of variance. These tests require that defined populations have been randomly sampled, but there are other assumptions about populations and samples that must be satisfied. These include: (i) normality of the population distributions; (ii) equal variance in those normal populations; and (iii) statistical independence of the samples. This review offers advice to investigators on how to recognize breaches of the assumptions of normality and equality of variance, and how to deal with them by modifying the usual t-test or by transforming the experimental data. The sample-size also has an important bearing on statistical inferences: (i) if it is too small, the risk of Type II error is inflated; and (ii) inequality of sample size exaggerates the effects of inequality of variance. The assumption of independence is breached if repeated measurements are made serially rather than in random order, but adjustments to analysis of variance can be made to correct for the inflated risk of Type I error. The review also considers the problem of making multiple comparisons of means, and recommends solutions.