Abstract
The power of mean tests with two and three groups, with small effect size and under non-normality and homo-heteroscedaticity. The power of mean contrasts is studied in conditions of small effect size, with two and three samples, and using several parametric and non-parametric statistical tests (Student's test, Welch test and Mann-Withney-Wilcoxon's U with two groups; ANOVA, James second order test and Kruskal-Wallis with three groups), both complying with the parametric assumptions of normality and homocedasticity and violating those assumptions. The main result is that, when it is not possible to have big samples (which is very common when investigating in applied Psychology) these tests are not useful and different ways of investigating must be accomplished.
