Basic principles underlying statistical power are examined; and issues pertaining to effect size, sample size, error variance, and significance level are highlighted via the use of specific hypothetical examples. Analysis of variance (ANOVA) and related methods remain popular, although other procedures sometimes have more statistical power against Type II error (not rejecting the null hypothesis when it is false). Most researchers recognize that when an ANOVA factor has three or more levels it may become necessary to conduct additional analyses to determine exactly where detected group differences actually arise. Many researchers approach this problem by conducting post hoc or unplanned tests if a statistically significant omnibus effect is isolated. A frequently superior alternative is to conduct planned tests. In addition to increasing the statistical power against Type II error, planned comparisons also force the researcher to think before selecting tests. These advantages can result in better research design and analysis. Sample data sets are used to illustrate the benefits of a priori or planned contrasts. The statistical power of planned comparisons is also explored using hypothetical factorial designs. Six tables illustrate the discussion. (SLD)
Paper presented at the Annual Meeting of the Southwest Educational Research Association (Austin, TX, January 25-27, 1990).
Planned Comparisons; Post Hoc Tests; A Priori Tests; Type II Errors