Determining the sample size for a statistical study is an important aspect of a quality research design; it is also a difficult process (Lenth, 2001). Several methods for determining sample sizes for ANOVA, MANOVA, and other analyses exist, including the power approach, the random sampling formula, and a priori estimation. Each of these methods requires the researcher’s knowledge of the effect size and power and is used before data for a particular statistical study is collected. When used with careful consideration and planning, these methods are effective tools.
The post hoc estimation of power is also an option for determining sample size; this method, however, is used after a study has actually been carried out and involves the researcher interpreting the results and identifying the effect sample size and effect size have on the power (Stevens, 2009). Not all researchers and statisticians favour this method. Lenth (2001) cautions against retrospective planning such as the post hoc, stating that the goal of this method involves “collect[ing] enough additional data to obtain statistical significance, while ignoring scientific meaning” (p. 191).
Regardless of which sample size estimation method a researcher chooses, he or she must acknowledge that sample size, effect size, and power are dependent on one another and that in order to estimate or determine one, information about the other two is needed. A wealth of
TUTORIAL IN STATISTICS: SAMPLE SIZE DETERMINATION 10
information, statistical software, and web resources are available to help researchers determine the appropriate sample size needed for their statistical studies so that this important task – as daunting as it may seem – is not overlooked or neglected altogether.