One of the most frequent requests we get as statistical consultants is sample size justification or sample size calculation. Our clients typically have a study they wish to conduct or are working on their dissertation and have completed their proposal or first couple of chapters but the process seems to grind to a crawl when faced with sample size calculation and the appropriate statistical test to test their carefully thought-out research design. Deadlines are looming and you need information fast. Sample size calculation need not be daunting but requires some basic understanding:
1. Sample size is a function of level of significance, effect size, and power.
This means your sample size is going to be dependent on the level of significance, effect size, and power. This also means if you change one of the three measures, your sample size will also change. This is not a complicated concept, but for more information see blog entries on the subject. This is important to understand in sample size calculation.
2. Sample size calculation is dependent on the statistical tests you are conducting.
Since effect size will vary with the statistical tests you are conducting, your sample size calculation will vary depending on the statistical tests you are planning to conduct. Measurements of effect size are different for each statistical test. For example, in sample size calculation, small, medium, and large effect sizes for t-test are 0.20, 0.50, and 0.80, respectively. For a one-way ANOVA the same measures of effect size are 0.10, 0.25, and 0.40, respectively. Since effect size is part of the sample size calculation, your sample size calculation will vary with statistical test.
3. Sample Size Calculation will be unique to your study.
We have established that sample size calculation utilizes the relationship between sample size, level of significance, effect size, and power. We also know that our basic effect size measurements are going to vary with the statistical tests.
However, it may be the case that you are replicating a study, using an instrument that someone has already used in a study, or have information regarding the effect sizes found by other researchers doing something similar. If in your literature review, you find the results of statistical tests conducted by other researchers on something similar to what you are doing, you might find the actual, reported effect size of their study.
For example you might find that a researcher conducting similar research found a large effect size. This would make your a priori sample size requirements considerably smaller, ceteris paribus, than if he had found say a small effect size. For a t-test at the 0.05 level of significance, a power of 0.80, a small effect size, your minimum sample to find your statistical test significant is 393 in each group for a total of 786 participants. With a large effect size your minimum sample would be 26 in each group for a total of 52 participants.
For a customized sample size calculation for your study, thesis, or dissertation, please call Statistics Solutions Inc. for a free 30 minute consultation. 877-437-8622
