Sample Size

Statistical Analysis

Yesterday we went over the basics of sample size calculation. What about individual tests? Since we know that sample size calculation will vary by individual test, it is important to calculate the minimum sample size necessary considering the type of statistical analysis you are doing. I am going to cover sample size calculation for independent samples *t*-tests today.

**Power Analysis for Independent Samples t-tests**

For this discussion I will refer to Jacob Cohen’s short journal article on power analysis titled, *Quantitative Methods in Psychology: A Power Primer. *This helpful, little journal article nicely identifies effects sizes for common statistical tests, as well as the necessary sample sizes to find those tests significant, given a particular level of significance (0.01, 0.05, and 0.10), effect size (small, medium, and large), and power of 0.80.

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Yesterday we covered the facets of sample size calculation and actually used the example of an independent samples *t*-test. We need a couple things to calculate the sample size necessary for our *t*-test:

· __Level of significance__: Our probability of committing a Type I error, or the probability of falsely rejecting the null hypothesis. Usually this is 0.05, making the probability of committing a Type I error 5%.We decide this.

· __Estimated effect size__: For simplicity purposes, we are going to think of this as the difference between the two groups. This is an estimate and will be determined by our software for the samples we are using. We have no control over this.

· __Power__: Our probability of committing a Type II error, or the probability of falsely accepting the null hypothesis. Usually this is 0.80, making the probability of committing a Type II error 20% or four times as likely as the probability of committing a Type I error. We also decide this.

**A priori Sample Size for Independent Samples t-tests**

Of all the sample size calculations, this is probably the easiest. Page 157 of *Quantitative Methods in Psychology: A Power Primer *tabulates effects sizes for common statistical tests. Number 1 is *t-*test for the difference between two independent means or the independent samples *t-*test. It tells us that a small effect size is 0.20, a medium effect size is 0.50, and a large effect size is 0.80.

While ideally you should have an effect size from empirical research, we are going to look for a 0.05 level of significance, estimate a medium effect size of 0.50, and look for a power of 0.80. Given these criteria, we turn the page to 158 and look for the same number one. We find that for our criteria, we need 64 participants in each of the groups for a total of 128 participants.

*For a customized sample size calculation for your study, thesis, or dissertation, please call Statistics Solutions Inc. (877)437-8622, for a free 30 minute consultation. *