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Friday, January 2, 2009

Sample Size Calculation for One-Way ANOVAs in Dissertations and Theses

I'm sure there are some of you out there looking for the minimum sample size necessary to find the analyses of variance (ANOVAs) in your dissertation or thesis significant. Sample size calculation for ANOVAs can be complicated if it's a factorial ANOVA or mixed ANOVA, so we'll start slow and focus on an ANOVA with only one independent variable.

What is the Power used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

For the purposes of this example, we are going to looking for the minimum sample size to give us a power of 0.80. To read more about this, click here. This is going to give us a 20% probability of falsely accepting the null hypothesis, or a 20% probability that we missed something. We're okay with this, since missing something is typically less severe than finding something that isn't really there. Click here for help with determining the appropriate power for your dissertation or thesis.

What is the level of significance used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

This is the probability of falsely rejecting the null hypothesis. The statistical significance for the purposes of calculating the sample size for the ANOVA is going to be 0.05. This means we are looking for less than a 5% probability that our results are due to chance. Get help with determining the ANOVA level of significance for the sample size calculation in your dissertation or thesis.

What is the effect size used in calculating the sample size of the ANOVA being used in my dissertation or thesis?

There are a couple things involved in determining this. Since choosing a small effect size will require that we gather thousands of observations to find our ANOVA significant, and choosing a large effect size will mean fewer people but not a very good chance of finding the test significant if the groups are not hugely different.

What we need here is something in the middle…the medium effect size. For the purposes of the dissertation or thesis, this is definitely acceptable. Get help with determining the ANOVA effect size for the sample size calculation in your dissertation or thesis.

What is the sample size needed for the ANOVAs in my dissertation or thesis?

Using the criteria above, the sample size needed for the one-way ANOVA, testing for differences on one independent variable with two groups, is 128, the same as the independent samples t-test. The sample size will vary with the number of groups in the independent variable, but for the independent variable with 3 groups, you will need 156 or approximately 52/group. Get help with a custom sample size calculation for your dissertation or thesis.