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 complex, so we’ll start with one-way ANOVAs involving one independent variable.
What is the Power used in calculating the sample size of the ANOVA being used in my dissertation or thesis?
For this example, we’ll determine the minimum sample size needed for a power of 0.80. Consequently, this allows for a 20% chance of falsely accepting the null hypothesis or missing an effect. To read more about this, click here. 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 level of significance do you use to calculate the sample size for the ANOVA in your dissertation or thesis?
This is the probability of falsely rejecting the null hypothesis. The statistical significance for ANOVA sample size calculation is 0.05. This means we aim for less than a 5% chance that our results occur by chance. Get help with determining the ANOVA level of significance for the sample size calculation in your dissertation or thesis.
What effect size do you use to calculate the sample size for the ANOVA in your dissertation or thesis?
There are a couple things involved in determining this. Small effect sizes need many observations, while large effect sizes need fewer but risk low significance.
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 sample size do you need for the ANOVAs in your 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.
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