Calculating the necessary sample size is important for the planning of a study, and sample size justification is often required when requesting funding. This is because we want to make sure we have enough participants to detect an effect if there is one and not too many that wastes resources (participant time/effort, cost, time), all while minimizing potential errors.
The two types of error occur when you 1) reject the null hypothesis when it is in fact true (type I) and 2) miss rejecting the null hypothesis when it is in fact false (type II error). In practice, you’ll never know if you made either of these errors, but using an appropriate sample size (based on prior knowledge) is a good way to do your best to minimize these possible errors. Most study’s primary objectives fall into the categories discussed in this section, and once you have the necessary estimates needed for the sample size calculations, these formulas can help you decide on the sample size for the study. Often when we are comparing two groups, equal sample sizes in each group are the best choice, but there are situations when unequal sample sizes are appropriate.
Sample size calculations are only as good as the preliminary data put into the formulas, so it is important to use the best information available, and if needed, to run pilot studies first to get good preliminary data.