# Power calculation

With a power calculation to determine sample size; is this the amount of people I need to interview for the study, or the number of people I will include in the study? (even if they decline)

And do I allow for dropout in the calculation.

• For a specific power it is the number of people you need to interview. Apr 14, 2017 at 2:38
• 1. It's not quite clear what you're asking re dropout. You should explain the design of the study properly so it's clear how dropouts impact what you're doing. (edit your question) ... 2. The power will be based on the number of observations you have, not the number of people you interview. The ones that decline don't give you any data. However, if there's a lot of declining you have to worry about whether those that decline and those that accept have different characteristics (this is a problem with surveys quite generally, and often not well dealt with). Apr 14, 2017 at 2:52

Generally, there are two major reasons to study power: a priori power analysis and posteriori power analysis.

A priori

This is the power analysis you do prior to your data collection with the aim to determine your sample size. Depending on your sampling technique and the statistical test you do there are many formulas that obtain the sample size dependent on the effect size and variance (some other variables) and the power you want to achieve. Here, you use estimated values for variance and effect size informed by prior studies or your own pilot study and the power that you strive for (in social sciences 80% is often used).

Posteriori

You conduct this power analysis after completing the experiment. That is you use your observed variance, effect size, and sample size and calculate the actual power your study had. Why would you do it? Imagine you are replication a significant study and your result is not significant. If you check with your posteriori power analysis that your power was very low, for example 0.4 (which unfortunately often is the reality in social sciences) then it is not surprising at all that you did not find a significant result: your chance of finding an effect - given it really exists - were still pretty low. Your study must not be seen as providing evidence against the original study.

Dropout

I assume dropout means that participants drop out of the study. It is important that you design your study in a way that dropouts are minimised. If you assume that 20% are dropping out you can use that in a prior power analysis. You would try to get more participants than you actually need. However, this is not very realistic in many research situations. So from my experience it is not very useful, but that is a personal preference. Compare no dropouts, 5%, 10% and so on and you will have a great overview of all likely scenarios.