The need to write-up a power analysis occurs a few times when conducting a research project: in the research proposal, ethics application, conference presentations, and the Method section of a thesis / empirical report.
Why Do I Need to Do a Power Analysis?
You need to conduct an a priori power analysis (a priori meaning it is conducted before you do your research) to calculate the minimum number of participants needed to test your study hypotheses / detect a significant effect (if one exists). Ethics committees care about power analysis because they don't want to see you unnecessarily recruiting (and potentially putting at risk) e.g., 500 participants, when you only needed 200 participants to detect an effect.
The most popular software for conducting power analysis is G*Power.
What do I need to Include in a G*Power Analysis Write-Up?
When you write-up the results of an a priori G*Power analysis (i.e., the number of participants required to detect an effect) you need to report three parameters that you input into G*Power:
alpha (usually set to α = .05),
power (usually set to .80)
effect size (this can vary - see below)
The expected effect size (i.e., the strength of the effect) that you input into G*Power is generally derived from:
A pilot study or published study that has looked at your variables; or
If there is no pilot data and no similar studies (i.e., your study is new), then you can use Cohen's (1988) general guidelines for detecting a ‘small"’, "‘medium"’, or "‘large’ "effects (these are reported in the G*Power manual).
From my experience, some universities/supervisors are BIG on power analysis; others, not so much. If they are BIG on power analysis, they may want you to go down path 1 and search the literature for a study similar to yours that has published an effect size that you can then input into G*Power. Because previous research is not likely to be identical to your study design, this search can be a challenge. In contrast, other supervisors will just recommend you make an educated guess of the expected effect (e.g., small, medium or large) based on Cohen's guidelines (this is often a medium effect - but make sure to discuss this with your supervisor!).
Example G*Power Write-ups
1. Where the effect size is from a pilot/published study:
"An a priori power analysis was conducted using G*Power version 3.1.9.7 (Faul et al., 2007) for sample size estimation, based on data from [pilot study/published study] (year) (N = XX), which compared X to Y. The effect size in [pilot study/published study]'s study was #, considered to be [extremely large/large/medium/small] using Cohen's (1988) criteria. With a significance criterion of α = .05 and power = .80, the minimum sample size needed with this effect size is N = # for [insert statistical test you are using to test your hypothesis]. Thus, the obtained sample size of N = # is more than adequate to test the study hypothesis."
2. Where a medium effect is expected:
“An a priori power analysis was conducted using G*Power version 3.1.9.7 (Faul et al., 2007) to determine the minimum sample size required to test the study hypothesis. Results indicated the required sample size to achieve 80% power for detecting a medium effect, at a significance criterion of α = .05, was N = # for [insert statistical test you are using to test your hypothesis]. Thus, the obtained sample size of N = # is adequate to test the study hypothesis."
Additional Tips:
If you have multiple hypotheses that each require different data analysis strategies (e.g., Hypothesis 1 is to be tested using correlation; Hypothesis 2 is to be tested using a multiple regression), you may need to perform a separate power analysis for each hypothesis. I recommend reporting the results of each power analysis and then selecting the larger sample size needed from among them as a basis of recruitment.
For analysis that compares groups, be sure to include the number of participants required per group (e.g., "G*Power suggests we would need # participants per group (N = #) in an independent samples t-test").
In your research proposal / ethics application you may want to increase your proposed sample size to account for potential attrition. Try to include a reference to justify this increased sample size. E.g., "Accounting for a potential attrition rate of 20% based on previous research [e.g., previous research that has used this intervention / investigated this topic] (see reference), an additional # participants will be recruited"].
I have included further G*Power resources below.
Happy Researching! 🎉
G*Power Resources:
Download G*Power here
The correct reference for G*Power is:
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39, 175–191. https://doi.org/10.3758/BF03193146
Please remember: If the content of this article conflicts with what you have been taught at your university... please follow the advice of your university! Always seek the advice of your supervisor!
***If you want more strategies and tips for writing your thesis, you can enrol in my on-demand workshop, Learn How to Write a Kick Ass Thesis: Part 1 - Setting Yourself up For Success in Your Literature Review and Introduction***