Free tool, data and statistics
Power analysis calculator
Sample size or power for common tests, from the effect size.
Give the effect size you expect and this tool says how many respondents your t-test, one-way ANOVA or correlation study needs. If data is already collected, switch the mode and it will give the power of that sample.
In the doctoral committee meeting somebody always asks why 120 respondents and why not 80. Scholars are coming to us after this question many times. If the study is only descriptive, a survey percentage method is enough to answer it. Your study compares groups, or tests whether two variables are related? Then they will want to see a power analysis. You need three informations for that. One is the effect size you are expecting. Other two are the alpha level and the power you want. Put these in the boxes and the tool gives the sample size, with the working shown.
Effect size helper
Not sure the answer fits your study? WhatsApp us or call, and we’ll look at it with you.
How the tool works
Power is simply the probability that your study catches an effect which is actually there in the population. In most of the theses we see, the target is 80% power with alpha at .05. The four numbers (effect size, alpha, power, sample size) move together. When you decide three of them, the last one gets decided on its own.
For t-test and ANOVA we have used the exact noncentral F distribution. G*Power works on the same distribution, that is why the answers come out matching. A t-test with two groups is handled like an ANOVA having two groups, with f taken as d divided by 2. Then it tries group sizes and stops at the smallest equal size giving your target power. Correlation is done with Fisher’s z approximation. You can open G*Power and test these three cases on your own.
- Two groups, d = 0.5, alpha .05, power 80%. Answer is 64 per group, total 128.
- With three groups at f = 0.25, alpha .05 and power 80%, it comes to 53 in each group. Total is 159.
- Correlation r = 0.3 at alpha .05 and 80% power gives 85 people here. In G*Power the exact method shows 84, so a difference of one person can come.
In the other mode, type the total sample you have and the tool shows its power. 64 per group with d = 0.5 gives a power of 80.1%. We round power downwards only. So if the true value is 79.96%, the tool will not tell you that the 80% target is met.
Effect size shifts the sample size the most, and many scholars just put some number. Cohen did give rough cut-offs. For d it is 0.2 small, 0.5 medium, 0.8 large. In f terms the same labels are 0.10, 0.25 and 0.40, and for r they are 0.1, 0.3 and 0.5. Still, if you can find one published study near to your topic, take the effect from there. The helper under the result is for this. Give it the two means, their SDs and the n of each group, and it calculates d from the pooled SD. If the paper reports eta squared, the helper takes the square root of η² ÷ (1 − η²) to get f. So η² of .06 becomes f = 0.25.
Doing a descriptive survey only? Then this is the wrong tool, please go to our sample size calculator. How to write the justification in Chapter 3 for both kinds of study is there in our sample size guide.
Questions scholars ask
There is no published study like mine. Which effect size do I use?
Ask yourself how much change would be worth something in practice in your area. Take that value and write in Chapter 3 why you took it. Take a study on some training programme. If the company will continue it only when scores go up by half SD, you put d = 0.5 and the reason is ready. Cohen’s labels are the last option, careful examiners notice when they are picked without reason.
What power should I aim for?
80% is fine for most theses, unless your field or committee wants more. Higher power will push the sample up. Take d = 0.5 with alpha .05 and two groups. For 80% power it is 64 per group. Raise it to 90% and you need 86 per group. At 95% the figure is 105 per group.
How do I report the power analysis?
Write down which test, the effect size and the source you took it from, then alpha, power and the name of the software. A single sentence will do, something like this one. “A power analysis done before data collection, for an independent t-test (d = 0.5, α = .05, power = .80), showed that 64 participants per group were needed.”
I’ve already collected the data. Should I report the power of my sample?
You can, but only when the effect size was fixed before you looked at your results, for example taken from an earlier paper. Power worked out from the effect you got in your own data adds hardly anything for the reader. Statisticians have written many papers against doing it, so better leave it out of the results chapter.
Why does my t-test answer differ from an online calculator?
Those quick calculators on the web mostly use the normal approximation. It gives a sample that is slightly smaller. Here we have used the exact method, and that is why the figures match with G*Power. Quote the exact figure in your thesis and mention G*Power or this method by name.
Is anything I enter saved?
No. Your numbers stay on your own device, the browser does all the working. The only thing our server comes to know is that the calculator got used one time.
Stuck on a chapter? Talk it through with us.
Call or WhatsApp, say where you are in your thesis, and we’ll tell you plainly what kind of help makes sense, if any.