Power Analysis & G*Power:
How to Choose Your Sample Size

Sooner or later, your committee or your IRB will ask how you arrived at your sample size. “Thirty per group seemed reasonable” isn’t an answer, and neither is a number borrowed from a published study whose design differs from yours. If you can’t show the reasoning, expect the question to come back at your proposal defense, and again at your final one.

In our 10 years of helping students with their statistics, we’ve found the power analysis is rarely the hard part. What’s hard is choosing and defending the inputs. In this post, I’ll give you ready-made sample sizes for the analyses dissertations use most, show you how to run one in G*Power, and give you a sample paragraph you can adapt for your methodology chapter, plus what to do if you can’t recruit enough people.

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What is a power analysis?

A power analysis is a calculation that tells you the sample size your study needs for a statistical test to have a good chance of detecting an effect of a given size, if that effect really exists. It rests on four linked numbers, and as the statistician Jacob Cohen put it in his short power primer, “each is a function of the other three.”

1. Effect size: how big a difference or relationship you expect, in standardized units.
2. Significance level (α): the risk you’ll accept of a false positive, almost always .05. It’s the threshold your p-value has to fall below for a result to count as significant.
3. Power (1 − β): the chance of detecting the effect if it’s real, usually .80.
4. Sample size (N): how many participants you need in your study.

So once you’ve decided on the first three, the power analysis calculates the fourth for you. That’s an a priori power analysis, and it’s the only kind that sets your sample size before you collect data.

Why .05 and .80? Both are conventions rather than laws. Cohen proposed 80% power as “arbitrary but reasonable” when a researcher has no other basis for choosing, in his book on statistical power analysis. In his power primer, he also pointed out that, alongside α = .05, it treats a false positive as about four times as serious as a missed effect, a “β:α ratio of 4:1.” Your field may expect something stricter, such as 90% power, so check your program’s guidance before you settle on one.

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Sample sizes for common analyses

The table below gives the total sample size for the analyses that come up most in dissertations, at Cohen’s conventional small, medium and large effects. Every figure assumes α = .05, power = .80 and, where it applies, a two-tailed test. Find your analysis, then look across to see how fast the number grows as the effect shrinks:

Analysis (effect size index)	Small	Medium	Large
Independent t-test (d = .2 / .5 / .8)	788	128	52
Paired t-test (dz = .2 / .5 / .8)	199	34	15
One-way ANOVA, 3 groups (f = .10 / .25 / .40)	969	159	66
Correlation (r = .1 / .3 / .5)	782	84	29
Multiple regression, 3 predictors (f² = .02 / .15 / .35)	550	77	36
Multiple regression, 5 predictors (f² = .02 / .15 / .35)	647	92	43
Chi-square, 2 × 2 table (w = .1 / .3 / .5)	785	88	32
Chi-square, 2 × 3 table (w = .1 / .3 / .5)	964	108	39

The two-group and three-group figures are totals, split equally across the groups (64 per group for a medium t-test; 53 per group for the ANOVA). The paired t-test counts pairs, so 34 means 34 people measured twice. We calculated every cell exactly, using the same methods G*Power uses, and checked each one with a second, independent statistics package.

If you compare these with the table in Cohen’s power primer, note that its t-test and ANOVA figures are per group, not totals. Even allowing for that, Cohen’s figures sit within three participants of the exact ones, some matching and others a little higher or lower (76 instead of 77 for the three-predictor regression, for example), except one: the large effect for a 2 × 2 chi-square reads 26 where the exact figure is 32. Report the figure your software gives you, not one from a printed table.

Here’s the t-test row drawn out at every step between small and large. Watch where the curve turns steep:

Two things in the table are worth a second look.

First, the small-effect column runs roughly six to nine times the medium one. For d, r, f and w, the sample you need grows with the inverse square of the effect, so halving the effect means about four times the participants. The regression rows behave differently, because f² is already a squared measure: halving f² roughly doubles the sample.

Second, the paired t-test’s effect size, dz, isn’t the same as the d used for two groups. It depends on how strongly the two measurements correlate, so don’t borrow a d from a two-group study and enter it as dz. Cohen defined the small, medium and large values for d, and the table applies the same numbers to dz for convenience, but a dz of .5 isn’t the same effect as a d of .5.

So the table gives you a starting point, but the real decision is which column you read from. Choose “medium” without a reason, and if the true effect is smaller, your study could be several times too small to detect it. That’s why the effect size needs its own justification, which is what the next section covers.

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How to choose your effect size

The effect size is the input that decides your sample size, and it’s the one your committee is most likely to question. Here’s the order to work through, strongest first:

1. The smallest effect that would matter. If a change smaller than a certain size would make no practical difference (to test scores, say, or to patient outcomes), power your study to detect that size. A widely cited guide to sample size justification calls this “the strongest possible sample size justification.”
2. Earlier studies of the same relationship. A meta-analysis is best; a few similar studies using the same measures come next. Many report an effect size you can enter directly, or a statistic you can convert.
3. Cohen’s conventions, as a last resort. Cohen himself, in his book on power analysis, recommended them only “when no better basis for estimating the ES index is available,” and that sample size guide goes further: they “should not be used in an a-priori power analysis.” If you use one anyway, say that’s what you did and why.

The conversion is usually simple. For a regression, a study reporting R² = .10 gives f² = R² / (1 − R²) = .111. That one step can change your sample considerably. With four predictors, a “medium” f² of .15 needs 85 participants, while the .111 from that earlier study needs 113.

That’s 28 more people, from one number in someone else’s results section.

Now, I understand the temptation to take the effect size from a small pilot study, but I’d advise against it. Effect sizes from small samples are too imprecise to plan around: a paper on the role of pilot studies in clinical research shows that a pilot finding d = .50 with 18 participants per group is consistent with a true effect anywhere from −0.17 to 1.17. Use a pilot to test your procedures and instruments instead.

Be wary of “medium” as a default, too. That guide to sample size justification notes that “medium” is what G*Power offers by default for an a priori analysis, and that in its author’s experience it’s the effect size researchers enter most often for an independent t-test.

In some fields, and for some kinds of effect, typical effects are much smaller. Cohen noted in his book that many effects in personality, social and clinical psychology “are likely to be small effects as here defined,” and a 30-year review of tests for categorical moderators in multiple regression found a median observed f² of just .002. So whichever size you choose, cite the evidence for it.

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How to run a power analysis in G*Power

G*Power is free software for Windows and Mac, distributed by Heinrich Heine University Düsseldorf. Here’s a complete run for a common dissertation design: a multiple regression with four predictors, using the f² of .111 from the example above. Each field is one you fill in, in the order G*Power shows them, with where its value comes from:

In G*Power’s menu, the type of power analysis reads in full as A priori: Compute required sample size – given α, power, and effect size. Once the fields are set, click Calculate, and G*Power reports a total sample size of 113.

Keep a screenshot of the window, or copy the protocol G*Power records beneath it. In our experience, some university programs require the screenshot in an appendix, alongside the justification in your methodology chapter, and either way it lets your committee check every input.

If your analysis isn’t a regression, the steps are the same and only the menu choices change. These are the selections for the analyses in the table above:

Analysis	Test family	Statistical test
Independent t-test	t tests	Means: Difference between two independent means (two groups)
Paired t-test	t tests	Means: Difference between two dependent means (matched pairs)
One-way ANOVA	F tests	ANOVA: Fixed effects, omnibus, one-way
Correlation	Exact	Correlation: Bivariate normal model
Multiple regression	F tests	Linear multiple regression: Fixed model, R² deviation from zero
Chi-square	χ² tests	Goodness-of-fit tests: Contingency tables

For a correlation between two continuous variables, use the Exact family’s bivariate normal model. The t tests family also lists a correlation option, the point biserial model, and its developers note it’s correct only when one of the two variables is binary.

Testing some predictors, not all

The regression option above tests all your predictors at once. Often, though, your hypothesis is about some of them: whether a new predictor adds anything once your control variables are in, say, or whether a moderator changes a relationship.

In situations like that, choose Linear multiple regression: Fixed model, R² increase instead. It asks for two numbers that confuse many students the first time:

• Number of tested predictors: the predictors your hypothesis is about, the ones whose added contribution you’re testing.
• Total number of predictors: every predictor in the final model, including the tested ones, your controls and any interaction terms.

A moderating variable is where this bites. Testing whether M moderates the effect of X means testing one interaction term (X × M) in a model that also holds X and M, so you’d enter 1 tested predictor out of 3 in total.

The sample you need then depends mainly on the interaction’s own effect size: the extra variance it explains, relative to what the full model leaves unexplained. At a medium f² of .15, it’s 55. At a small f² of .02, it’s 395. Observed interaction effects are often far smaller than “medium”, as that review found for categorical moderators. At its median f² of .002, the same design would need 3,927 participants. So base the interaction’s effect size on studies like yours, and cost the design before you commit to it.

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One-tailed or two-tailed?

For t-tests and correlations, G*Power asks (under Tail(s)) whether your test is one-tailed or two-tailed, and the choice changes the answer. A one-tailed test only looks for an effect in one direction, so it needs fewer participants: 102 instead of 128 for a medium independent t-test, or 27 instead of 34 for a medium paired t-test.

That’s exactly why you should be careful with it. I’d only use a one-tailed test if you committed to the direction in advance, and an effect in the other direction would mean the same to you as no effect at all. Most dissertation hypotheses don’t meet that bar, and Cohen’s own table is for two-tailed tests.

A widely shared G*Power walkthrough arrives at 27 for a paired t-test with a one-tailed setting, and its steps never mention tails (the setting shows only in its screenshot and its write-up template), so a student following them could easily report it as standard. Unless you have a specific reason, and can state it in your methodology chapter, use two tails.

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Allowing for dropout and non-response

Your power analysis gives you the number of usable cases you need at the end, not the number you should recruit. Some participants will drop out, and some survey responses will be incomplete or fail your attention checks. To allow for that, divide your required sample by the share you expect to keep:

The common mistake is to multiply instead: 113 × 1.2 = 135.6, or 136. Lose 20% of 136 and you’re left with about 109, short of the 113 you needed. A journal guide to tricky sample size calculations names this as “a common error in the dropout rate calculation.” If you’re recruiting through a survey, you can apply the same logic once more: if you need 142 completed surveys and expect one invitation in four to be answered, you’ll need to invite about 568 people.

Whatever allowance you choose, state it and give its basis (an earlier study’s attrition, your organization’s usual response rate). An unexplained buffer looks like padding, and a committee may ask you to justify the extra participants as well.

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How to justify your sample size

In your methodology chapter, your proposal and your IRB application, the justification needs to let a reader re-run your calculation. That means stating every input: the test, the software, the effect size and where it came from, α, power, tails where relevant, the resulting N, and your allowance for dropout. Here’s a paragraph you can adapt:

If you’re running several tests on the same data and correcting for that (with a Bonferroni correction, for instance), use the corrected α in your power analysis, not .05. The sample size guide quoted earlier gives the example: with four tests and a Bonferroni correction, the power analysis “should be based on a corrected alpha level of .0125.”

Real dissertations vary in how much they report. Here’s how a published psychology PhD sets out its power analysis in the participants section of its first experiment:

Notice what it gets right: the software and version, the effect it’s powered to detect, the power level, the resulting N and an allowance for exclusions. Later, in the limitations, the author is candid that no earlier study had examined this interaction, so “there was not a relevant effect size to base the reported power analyses on,” and that the analysis “was not adjusted for the multiple dependent variables being examined.” That honesty is worth copying.

What the paragraph doesn’t give are the other inputs G*Power asks for, such as the degrees of freedom for the interaction and the number of covariates, so a reader can’t re-run the calculation from it. Nor does it say how big the allowance was meant to be, or what it was based on (303 were recruited against the 244). In your own write-up, put every input, and the size and basis of your buffer, in the same paragraph, so nobody has to go looking.

What if you can’t recruit enough people?

Sometimes the power analysis comes back with a number you can’t reach: the population is small, access is limited, or your timeline won’t stretch.

That’s common, and it isn’t the end of your design. Resource limits are a legitimate part of a sample size justification. As that guide to sample size justification puts it, “sample sizes are always limited by the resources that are available.”

What you shouldn’t do is inflate the effect size or loosen α until the number fits. Your committee will see a medium effect chosen with no source, and you can expect to be asked why you chose it at your defense.

Instead, run a sensitivity analysis. Set the type of power analysis in G*Power to sensitivity, enter the sample you can realistically get, and it tells you the smallest effect your study can detect with 80% power. With four predictors and 80 participants, that’s f² ≈ .16. With 30 per group in a two-tailed t-test, it’s d ≈ .74, close to Cohen’s “large” of .8. You then report that figure honestly, and discuss in your limitations what a smaller true effect would mean for your results.

Don’t run a “post hoc” power analysis after collecting your data, using the effect you observed. It can’t tell you anything your p-value hasn’t already, because, as a paper in The American Statistician on the fallacy of post hoc power showed, “the observed power is a 1:1 function of the p value.” A non-significant result will look underpowered by that measure. If a reviewer asks for one, the sample size guide recommends offering a sensitivity analysis in its place.

If even the sensitivity analysis looks weak, talk to your chair early. You may be able to change the analysis, simplify the model (fewer predictors need fewer people) or widen your sampling frame, and each of those is easier before your proposal is approved than after.

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Power analysis vs survey calculators

Many students reach for an online survey calculator such as Raosoft’s instead of a power analysis. The two answer different questions. A survey calculator asks how many responses you need to estimate a percentage within a margin of error. Raosoft’s defaults (a 5% margin, 95% confidence, a population of 20,000 and a 50% response distribution) give 377 responses, enough to say, for example, that 50% of your population drink coffee in the morning, give or take 5%.

A power analysis asks how many you need to detect a difference or relationship with a statistical test. So if your research questions are about how many people do or believe something, the margin-of-error approach fits. If they’re about whether one variable predicts another, or whether groups differ, as they are in many quantitative dissertations, you need a power analysis.

Whichever approach fits your study, the number itself is the easy part. What your committee will test is the reasoning behind it. If you’d like a second pair of eyes on your power analysis before it goes into your proposal, our coaches help students with dissertation statistics, from choosing the effect size to writing the justification.

Still have questions?

What does 80% power mean?

It means that if the effect you’re looking for really exists at the size you assumed, your study has an 80% chance of producing a statistically significant result, and a 20% chance of missing it. Cohen proposed 80% as a convention because, alongside a 5% significance level, it treats a false positive as about four times as serious as a missed effect.

Is G*Power free?

Yes. G*Power is free for everyone, including commercial users, and is distributed by Heinrich Heine University Düsseldorf. The current Mac version was built for Intel processors, and the developers say they’re working on G*Power 4, a native Apple silicon version.

Can I do a power analysis after collecting data?

Not to justify your sample size. A “post hoc” power analysis that uses the effect you observed only restates your p-value, so it adds no information. If you need to show what your study could detect, run a sensitivity analysis instead: enter the sample you actually have, and G*Power reports the smallest effect it could detect with 80% power.

Why is 30 a good sample size?

It isn’t, for a hypothesis test. Thirty is a common rule of thumb, but there’s no power analysis behind it. With 30 participants per group, a two-tailed independent t-test has 80% power only for an effect of about d = .74 or larger, close to Cohen’s “large” of .8, so a smaller effect could easily be missed.

What effect size should I use with no prior studies?

Start with the smallest effect that would make a practical difference in your setting, and power your study to detect that. If you can’t define one, look for studies of closely related variables or measures. Cohen’s conventions (such as d = .5 for a medium effect) are the last resort, and if you use one, say so and explain why.

Does G*Power calculate sample size for SEM?

No. G*Power has no module for structural equation modeling, so SEM studies are often powered with methods built for it, such as an approach based on the RMSEA fit index or a Monte Carlo simulation. Ask your committee which approach your program expects.

How many responses do I need for a survey?

It depends on what you want to do with the answers. To estimate a percentage within a margin of error, a survey calculator applies: at a 5% margin, 95% confidence and the default 50% response distribution, a population of 20,000 needs 377 responses. To test whether variables are related or groups differ, you need a power analysis, which can give quite a different number.

Do qualitative studies need a power analysis?

No. Qualitative research doesn’t test hypotheses statistically, so power analysis doesn’t apply. Its sample size is justified by the depth the research questions need, by comparable studies and often by data saturation, the point at which new data stops producing new insights. Our guide to sampling methods covers how to choose who to include.

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Jansen, D. (2026). Power Analysis & G*Power: How to Choose Your Sample Size. Grad Coach. https://gradcoach.com/power-analysis/

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