“How many participants do I need?” is the question every thesis supervisor, ethics committee, and journal reviewer asks — and most students answer it with a shrug and a round number like 100. There is a better way. G*Power is a free program that tells you exactly how many participants your study needs before you collect a single response, and this guide walks you through it click by click.
What G*Power Actually Does (in 60 Seconds)
G*Power is a free power-analysis program developed by researchers at Heinrich Heine University in Düsseldorf. It answers four related questions, but the one you need most is the a priori question:
Given the effect I’m looking for, how many participants must I recruit to have a good chance of finding it?
To answer that, you give G*Power three ingredients, and it computes the fourth:
- Effect size — how big a difference or relationship you expect (small, medium, or large, following Cohen’s well-known conventions).
- Alpha (α) — your significance level, almost always .05.
- Power (1 − β) — your chance of detecting the effect if it’s really there. The convention is .80, meaning an 80% chance.
- Sample size (N) — the number G*Power hands back to you.
The logic is simple and worth internalizing: bigger expected effect = fewer participants needed; smaller effect = more participants needed. A huge, obvious difference can be spotted with 30 people; a subtle one might need 300.
A quick effect-size cheat sheet
Cohen (1988) gave us conventional benchmarks that the whole field still uses. You don’t need a pilot study to pick one — you can plan for a medium effect when you have no better information, which is honest and defensible:
- Correlation (r): .10 = small, .30 = medium, .50 = large
- t-test (Cohen’s d): .20 = small, .50 = medium, .80 = large
- ANOVA (f): .10 = small, .25 = medium, .40 = large
- Chi-square (w): .10 = small, .30 = medium, .50 = large
These are conventions, not laws. If earlier research in your area reports an effect size, use that instead — it’s always better than a convention.
Step 1: Download and Open G*Power
G*Power is free for Mac and Windows. Search for “G*Power Heinrich Heine University” and download it from the university’s official page. Installation takes about a minute.
When you open it, the main window looks a little old-fashioned — that’s fine, it works beautifully. At the top you’ll see five dropdowns: Test family, Statistical test, Type of power analysis, input fields, and output fields.
Step 2: Choose Your Test Family and Statistical Test
Click the Test family dropdown. You’ll see options like t tests, F tests, χ² tests, z tests, and Exact. This is where many beginners go wrong — you must match the test to the analysis you plan to run. Planning an independent-samples t-test? Choose t tests.
With the family selected, click Statistical test and pick the specific test. For our walkthrough we’ll use “Means: Difference between two independent means (two groups)” — the classic independent-samples t-test.
Step 3: Select “A Priori” Power Analysis
In the Type of power analysis dropdown, choose “A priori: Compute required sample size – given α, power, and effect size.”
G*Power offers other options — post hoc (computing power from your observed effect) and sensitivity (finding the smallest effect you could detect). For planning your study, a priori is the one reviewers want to see. (More on why post-hoc power is a bad idea in the mistakes section below.)
Step 4: Enter Your Inputs
Now fill in the three ingredients. Let’s use an illustrative example: imagine you’re comparing stress scores between an intervention group and a control group — a two-group design with an independent-samples t-test.
Enter these values:
- Tail(s): Two (we’re looking for a difference in either direction)
- Effect size d: 0.5 (a medium effect, per Cohen’s conventions)
- α err prob: 0.05
- Power (1−β err prob): 0.80
- Allocation ratio N2/N1: 1 (equal group sizes)
Not sure about one-tailed vs two-tailed? Stay with two-tailed unless you have a strong, pre-registered reason to look in only one direction — reviewers overwhelmingly expect two-tailed tests.
Step 5: Calculate and Read the Output
Click Calculate. G*Power fills in the output panel. For our example, it tells you:
Total sample size: 128 — that’s 64 participants per group.
That means: with 64 people in each group, you have an 80% chance of detecting a medium-sized difference (d = 0.5) at α = .05. If you recruit fewer, your study is underpowered; if you recruit far more, you may be wasting resources (and your participants’ time).
Click the Protocol of power analyses tab or the little “X-Y plot” button to see a power curve — the graph shows how power climbs as sample size grows. It’s a great visual for your thesis appendix.
One Worked Example, Start to Finish
Let’s do a second, different design so you see how the inputs change. Imagine a study testing whether gender is associated with choosing a STEM major — a chi-square test of independence with 1 degree of freedom (a 2×2 table).
- Test family: χ² tests
- Statistical test: “Goodness-of-fit tests: Contingency tables”
- Type of power analysis: A priori
- Inputs: Effect size w = 0.3 (medium), α err prob = 0.05, Power = 0.80, Df = 1
- Calculate → Total sample size: 88
So you’d need 88 participants for an 80% chance of detecting a medium association. Notice how a different test and effect-size metric give a different answer — this is exactly why guessing round numbers is risky.
Pro tip: Before you recruit anyone, add a 10–20% buffer for dropouts and incomplete responses. If G*Power says 128, plan to recruit about 145–150. Ethics committees love seeing this buffer — it shows you’ve thought about real-world data collection.
6 Common Mistakes to Avoid
- Computing “observed” (post-hoc) power after the fact. Feeding your study’s actual effect size back into G*Power after collecting data tells you nothing new — it’s mathematically redundant with your p-value. Reviewers know this. Always do power analysis before data collection.
- Choosing your effect size to get a convenient sample size. Picking a large effect size just because it returns N = 40 is wishful thinking, not science. Use prior research, pilot data, or an honest medium-effect convention — and say which one you used.
- Forgetting to match the test family. Running an ANOVA but powering for a t-test (or vice versa) gives you the wrong number. Your power analysis must mirror the exact analysis you plan.
- Ignoring multiple comparisons. If you’re testing five hypotheses, your effective alpha per test shrinks. Either adjust your power analysis or acknowledge the issue in your methods section.
- Using one-tailed tests to shrink the sample. Yes, a one-tailed test needs fewer participants — but only use it if your hypothesis is genuinely directional and pre-registered. Switching to one-tailed after peeking at the data is a classic questionable practice.
- Treating the G*Power number as a ceiling, not a floor. The calculated N is the minimum for your target power. Recruiting a bit above it (plus your dropout buffer) is good practice; recruiting far below it means you’ve designed an underpowered study.
How to Report It in APA Style
One sentence in your Method section is enough. Here’s a template — fill in your own numbers:
“An a priori power analysis conducted using G*Power (Faul et al., 2007) indicated that a total sample of 128 participants (64 per group) was required to detect a medium effect (d = 0.50) with α = .05 and power = .80 for a two-tailed independent-samples t-test.”
Reference entry (APA 7th):
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(2), 175–191.
FAQs
Is G*Power really free?
Yes — completely free for Windows and Mac, developed and maintained at Heinrich Heine University Düsseldorf. It’s been cited in hundreds of thousands of papers, so reviewers accept it without question.
What if I genuinely have no idea what effect size to expect?
Use the medium-effect convention for your planned test (d = 0.50, f = 0.25, r = .30, w = .30) and state that openly: “In the absence of prior effect-size estimates, a medium effect was assumed following Cohen’s (1988) conventions.” Honesty about uncertainty is a strength, not a weakness.
My analysis isn’t in G*Power’s list. What now?
G*Power covers the most common tests. For complex designs (multilevel models, SEM), the convention is to power the closest simpler analysis and note the limitation, or use simulation-based power analysis in R. For a student thesis, the simpler-tests coverage is almost always enough.
One-tailed or two-tailed?
Two-tailed, unless your hypothesis is strictly directional and you decided that before collecting data. When in doubt, two-tailed — it’s the default reviewers expect.
Does a bigger sample always mean a better study?
Not exactly. Power rises steeply at first and then flattens — beyond a point, each extra participant buys you very little. That’s the beauty of a priori analysis: it finds the sweet spot instead of letting you guess.
The Bottom Line
Sample size is not a number you pick — it’s a number you justify. Five minutes in G*Power turns “I recruited 100 participants” into “an a priori power analysis indicated 128 participants were required to detect a medium effect with 80% power” — and that single sentence can be the difference between a methods section that sails through review and one that comes back with questions. Download it, run your numbers before you collect data, and add the dropout buffer. Your future self (and your supervisor) will thank you.