"How many participants do I need?" is one of the first questions a committee or review board will ask about your quantitative study, and answering it with a guess or with a round number that feels right is one of the fastest ways to have a proposal sent back. The defensible answer comes from a power analysis: a calculation that tells you the minimum sample size needed to detect an effect of a given size, before you collect a single data point. The standard free tool for this is GPower, and knowing how to use it, and just as importantly, how to justify the numbers you put into it, is a skill every quantitative researcher needs at the proposal stage. This guide walks through what a power analysis is, how the pieces fit together, how to run one in GPower step by step, and how to report it so it survives review. When you want the analysis run and the justification written to committee standards, our dissertation data analysis service does exactly that.
Quick Answer:
A power analysis links four quantities: sample size, effect size, the significance level (alpha, usually .05), and statistical power (usually .80 or .90). Fix any three, and the fourth is determined. An a priori power analysis, the type your committee expects, fixes the effect size, alpha, and power, and determines the sample size you need before collecting data. In G*Power, you select the test family, choose the a priori analysis, enter your effect size, alpha, and power, and read off the required N. The hardest and most important input is the effect size, which should come from prior literature or the smallest effect size of interest rather than a default "medium" benchmark. Never use post hoc observed power to explain a non-significant result: it is circular and uninformative.
What a Power Analysis Actually Does
Statistical power is the probability that your study will detect an effect that is really there. Put the other way around, a study with low power has a high chance of missing a true effect, returning a non-significant result, not because there is nothing to find, but because the study was too small to find it. That is a false negative, or Type II error, and its probability is called beta. Power is one minus beta. A study powered at .80, the common convention, has an 80 percent chance of detecting the effect it is looking for, and therefore a 20 percent chance of missing it.
A power analysis is the calculation that connects power to the other features of your design, so you can plan a study large enough to give yourself a fair chance of detecting what you are looking for. It matters for two reasons. First, an underpowered study wastes resources and participants on a design that may not be able to answer its own question. Second, and less widely understood, low power does not just cause false negatives; it also undermines the significant results you do get. Button and colleagues showed this in their influential analysis of power in neuroscience. Low power reduces the likelihood that a statistically significant finding reflects a true effect, and it inflates the size of the effects that do reach significance, a phenomenon known as the winner's curse (Button et al., 2013). Adequate power is not bureaucratic box-ticking; it is what makes your findings trustworthy.
The Four Quantities, and How They Fit Together
The whole of power analysis rests on a single relationship among four quantities that are mathematically interlocked. Fix any three of them, and the fourth is determined.
The first is the sample size, N, the number of observations in your study. The second is the effect size, a standardized measure of how large the effect you are looking for is, such as Cohen's d for a difference between means or r for a correlation. The third is alpha, the significance level, the probability of a false positive or Type I error that you are willing to accept, conventionally set at .05. The fourth is power, one minus beta, conventionally set at .80 or, more stringently, .90.
The relationships among them are intuitive once you see them. As Cohen put it in his classic power primer, the required sample size increases as you demand more power, as the effect you are looking for gets smaller, and as you make alpha more stringent (Cohen, 1992). A small effect requires a large sample to be detected reliably; a large effect can be detected with fewer participants. Demanding 90 percent power rather than 80 percent requires more participants than a lower bar would. This is the engine of every power analysis: you specify three of the four quantities and solve for the one you care about.
Table 1: The Four Interlocking Quantities of a Power Analysis
Quantity | What It Is | Conventional Value |
|---|---|---|
Sample size (N) | The number of observations in the study | The quantity you usually solve for |
Effect size | How large the effect you are looking for is | From literature or a smallest effect of interest |
Alpha (significance level) | Accepted probability of a false positive (Type I error) | .05 (a convention) |
Power (1 − beta) | Probability of detecting a true effect | .80 or .90 (conventions) |
It is worth being clear that alpha of .05 and power of .80 are conventions, not natural laws. Cohen proposed .80 as a reasonable default, reflecting an implicit judgment that a false positive is roughly four times as serious as a false negative, giving the familiar pairing of .05 and .20. Many clinical trials use .90 power because missing a real treatment effect is costly. You can and sometimes should depart from the conventions, but you should do so deliberately and say why.
What G*Power Is and Where to Get It
GPower is a free power-analysis program developed at Heinrich Heine University Düsseldorf, and it is the tool most committees and reviewers recognize. It computes power analyses for a wide range of tests: t-tests, F-tests such as ANOVA, chi-square tests, z-tests, and a set of exact tests, along with correlation and regression analyses. Two primary papers are the ones you cite in your methods. The original GPower 3 paper covers the t, F, chi-square, and z families (Faul, Erdfelder, Lang, & Buchner, 2007), and the G*Power 3.1 paper added correlation and regression tests (Faul, Erdfelder, Buchner, & Lang, 2009).
One practical point that trips people up: the current version differs by platform. At the time of writing, the current release is version 3.1.9.7 for Windows and version 3.1.9.6 for Mac, with a native Apple Silicon version in development. State the exact version you used in your methods, since power results should be reproducible. Download G*Power only from the official university page, never from third-party download sites, which are not authoritative and can bundle unwanted software. The official page also hosts the manual and a mailing list for update notifications.
Running an A Priori Power Analysis, Step by Step
The type of analysis your committee expects is the a priori power analysis: you specify the effect size, alpha, and power, and G*Power returns the sample size you need before you collect data. Here is the sequence.
First, select the test family and the specific test. In G*Power, first choose the Test family (t tests, F tests, chi-square tests, and so on). Then choose the Statistical test that matches your planned analysis, for example, "Means: Difference between two independent means (two groups)" for an independent-samples t-test, or "Correlation: Bivariate normal model" for a Pearson correlation. This step is why you must know which statistical test you will run before you can power it; the power analysis is specific to the test.
Second, set the Type of power analysis to "A priori: Compute required sample size, given alpha, power, and effect size." This is the key dropdown, and choosing the wrong analysis type here is a common error.
Third, enter the input parameters. Set the tails (one or two, almost always two unless you have a directional hypothesis with strong justification). Enter the effect size, the input that deserves the most thought and is covered in the next section. Set alpha, conventionally .05. Set power, conventionally .80 or .90. For tests involving groups, set the allocation ratio if your groups are unequal.
Fourth, click Calculate. G*Power returns the total sample size required, along with the actual power achieved at that N and the critical value of the test statistic. Read off the total sample size, and remember that for a two-group design, this is the total across both groups, which you then divide according to your allocation.
The whole process takes a minute once you have your effect size, which is exactly why the effect size, not the software, is the hard part.
The Effect Size: The Input That Decides Everything
The effect size is the single most consequential number in a power analysis, because it drives the required sample size more than any other input, and it is also the hardest to pin down. Where you get it from matters enormously, and there is a clear hierarchy of good practice.
The best source is prior evidence: a meta-analysis or well-conducted prior studies using the same design and measures, from which you can take a realistic estimate of the effect you expect. The next best is the smallest effect size of interest, the smallest effect that would be practically or theoretically meaningful in your context; powering to detect that effect ensures your study can find anything worth finding. Pilot data can be used but should be treated with caution, because effect-size estimates from small pilots are imprecise and often biased, and powering a main study on a noisy pilot estimate often results in an underpowered study even when everything else is done correctly.
What you should avoid is the most common shortcut: defaulting to Cohen's "medium" benchmark because you do not have a better number. Cohen offered rough benchmarks, around 0.2, 0.5, and 0.8 for small, medium, and large values of d, but he described them as last-resort conventions to be used only when no better basis is available, and warned that they are relative to the specific field and method. Methodologists have since argued pointedly against using them as power-analysis defaults. As Correll and colleagues put it, these labels are arbitrary and inconsistent, and relying on them can lead researchers to collect samples twice as large as necessary, or only half as large as necessary, without realizing it (Correll et al., 2020). Use a literature-based estimate or the smallest effect size of interest, and reserve the benchmarks for a truly justified last resort. Lakens's comprehensive treatment of sample-size justification is the definitive modern guide to doing it well (Lakens, 2022). This is precisely the judgment that turns a power analysis from a number into a defensible argument, and it is where a well-built research proposal earns its credibility.
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The Five Types of Power Analysis, and When to Use Each
A priori is the type you will use most, but G*Power offers several options, and understanding the differences is part of understanding the tool. There are five, and four matter in practice.
An a priori analysis computes the required sample size from a fixed effect size, alpha, and power. This is the standard planning analysis and the one your committee expects. A sensitivity analysis computes the minimum detectable effect size given a fixed sample size, alpha, and power. It is invaluable when your sample size is constrained, for example, by a fixed clinical population, because it lets you state plainly what effect your study can and cannot detect. A compromise analysis fixes the ratio of beta to alpha and lets you balance the two error rates when neither the conventional alpha nor the conventional power is feasible. A criterion analysis solves for alpha, which is rarely used.
The fifth type, post hoc power, deserves a warning rather than a recommendation. A post hoc analysis computes the achieved power using the effect size observed in your completed study. It is frequently requested by reviewers and frequently misused, and you should understand why it is criticized. Because observed power is a direct mathematical function of the p-value, it carries no information beyond the p-value itself, and a non-significant result will always yield low observed power by definition. Using it to argue that a non-significant finding was "just underpowered" is therefore circular. As Hoenig and Heisey established in their well-known critique, computing power after the fact to interpret a result is fundamentally flawed logic (Hoenig & Heisey, 2001). If your completed study turns out to be underpowered, the correct response is to report your effect size with its confidence interval and discuss the limitation, not to compute observed power.
Table 2: The Types of Power Analysis in G*Power, and When to Use Each
Type | What It Solves For | When to Use It |
|---|---|---|
A priori | Required sample size | Planning your study (the standard, expected type) |
Sensitivity | Minimum detectable effect size | When N is fixed by a constrained population |
Compromise | A balance of alpha and beta | When neither conventional alpha nor power is feasible |
Criterion | The alpha level | Rarely used |
Post hoc | Achieved power from observed effect | Avoid; circular and uninformative for interpreting results |
Planning for Attrition and Secondary Analyses
Two practical adjustments separate a power analysis that works on paper from one that works in the real study. The first is attrition. The sample size G*Power gives you is the number you need to analyze, not the number you need to recruit, and participants drop out. You inflate the required analyzable N to an enrollment target by dividing it by 1 minus your expected dropout rate. If you need 100 completers and expect 20 percent attrition, you enroll 100 divided by 0.80, which is 125. Simply adding 20 percent is a common miscalculation that leaves studies short. Base your dropout estimate on similar studies in your area.
The second is that a power analysis is used to power one specific test. If your study has a primary analysis and several secondary or interaction analyses, powering only the primary one can leave the others underpowered, and interaction effects in particular usually require substantially larger samples than main effects. Decide which analyses your conclusions depend on and make sure your sample size supports them, not just the headline test.
What Your Committee, Review Board, and Journal Expect
An a priori power analysis is not optional at the proposal stage; it is a routine expectation of dissertation committees, institutional review boards, and journals, and knowing what each wants helps you report it correctly. Under the APA Journal Article Reporting Standards for quantitative research, JARS-Quant, you are expected to describe how you determined your sample size, including the power analysis or other method used, along with your intended and achieved sample sizes (American Psychological Association, JARS-Quant). In clinical trials, the CONSORT guideline explicitly requires reporting the method used to determine the sample size. Review boards want to see that you are not enrolling more participants than necessary, which is an ethical as well as a statistical concern, or so few that the study cannot answer its question.
A complete report states the test you powered for, the effect size and its source, the alpha and power you set, the resulting sample size, and your enrollment target after accounting for attrition. Framing this as a reasoned justification, in the language Lakens sets out, rather than a bare number, is what satisfies a careful reviewer. This belongs in your methodology chapter and flows directly into your analysis plan, which is one of the things our dissertation chapter support is built to make coherent. A missing or weak power analysis is also a recurring theme in our overview of the ten common dissertation mistakes.
A Note for Nursing and DNP Candidates
The picture differs for DNP scholarly projects, and getting the distinction right saves a lot of confusion. A DNP quality improvement project that tracks a measure over time with run charts or statistical process control charts does not rest on a traditional power analysis at all. Its analytical logic is about detecting signals of change over time rather than testing a hypothesis in a fixed sample. For that kind of project, you justify the number of data points and the measurement period rather than computing a power-based N. If, however, your project includes a comparative research component, such as a two-group outcome comparison, that component does require an a priori power analysis in the ordinary way. Decide early which kind of project you have, because it determines whether a power analysis is the right tool or the wrong one, a distinction our dissertation support helps candidates settle at the design stage.
Frequently Asked Questions
What is a power analysis, and why do I need one?
A power analysis is a calculation that links four quantities: sample size, effect size, alpha, and statistical power, so you can determine the sample size needed to detect an effect before you collect data. You need one because an underpowered study is likely to miss a real effect, wasting resources and participants, and because low power also makes the significant results you do get less reliable and inflates their apparent size. Committees and review boards expect an a priori power analysis at the proposal stage.
How do I calculate sample size in G*Power?
Select the test family and specific test that match your planned analysis, set the type of analysis to "A priori: Compute required sample size," and enter your effect size, alpha (usually .05), power (usually .80 or .90), and tails. Click Calculate, and G*Power returns the total sample size required. The process is quick once you have an effect size, which is the input that most determines the result and requires the most justification.
What effect size should I use for a power analysis?
Use an effect size from prior evidence wherever possible: a meta-analysis or well-conducted prior studies with the same design. Alternatively, use the smallest effect size of interest, the smallest effect that would be meaningful in your context. Pilot data should be used cautiously, as small pilots can yield imprecise estimates. Avoid defaulting to Cohen's "medium" benchmark; methodologists warn that his small, medium, and large labels are arbitrary for this purpose and can badly mis-size your study.
What is the difference between a priori and post hoc power analysis?
An a priori power analysis is conducted before data collection and computes the sample size needed, given a target effect size, alpha, and power. A post hoc power analysis is done after data collection and computes the achieved power using the observed effect size. A priori is the standard planning analysis your committee expects. Post hoc observed power is criticized as circular and uninformative, because it is a direct function of the p-value and cannot explain a non-significant result.
Can I use post hoc power to explain a non-significant result?
No. This is a well-documented statistical fallacy. Because observed power is mathematically a function of the p-value, a non-significant result will always yield low observed power. Reporting it adds nothing and cannot show that your study was "just underpowered." Hoenig and Heisey established that using power calculations this way is fundamentally flawed logic. If your study is underpowered, report your effect size with its confidence interval and discuss the limitations instead.
What alpha and power values should I use?
The conventional defaults are alpha of .05 and power of .80, but these are conventions, not rules. An alpha of .05 sets a 5 percent chance of a false positive; a power of .80 sets an 80 percent chance of detecting a true effect. Many clinical trials use .90 power because missing a real effect is costly. You can depart from the conventions when your context justifies it, for example, using more stringent power for a high-stakes outcome, but state your choice and your reason.
How do I account for dropout in my sample size?
The sample size from G*Power is the number you need to analyze, not the number to recruit. Inflate it to an enrollment target by dividing by one minus your expected dropout proportion. For 100 completers with 20 percent expected attrition, enroll 100/0.80 = 125. Do not simply add the dropout percentage, which under-recruits. Base your attrition estimate on comparable studies, and remember to power any secondary analyses that underlie your conclusions, not just the primary test.
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Getting the Number Right Before You Collect
A power analysis determines whether a quantitative study is adequately powered or underpowered, and it occurs before you collect a single data point. Decide which test you will run, source a defensible effect size from the literature or a smallest effect of interest, set your alpha and power deliberately, run the a priori analysis in G*Power, and inflate the result for attrition. Report the whole chain as a justification, not a bare number, and never fall back on post hoc power to rescue a null. Do that, and the first hard question about your study, how many participants you need, becomes one you have already answered convincingly.
If you would rather a PhD statistician source the effect size, run the analysis in G*Power, and write the justification your proposal and review board require, send us your design and research questions. You will have an itemized quote within 2 to 4 business hours, with no obligation.
