A power analysis is a calculation done before a study begins (a priori) to determine the sample size needed to detect an effect with a chosen level of statistical power. It bridges planning and statistics. Many journals, funders and ethics boards expect power analyses in the Methods section, though APA 7 does not mandate them. Reviewers often reject power analyses that lack critical details. This guide shows you the exact components, APA 7 sentence templates, and common mistakes to avoid.
What you need before you write a single word
- The test you plan to run (t-test, ANOVA, correlation, etc.).
- Effect size and its source: literature, pilot data, or smallest effect size of interest.
- Significance level (α), almost always .05, two-tailed (unless specified otherwise).
- Desired power, almost always .80 or .90 (power = 1 − β, where β is the Type II error rate).
- Software name and version (e.g. G*Power 3.1.9.7, R pwr package 1.3-0).
- Resulting sample size, rounded up (because you cannot recruit half a person).
- Attrition allowance, if applicable (add to final N before recruiting).
APA 7 format templates
A priori power analysis (planned, before the study)
A priori power analysis using [software, version] for a [test name] with effect size [d/f/r] = [X], α = [alpha], and power = 1 − β = [power], [tails], indicated a required sample size of N = [X]. Accounting for [X]% attrition, [Y] participants were recruited.
Simpler version:
Sample size was determined a priori using power analysis. [Test name] with d = [X] and power = .80 at α = .05 (two-tailed) required [N] participants per group.
Sensitivity analysis (when N is fixed)
When you cannot increase N to meet power .80, report what you can detect instead:
A sensitivity analysis indicated that with N = [X] at α = [alpha] and power = .80, the smallest detectable effect size was d = [X].
Worked examples from real power calculations
Example 1: Independent samples t-test
You plan to compare anxiety scores in a mindfulness intervention versus waitlist control. From prior literature, you expect a medium effect (d = 0.50). You want power = .80 at α = .05 (two-tailed).
Calculation: Using G*Power 3.1.9.7, Test family: t-tests, Statistical test: Means: Difference between two independent means (two groups), Type of power analysis: A priori.
- Effect size d: 0.50
- Error probability α: 0.05
- Power (1 − β): 0.80
- Allocation ratio N2/N1: 1 (equal groups)
- Tails: two
Result: n = 64 per group (total N = 128).
Write it:
A priori power analysis using G*Power 3.1.9.7 for an independent samples t-test, with a medium effect size (d = 0.50) based on prior literature, α = .05, and power = .80, indicated a required sample size of 64 participants per group (total N = 128).
For power .90 (stricter), the same analysis yields n = 86 per group (total N = 172).
Example 2: One-way ANOVA with three groups
You plan to compare symptom severity across three treatment conditions. You expect a medium effect (f = 0.25, equivalent to d = 0.50 in a two-group scenario by f = d / 2) and want power = .80.
Calculation: Using G*Power 3.1.9.7:
- Test family: F tests
- Statistical test: ANOVA: Fixed effects, omnibus, one-way
- Type of power analysis: A priori
- Effect size f: 0.25
- Error probability α: 0.05
- Power (1 − β): 0.80
- Number of groups: 3
Result: G*Power outputs total N = 159 (so 159 / 3 = 53 per group).
Write it:
Sample size was calculated using G*Power 3.1.9.7 for a one-way ANOVA with three groups, assuming a medium effect size (f = 0.25), α = .05, and power = .80. A total of 159 participants was required (53 per group).
Example 3: Pearson correlation
You plan to examine the correlation between sleep quality and academic performance. From a pilot study, you expect r = .30 (medium). You want power = .80.
Calculation: Two equivalent methods:
Fisher z formula:
- r = 0.30
- α = 0.05 (two-tailed)
- Power = 0.80
- N = 3 + [(z_α + z_β) / arctanh(r)]^2, where z_α = 1.96 and z_β = 0.84
- N = 3 + [(1.96 + 0.84) / 0.3095]^2 = 85
G*Power exact bivariate normal model: Exact > Correlation: Bivariate normal model gives N = 84. Both 84 and 85 are acceptable.
Write it:
Sample size was determined a priori for a Pearson correlation with r = .30, α = .05 (two-tailed), and power = .80, using the Fisher z approximation. This required N = 85 participants.
Example 4: Paired samples t-test
You plan to measure anxiety before and after a single-session intervention in the same individuals. From pilot data, you expect the mean difference (between pre and post) will be 0.60 SD of differences (d_z = 0.60). You want power = .85.
Calculation: Using G*Power 3.1.9.7:
- Test family: t tests
- Statistical test: Means: Difference between two dependent means (matched pairs)
- Type of power analysis: A priori
- Effect size d_z: 0.60 (mean difference / SD of differences; d_z is not on the same scale as the independent-groups Cohen's d, so its benchmarks do not transfer)
- α = 0.05 (two-tailed)
- Power (1 − β): 0.85
Result: n = 27 pairs.
Write it:
An a priori power analysis for a paired samples t-test with d_z = 0.60 (mean difference / SD of differences), α = .05 (two-tailed), and power = .85 indicated a required sample size of 27 participant pairs.
How effect size becomes your bottleneck: Justifying d, f, or r
The effect size is the hardest part of a power analysis, and reviewers scrutinize it closely. These are your options:
- Published literature. State the study or meta-analysis you used: "Based on prior work by Smith et al. (2024, d = 0.52) in comparable populations."
- Effect size conventions. Cohen's benchmarks (small/medium/large) are known but criticized as arbitrary. Use them only if you say so: "We used the conventional medium effect size (d = 0.50), acknowledging that this may differ in our population."
- Smallest effect size of interest (SESOI). Ask: what is the smallest effect that would still matter in practice or theory? Set it before looking at what your sample can detect. This is the strongest justification but requires thought from your field.
- Pilot data. If you ran a small pilot study or have preliminary data, use the observed effect size. Be cautious: pilot estimates overshoot due to selection and imprecision in small samples.
Sensitivity analysis: when power .80 is impossible
Sometimes budget, time, or ethics constrains your N. When you cannot recruit enough people for power .80, do a sensitivity analysis instead to show what you can detect:
Example: You have 50 participants per group but no more budget. You want to know what effect size you could detect at power .80.
Calculation: Using G*Power, set N = 50, α = .05, power = .80, and solve for effect size d.
Result: d = 0.57.
Write it:
Due to recruitment constraints, the final sample was N = 50 per group. A sensitivity analysis indicated that this sample size would be sufficient to detect a medium-to-large effect (d = 0.57) with power = .80 at α = .05 (two-tailed). Effects smaller than this would be underpowered.
This is honest and helps readers interpret null findings.
Why post hoc ("observed") power is not reported
Post hoc power is the power to detect the effect size you actually observed, calculated after the study ends. Do not report it. Here is why:
Post hoc power is just p rephrased. If you observe p = .05, post hoc power will always be around .50. If p = .01, post hoc power will be higher. They are deterministic functions of each other: you are not calculating something new, you are converting your p-value to a different scale.
Example: Suppose you ran a t-test (n = 60 per group), observed d = 0.58, and got p = .002. The post hoc power is .88. But this power depends entirely on the p-value and n, not on your original study plan. It provides no new information about your ability to detect effects.
| p-value | Implied d | Post hoc power |
|---|---|---|
| .050 | 0.36 | .50 |
| .010 | 0.48 | .74 |
| .002 | 0.58 | .88 |
| .001 | 0.62 | .92 |
The boundary truth: When p crosses .05, post hoc power crosses .50. This is mechanical and uninformative. Report your a priori power plan instead.
Mistakes reviewers catch
- No effect size source. Stating d = 0.50 with no justification raises the question: why that number? Always cite literature or a pilot, or name Cohen's convention explicitly.
- Mismatching effect size units. Using d for ANOVA instead of f, or vice versa. (Relationship: for two equal groups, f = d / 2; e.g. d = 0.50 gives f = 0.25.)
- Forgetting attrition. If you plan N = 64 per group and expect 20% dropout, recruit N_recruit = 64 / (1 - 0.20) = 80 per group.
- Post hoc power. If you see "post hoc power" or "observed power" in your draft, delete it. (The exception: sensitivity analysis, which is forward-looking and legitimate.)
- No software or version. GPower 3.1.9.7 and GPower 3.1.9.2 can differ slightly. Always name the version.
- Rounding down. If power analysis gives n = 63.77, round up to 64, not down to 63.
Software and where the numbers come from in G*Power
If you use G*Power 3.1.9.7, here is how to navigate it:
- Select a test family: t tests, F tests, χ² tests, z tests, or Exact.
- Select the statistical test.
- For independent t-test: t tests > Means: Difference between two independent means (two groups)
- For paired t-test: t tests > Means: Difference between two dependent means (matched pairs)
- For one-way ANOVA: F tests > ANOVA: Fixed effects, omnibus, one-way (outputs total N)
- For Pearson correlation: Exact > Correlation: Bivariate normal model
- Select "A priori" power analysis (or "Sensitivity" if you are working backwards from a fixed N).
- Fill in the input fields: effect size, α, desired power, and number of groups (for ANOVA).
- Click "Calculate." The output shows the required sample size.
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Frequently asked questions
Why power .80 and not .90? Power .80 is the conventional minimum (Type II error rate β = .20). Power .90 is stricter but requires larger N. Choose based on the consequences of a Type II error in your field: if missing the effect is costly, use .90.
What if I have unequal group sizes? G*Power and other software ask for a "group ratio" (e.g. N2/N1). If you plan 40 in one group and 60 in another, the ratio is 1.5. Unequal groups reduce power and increase required N overall, so plan equal groups if you can.
Do I report power analysis if I am using a pre-existing dataset? If the dataset was collected for another reason, you can do a sensitivity analysis instead: "With N = [X], we were powered to detect effect sizes of d ≥ [X] at power .80." You were not powered for an a priori goal, but you can still say what you could detect.
Can I use G*Power for mixed models or multilevel regression? G*Power does not handle these well. Use R packages like simr (simulation-based power) or consult a statistician.
What is the relationship between f (effect size for ANOVA) and d (effect size for t-tests)? For two equal groups compared in a t-test or ANOVA, f = d / 2. Example: d = 0.50 gives f = 0.25. For k > 2 groups, there is no simple conversion; use the ANOVA effect size f directly.
Related guides
- How to calculate sample size for a survey: proportions and margin of error, not power-based.
- How to report effect sizes in APA 7: Cohen's d, eta squared, and r with formatting rules.
- How to report an independent t-test in APA 7: the result that power analysis predicts.
- How to report a one-way ANOVA in APA 7: multi-group comparisons.
- How to check statistical test assumptions: power analysis assumes these are met.