Advanced GPower Techniques: Power Curves, Effect Sizes, and More

Common Mistakes to Avoid When Using GPowerPower analysis is a crucial step in designing experiments and studies. GPower is a widely used, free tool for conducting power analyses for a variety of statistical tests. While G*Power makes many calculations straightforward, users often make mistakes that can lead to underpowered studies, incorrect sample sizes, or misinterpretations of results. This article covers common pitfalls and provides practical guidance to avoid them.

1. Confusing effect size types and inputs

One of the most frequent issues is misunderstanding which effect size measure to use. G*Power accepts several standardized effect sizes (Cohen’s d, f, f2, r, φ, w), and selecting the wrong one or entering it incorrectly will produce misleading results.

Understand what each effect size represents:
- Cohen’s d for differences between two means.
- f for ANOVA (between-group effects).
- f2 for multiple regression.
- r (Pearson) for correlation tests.
- φ and w for chi-square tests (contingency tables).
Convert effect sizes appropriately when necessary. For instance, converting from Cohen’s d to r uses r = d / sqrt(d^2 + 4).
Use domain-specific benchmarks cautiously: Cohen’s conventions (small, medium, large) are general guidelines, not absolutes.

2. Using arbitrary or unjustified effect sizes

Choosing an effect size without justification is common and risky. Instead:

Base effect sizes on prior research (meta-analyses, previous studies) or pilot data.
If using conventions (e.g., Cohen’s rules), state this explicitly and consider sensitivity analyses to show how required sample size changes with different plausible effect sizes.
When only minimal prior information exists, present a range of calculations for small-to-large effect sizes.

3. Misinterpreting one-tailed vs two-tailed tests

G*Power lets you choose one-tailed or two-tailed tests. Mistakes here change required sample sizes and error rates.

Use two-tailed tests when effects could be in either direction or when direction is not strongly theoretically justified.
One-tailed tests reduce required sample size but must be justified a priori. Do not switch to one-tailed post hoc to obtain significance.
Ensure the directionality entered in G*Power matches your hypothesis and analysis plan.

4. Confusing alpha (Type I error) and beta (Type II error) settings

Users sometimes set inappropriate significance levels or misunderstand power conventions.

Common practice: α = 0.05 and power (1 − β) = 0.80 or 0.90, but justify deviations (e.g., α = 0.01 for multiple comparisons).
Remember that lowering α or increasing desired power increases required sample size.

5. Neglecting design specifics (paired vs independent, directional hypotheses, number of groups)

The exact statistical design matters for sample-size calculations.

Choose the correct test family and exact test in G*Power (e.g., means: difference between two independent groups vs paired samples).
For ANOVA, specify the number of groups and whether measures are repeated.
For regression, include the correct number of predictors and whether tests are for the overall model or a particular coefficient.

6. Overlooking assumptions: variance, sphericity, normality

G*Power requires effect sizes that implicitly assume certain data properties.

If variances differ across groups (heteroscedasticity), typical calculations may be biased.
For repeated measures and ANOVA, violations of sphericity affect required sample sizes; apply corrections or use alternative methods.
If data are non-normal, consider nonparametric alternatives and corresponding power approaches.

7. Forgetting to account for attrition and nonresponse

Calculated sample sizes are for analyzable cases; real-world data collection often yields fewer usable observations.

Inflate sample sizes to account for expected dropout, nonresponse, or unusable data (e.g., +10–30% depending on context).
For longitudinal studies, consider differential attrition and its effect on power.

8. Misusing post-hoc power analysis

Many users run post-hoc power analyses after obtaining non-significant results; this is often uninformative.

Post-hoc power calculated from observed effect sizes is directly determined by the p-value and offers little additional insight.
Instead of post-hoc power, report confidence intervals and consider sensitivity analyses showing detectable effect sizes given the sample.

9. Not conducting sensitivity analyses

Relying on a single calculation can obscure how robust conclusions are to assumptions.

Run sensitivity analyses varying effect sizes, α, and power to display a range of required sample sizes.
Report these ranges to inform readers and stakeholders about uncertainty.

10. Entering incorrect sample allocation or ratio parameters

For two-group comparisons, G*Power allows unequal group sizes via allocation ratios.

Make sure the allocation ratio matches your planned sampling scheme (e.g., 1:1, 2:1).
Incorrect ratios can substantially alter required per-group sample sizes.

11. Ignoring multiple testing and familywise error

When running multiple hypotheses, controlling for multiple comparisons changes α and therefore sample size.

Adjust α (e.g., Bonferroni, Holm, FDR) when appropriate and rerun power calculations.
For complex designs with many outcomes, consider multivariate approaches or plan for adjusted thresholds.

12. Overreliance on G*Power without methodological consultation

G*Power is a tool — not a substitute for statistical reasoning.

Consult a statistician for complex designs (multilevel models, cluster-randomized trials, mixture models).
For cluster-randomized or hierarchical data, G*Power’s simple tests may be inappropriate; use specialized tools or formulas that incorporate intraclass correlation (ICC).

13. Failing to document power-analysis decisions

Transparent reporting is crucial for reproducibility.

Report test family, exact test, effect size and its justification, α, desired power, allocation ratios, and any adjustments (attrition, multiple testing).
Include sensitivity analyses and software version (G*Power version number).

14. Using default settings blindly

G*Power’s defaults may not match your study needs.

Verify every parameter: tail direction, effect size input type, test family, and sample allocation.
Check that the computed output reflects your intended hypotheses.

15. Misinterpreting output (total vs per-group sample sizes, noncentrality parameters)

G*Power presents several outputs; users can misread these.

Confirm whether the reported sample size is total N or per-group N.
Understand noncentrality parameters and critical values only when necessary for deeper interpretation.

Practical checklist before finalizing sample size in G*Power

Define the exact statistical hypothesis and corresponding test in G*Power.
Choose and justify an effect size (use prior data or show a range).
Set α and desired power; justify choices.
Specify sample allocation and account for expected dropout.
Adjust for multiple comparisons if relevant.
Run sensitivity analyses across plausible parameter ranges.
Document all settings, assumptions, and software version.

Using G*Power effectively requires attention to detail and a clear match between your study design and the tool’s options. Avoid the common mistakes above by planning carefully, documenting decisions, and consulting a statistician for complex cases.