The best sample size tool for most dissertations is G*Power, which is free, covers the great majority of standard designs, and produces output examiners recognise. R’s pwr and simr packages handle designs G*Power cannot, and commercial tools such as PASS and nQuery are worth their cost only for clinical trials and complex multilevel models.

Which tool should you use?

Match the tool to the design rather than to your budget. Most dissertations use a t-test, ANOVA, correlation, chi-square or multiple regression — all of which G*Power handles natively.

Why is G*Power still the default recommendation?

Three reasons, and only one of them is that it costs nothing. G*Power covers the standard inferential tests used in the overwhelming majority of social science, education, health and business dissertations. It reports the exact parameters an examiner wants to see — effect size, alpha, power and the resulting N. And it produces a protocol you can copy directly into an appendix, which makes the analysis auditable.

Its limits are real but predictable. It does not handle multilevel or mixed-effects models, structural equation models, or any design requiring simulation. If your data are nested — students within schools, patients within clinics — G*Power will give you a number, but that number will be wrong, because it ignores the clustering. Our step-by-step guide to power analysis with G*Power covers the standard workflow in detail.

When do you actually need R instead?

Move to R when your design breaks G*Power’s assumptions. Three situations account for most cases.

Nested or repeated-measures data with random effects require simulation-based power, for which the simr package is the standard tool: you specify a model, set an effect size, and simulate repeatedly to estimate power. Structural equation models need either Monte Carlo simulation through lavaan or a specialist package. And any non-standard estimator — zero-inflated counts, mixture models, unusual survival specifications — will have no closed-form solution at all.

The trade-off is transparency for effort. R gives you exactly the design you specified; it also gives you no guardrails if you specify it wrongly. If you are choosing an analysis environment more broadly, our comparison of JASP, jamovi, SPSS and R for thesis statistics covers the wider decision.

Are online sample size calculators good enough?

For a quick sanity check, yes. For your methodology chapter, usually not.

The problem is not accuracy — the arithmetic in most reputable online calculators is fine. The problem is citability and transparency. Many calculators do not state which test they assume, whether the alternative is one- or two-tailed, or how they handle unequal group sizes. An examiner reading “sample size was calculated using an online calculator” has no way to verify anything, and that is a straightforward invitation to a correction.

If you do use one, reproduce the calculation in G*Power or R before writing it up, and report the software, version, and every input parameter.

What does a reportable power analysis contain?

Whichever tool you use, the write-up needs the same six elements. Missing any one of them makes the calculation unverifiable.

1. The statistical test the analysis assumes, matching the test you will actually run.
2. The effect size and — critically — its justification, whether from a meta-analysis, a comparable prior study, a pilot, or a smallest effect size of interest.
3. Alpha, conventionally .05, and whether the test is one- or two-tailed.
4. Target power, conventionally .80, with .90 increasingly expected in health research.
5. The resulting sample size, and for group designs the allocation ratio.
6. Software and version, e.g. “G*Power 3.1.9.7”.

The effect size justification is where most dissertations lose marks. Writing “a medium effect size was assumed” without saying why is the single most common weakness examiners flag in this section. Our guide to effect sizes and confidence intervals covers how to source and defend that number.

What about post hoc power?

Avoid it. Calculating “observed power” after a non-significant result is circular — it is a deterministic function of the p value and adds no information. Journals and examiners increasingly flag it as a methodological error.

If your study came in underpowered, the honest response is to report the confidence intervals around your estimates and discuss precision in your limitations section. Our guidance on writing the limitations section covers how to frame this without undermining the whole thesis.

Which tool for which dissertation design?

That last row matters. Power analysis is a frequentist concept that does not transfer to qualitative designs, where sample size is justified by information power and saturation rather than by a calculation. Our guide to data saturation and knowing when to stop covers the equivalent reasoning for qualitative work.

Frequently asked questions

Is G*Power still maintained?

G*Power is stable rather than actively developed, with version 3.1.9.x remaining the standard reference across the social sciences. Its stability is an advantage for reproducibility: a calculation run today matches one run a decade ago.

What sample size do I need for my dissertation?

There is no universal number. It depends on your test, your expected effect size, your alpha and your target power. A two-group t-test detecting a medium effect (d = 0.5) at 80% power and α = .05 needs roughly 64 participants per group; halve the effect size and the requirement roughly quadruples.

Can I justify my sample size without a power analysis?

Sometimes. Census designs, secondary datasets of fixed size, and qualitative studies all use different justifications. What examiners object to is an unjustified sample size, not the absence of a power calculation specifically.

Do I need a power analysis for secondary data analysis?

You cannot change the sample size, so a prospective calculation is meaningless. Report a sensitivity analysis instead: given the N you have, what is the smallest effect you could detect at 80% power? G*Power computes this directly.

Is a free tool acceptable in a doctoral thesis?

Entirely. G*Power and R are the tools most frequently cited in published methodology sections. Cost is not a proxy for rigour, and no examiner will criticise a correct calculation for having been performed in free software.

How do I report the software version?

Name the software, the version number, and cite it formally in your reference list. G*Power and R packages all have canonical citations; our guide to citing datasets, software and code covers the formats.

From calculation to chapter

A power analysis takes ten minutes; writing a methodology chapter that defends every choice around it takes considerably longer. Tesify helps you draft and refine methodology sections in consistent academic prose, with citations formatted correctly as you write.