Sample Size and Power Analysis for Your Dissertation: A Complete G*Power Guide (2026)

One of the most common — and most costly — errors in dissertation research is choosing a sample size without any statistical justification. Whether you are conducting a survey, an experiment, or a comparative study, your examiners will ask: “How did you determine your sample size?” If your answer is “it seemed reasonable” or “it was what I could get,” you are likely to lose marks. Power analysis is the statistically defensible method for determining the minimum sample size needed to detect a real effect in your data — and this guide will show you exactly how to do it using the free G*Power software.

A power analysis for a dissertation is not as complex as it sounds. Once you understand four key inputs — effect size, significance level (alpha), statistical power (1-β), and your chosen test — you can produce an examiner-ready sample size justification in under 30 minutes. This guide covers the theory, the step-by-step process in G*Power, worked examples for common dissertation tests, and how to write up your sample size rationale in your methodology chapter.

What Is Power Analysis and Why Does It Matter?

Statistical power is the probability that your study will detect an effect when one genuinely exists. It is the complement of a Type II error (β): the mistake of concluding there is no effect when there actually is one. Power = 1 − β. A study with 80% power has a 20% chance of missing a real effect — this is the conventional minimum accepted in most academic disciplines.

Power analysis matters because it directly affects the validity of your conclusions. An underpowered study — one with too few participants — will frequently fail to detect real effects, leading to false negative results. An overpowered study — one with an unnecessarily large sample — wastes resources and may detect trivially small effects that are not practically meaningful. Getting your sample size right is a methodological necessity, not a statistical technicality.

There are two types of power analysis:

• A priori power analysis: Conducted before data collection to determine the required sample size. This is what your ethics committee and examiners expect to see in your methodology chapter.
• Post hoc power analysis: Conducted after data collection to determine the power your study achieved with the actual sample obtained. This is useful for reporting in studies where access to participants was limited, but it does not replace a priori analysis.

The Four Key Parameters of Power Analysis

Every power analysis involves four interrelated parameters. Setting any three determines the fourth. For dissertation planning, you typically set three and solve for N (required sample size).

The relationship between these parameters is intuitive: larger effect sizes require fewer participants; stricter alpha levels (e.g., 0.01) and higher power thresholds (e.g., 0.90) require larger samples. If you cannot recruit your required N, you must either accept lower power (and report this as a limitation), use a within-subjects design, or adjust your research question to target a larger effect.

How to Determine Effect Size for Your Study

Effect size is the most important — and most frequently misunderstood — input in a power analysis. It describes how large you expect the effect in your study to be. You have three main options for estimating it:

Option 1: Use Prior Literature

Search for published studies that address the same or a similar research question. Extract the reported effect sizes (Cohen’s d, Pearson’s r, η², Cramér’s V, etc.) and use these as your estimate. Meta-analyses are ideal because they aggregate effect sizes across multiple studies, giving you a more reliable estimate. This is the gold-standard approach and the one most examiners expect.

Option 2: Use Cohen’s Conventional Benchmarks

Jacob Cohen (1988) proposed benchmark effect size values for common statistical tests. These are widely used when prior literature is unavailable or inconsistent:

Be cautious about always defaulting to a “medium” effect size — this is a common shortcut that reviewers recognise. If you choose Cohen’s benchmarks, your methodology chapter should explain why the literature does not provide a more precise estimate.

Option 3: Pilot Study Data

If no relevant prior literature exists, a small pilot study (15–30 participants) can provide a preliminary effect size estimate. See the pilot study section below for guidance on design and analysis.

G*Power Step-by-Step: Installing and Using the Software

G*Power is a free, widely cited statistical power analysis program available for Windows and macOS. It was developed at Heinrich Heine University Düsseldorf and is accepted by virtually all academic institutions. A 2021 paper in Medicine documented over 100,000 citations, confirming it as the standard tool for dissertation power analysis.

Step 1: Download and Install G*Power

Download G*Power 3.1 from the official Heinrich Heine University website. It is free and requires no licence or registration. Installation is straightforward on both Windows and macOS.

Step 2: Select Your Statistical Test

In the G*Power interface:

1. Click the Test family dropdown (e.g., t tests, F tests, χ² tests)
2. Select the Statistical test type (e.g., “Means: Difference between two independent means (two groups)” for an independent samples t-test)
3. Set the Type of power analysis to “A priori: Compute required sample size”

Step 3: Enter Your Parameters

Enter the following values in the input panel:

• Effect size (d): Your estimated effect size (e.g., 0.5 for medium)
• α err prob: Your significance level (typically 0.05)
• Power (1-β err prob): Your desired power (typically 0.80)
• Allocation ratio N2/N1: For equal groups, set to 1
• Tails: Two-tailed for most research hypotheses

Step 4: Click Calculate

G*Power will output the required total sample size and the sample size per group. It also generates a power curve showing how power changes as sample size increases — a useful figure to include in your methodology chapter or appendix.

Worked Examples for Common Dissertation Tests

Example 1: Independent Samples t-Test

Scenario: You are comparing mean anxiety scores between students who use AI writing tools and those who do not. Prior literature suggests a medium effect size (d = 0.50).

• Test: t-tests → Means: two independent groups
• Effect size d = 0.50
• α = 0.05, Power = 0.80, two-tailed
• Result: N = 102 (51 per group)

Add 10–15% to account for dropout/incomplete responses: recruit 57–59 per group.

Example 2: One-Way ANOVA

Scenario: You are comparing academic performance across three revision method groups. You expect a medium effect (Cohen’s f = 0.25).

• Test: F tests → ANOVA: Fixed effects, omnibus, one-way
• Effect size f = 0.25, α = 0.05, Power = 0.80
• Number of groups = 3
• Result: N = 159 (53 per group)

Example 3: Pearson Correlation

Scenario: You are examining the correlation between hours of thesis writing per week and perceived self-efficacy. Expected medium correlation (r = 0.30).

• Test: t tests → Correlation: Point biserial model
• Correlation ρ = 0.30, α = 0.05, Power = 0.80, two-tailed
• Result: N = 84

Example 4: Multiple Regression

Scenario: You are predicting thesis completion likelihood from 5 predictor variables. You expect a medium effect (f² = 0.15).

• Test: F tests → Linear multiple regression: Fixed model, R² deviation from zero
• Effect size f² = 0.15, α = 0.05, Power = 0.80
• Number of predictors = 5
• Result: N = 92

Quick Reference: Required N by Test and Effect Size

All calculations assume α = 0.05, power = 0.80, two-tailed tests. Values are from G*Power 3.1.

Sample Size for Qualitative Research

Power analysis does not apply to qualitative research in the same way. You cannot run a G*Power calculation for a phenomenological study or grounded theory. Instead, qualitative sample sizes are justified using the principle of theoretical saturation (also called data saturation): you continue recruiting until new participants no longer add new themes or insights to your analysis.

Research-based guidelines for qualitative sample sizes by method:

For qualitative studies, your methodology chapter should explain your sampling strategy (purposive, theoretical, snowball), the criterion for saturation, and why your chosen sample size is appropriate for your specific method and research question. Citing Guest et al.’s (2006) landmark saturation study (which found thematic saturation at 12 interviews in many homogeneous samples) is a useful anchor for your justification.

How a Pilot Study Improves Your Power Analysis

A pilot study is a small-scale preliminary investigation that tests your procedures, instruments, and hypotheses before the main data collection begins. For power analysis purposes, its most valuable output is a preliminary effect size estimate based on real data from your population.

How to Design a Dissertation Pilot Study

1. Recruit 10–30 participants from the same population as your main study (not from the main study sample itself)
2. Run your full protocol: Administer the survey, interview questions, or experimental procedures exactly as planned
3. Calculate the effect size from the pilot data using your planned statistical test
4. Use the pilot effect size as the input for your a priori power analysis
5. Report the pilot study briefly in your methodology chapter as justification for your effect size estimate

A pilot study also allows you to identify practical problems — ambiguous questions, timing issues, recruitment difficulties — before they affect your main dataset. Most supervisors will recommend a pilot study if you have time; it demonstrates methodological rigour that examiners notice.

How to Write Up Your Sample Size in Your Methodology Chapter

Your methodology chapter should include a dedicated subsection explaining your sample size determination. Below is a template paragraph you can adapt, based on an independent samples t-test with medium effect size:

Key elements to include in your write-up:

• The software used (G*Power 3.1) and its citation
• The specific test performed
• Your effect size estimate and its source (prior literature / Cohen’s benchmarks / pilot study)
• Your alpha level and whether the test was one-tailed or two-tailed
• Your desired power level
• The calculated minimum N and the actual recruited N (including attrition buffer)

Frequently Asked Questions