Power Analysis and Sample Size Planning for Dissertation and Assignment Studies
Power analysis and sample size planning are essential steps in designing rigorous dissertations, essays and assignments. Underpowered studies risk false negatives; overly large samples waste resources and can detect trivial effects. This guide walks you through purpose, methods, practical examples, tools, and common pitfalls so you can plan a defensible sample size for your thesis or coursework.
Why power analysis matters
- Ensures scientific validity: Adequate power reduces the risk of Type II errors (missing real effects).
- Supports ethical and resource decisions: You avoid recruiting more participants than necessary.
- Strengthens your methods chapter: Reviewers expect sample size justification in dissertations.
Typical default settings:
- Alpha (α) = 0.05 (probability of Type I error)
- Power (1 − β) = 0.80 (80% chance to detect the effect if it exists) — consider 0.90 for high-stakes research
- Effect size = small, medium, or large estimate from literature or pilot data
Core concepts (brief)
- Effect size: The magnitude of the expected effect (Cohen’s d, r, odds ratio, proportion difference).
- Alpha (α): Significance threshold (commonly 0.05).
- Power (1 − β): Probability of detecting the effect if it exists.
- One-tailed vs two-tailed tests: Two-tailed tests require slightly larger samples to detect effects.
Step-by-step sample size planning
- Define the primary research question and outcome (mean difference, proportion, correlation, etc.).
- Choose the statistical test that matches the design (see our decision tree: Selecting the Right Statistical Tests for Dissertations, Essays and Assignments: A Practical Decision Tree).
- Estimate effect size from prior studies, pilot data, or conventions (Cohen’s benchmarks).
- Set α and desired power.
- Use a formula or software to calculate required n.
- Adjust for design effects (cluster sampling), expected attrition, and multiple comparisons.
- Report your assumptions and sensitivity analyses in the methods section.
Quick reference sample-size table (two-sample t-test, α=0.05, power=0.80)
| Cohen's d (effect size) | Approx. n per group | Total n |
|---|---|---|
| 0.20 (small) | 393 | 786 |
| 0.50 (medium) | 63 | 126 |
| 0.80 (large) | 25 | 50 |
Note: These are approximate values for equal-sized groups using a two-sided t-test. Add 10–20% for expected attrition.
Common study scenarios and formulas
- Two-sample t-test (means): use G*Power or R (power.t.test) for exact calculations.
- Correlation studies: estimate sample size to detect a target Pearson r (R’s pwr.r.test).
- Proportions: for estimating a proportion with margin of error E, n ≈ p(1−p)*(Z/E)^2. For 95% CI and 5% margin, worst-case n ≈ 385.
- ANOVA and regression: need software (G*Power, pwr.anova, pwr.f2.test) to account for multiple groups/predictors.
Software and tools (comparison)
| Tool | Strengths | Use case |
|---|---|---|
| G*Power | Free, GUI, supports many tests | Quick power/sample-size for t-tests, ANOVA, correlations |
| R (pwr, stats) | Scriptable, reproducible | Batch analyses, simulation-based power |
| Python (statsmodels) | Integrates with analysis workflow | Power for regression, proportions, programmatic workflows |
| Online calculators | Fast, accessible | Simple checks and student use |
For reproducible workflows, see: Reproducible Analysis Workflows for Dissertations, Essays and Assignments Using R and Python.
Practical tips for dissertations and assignments
- Anchor effect-size estimates to prior literature. If uncertain, report a sensitivity analysis (what effect sizes your sample can detect).
- Plan for attrition: add 10–20% depending on expected dropout. For online surveys, allow more.
- Adjust for clustering: for cluster or multistage samples, multiply n by the design effect (DEFF = 1 + (m − 1)ICC).
- Multiple comparisons: control family-wise error (Bonferroni) or use false discovery rate; both affect required sample size.
- Pilot studies: useful for estimating SDs or ICCs, but be cautious—pilot estimates are noisy.
- Feasibility: when ideal n is unattainable, state this limitation and perform power or sensitivity analysis to justify interpretations.
Example: Dissertation comparing two teaching methods
- Research design: randomized two-group experiment, outcome = exam score
- Expected effect size: d = 0.5 (medium) from literature
- α = 0.05, power = 0.80
- Required: ~63 participants per group → total 126.
- If expect 15% dropout: recruit 126 / (1 − 0.15) ≈ 148 participants.
Reporting your sample-size justification (what examiners expect)
- State the test and design (e.g., two-sample t-test, independent groups).
- List assumptions: α, power, effect size source, SDs, one- or two-tailed test.
- Provide calculation method or software (e.g., G*Power vX.X, R code).
- Show sensitivity analysis: how detectable effect size changes with n.
- If constraints limited sample size, explain and interpret results cautiously.
For guidance on connecting analysis and reporting, see: Interpreting Statistical Output for Dissertations, Essays and Assignments: Writing Clear Results.
Common pitfalls and how to avoid them
- Relying on arbitrary effect sizes — instead, use literature or pilot data.
- Forgetting multiple testing and clustering adjustments.
- Treating power analysis as optional — include it in methods.
- Overlooking data issues: missing data and outliers affect effective sample size (see: Handling Missing Data and Outliers in Dissertations, Essays and Assignments: Strategies and Examples).
- Choosing only statistical significance over practical significance — report effect sizes and confidence intervals.
When qualitative or mixed methods are involved
Power analysis is most relevant for quantitative components. For qualitative samples, justify saturation or purposive sampling instead. For mixed-methods studies, integrate quantitative power planning with qualitative sampling rationale. See: Mixed-Methods Data Integration: Techniques for Dissertations and Assignments.
Further reading and related resources
- Selecting the Right Statistical Tests for Dissertations, Essays and Assignments: A Practical Decision Tree
- Regression, ANOVA and Beyond: Applied Statistics for Dissertations, Essays and Assignments
- Data Visualization Best Practices for Dissertations, Essays and Assignments: Charts, Tables and Figures That Communicate
- Qualitative Trustworthiness and Quantitative Validity: Reporting Standards for Dissertations, Essays and Assignments
- Beginner’s Guide to Qualitative Coding and Thematic Analysis for Dissertations, Essays and Assignments
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