How do you do a sample size calculation for a research study?

Direct answer: Your sample size is the number of observations, patients, students, survey respondents; you collect. It matters because statistical power depends on it: an underpowered study can miss a real effect entirely, producing a false negative. Reviewers treat sample-size justification as a marker of a serious, reproducible design, so the calculation belongs in your protocol, not your discussion.

Evidence: Hickey et al. (2018), writing across pages 4 to 9 of the European Journal of Cardio-Thoracic Surgery, describe the sample-size calculation as a core part of trial design and warn that small studies "may possess insufficient power to detect a clinically significant difference, if such a difference exists." Serdar et al. (2021) add that an undersized study risks a Type II error while a needlessly large one wastes resources and raises ethical concerns, both are design failures a reviewer can see.

Direct answer: An a priori (before-data) calculation needs three inputs, and the software solves for the fourth, the sample size. You choose the alpha level (usually 0.05), the power you want (usually 0.80) and the effect size you expect. Fix any three and the required N follows.

Evidence: An alpha of 0.05 is equivalent to a 5% chance of a false positive, and a power of 0.80 means an 80% chance of detecting a true effect. Kang (2021) sets out the same four interlinked quantities: "the sample size calculation and power analysis are determined by the following factors: effect size, power (1-β), significance level (α), and type of statistical analysis" (Kang, 2021). Fixing three determines the fourth, with 0.05 and 0.80 as the conventional defaults in health-professions research. Cohen's (1992) "power primer", 5 pages long and running from page 155 to 159 of Psychological Bulletin, is the original source of the widely used 0.80 power convention, framed as accepting a Type II error rate four times the Type I rate.

Direct answer: The effect size is the hardest input and the one that most changes your N, the smaller the effect you want to detect, the more participants you need. Estimate it three ways, in order of preference: from a similar published study, from a small pilot, or, as a last resort, from Cohen's conventional small/medium/large benchmarks.

Always justify your choice in writing.

Evidence: Serdar et al. (2021) recommend deriving the expected effect from prior literature or a pilot wherever possible, using standardised benchmarks only when no better estimate exists. Cohen (1992) provides the conventional cut-offs that researchers fall back on, summarised below.

Cohen's conventional benchmarks (Cohen, 1992). Use them only when no better estimate exists.

Direct answer: G*Power is free, widely accepted, and handles most common designs. The workflow is: choose the statistical test that matches your analysis, set the test family, enter alpha, power, and effect size, then click Calculate to get the required N. The single most common mistake is selecting a test that does not match the analysis you will actually run.

Evidence: Kang (2021) and Faul et al. (2007), whose Behavior Research Methods paper on the software ran from page 175 to 191, both stress that the chosen test in G*Power must mirror the planned analysis (t-test, ANOVA, regression, chi-square), because each test has its own power function and effect-size metric. Picking the wrong family silently produces the wrong number.

Direct answer: Use Cochran's formula when you can state your own confidence level and margin of error, because it shows every input. Yamane and Krejcie and Morgan are shortcuts that fix a 95% confidence level and p = 0.5. For a population of 2,000 and a 5% margin, the three give 333, 322 and 323.

Evidence: Israel (2009) calls Yamane's formula a "simplified formula" that assumes a 95% confidence level and p = .5, and he works a population of 2,000 through it to 333. Because both shortcuts fix those settings, they only suit a survey that estimates a proportion at 95% confidence. At the same population, Krejcie and Morgan's table prints 322 and Cochran with the correction gives 323 (Israel, 2009; Krejcie & Morgan, 1970). The Z values behind all three are 1.645, 1.960 and 2.576 for 90%, 95% and 99% confidence (Harris, 2019). Bartlett et al. (2001) warn that tables built on the Krejcie and Morgan formula "assume an alpha of .05 and a degree of accuracy of .05", so do not use them when yours differ.

A note on the name Slovin. Some guides call n = N / (1 + N e²) Slovin's formula. We found no reliable source saying that Slovin's and Yamane's formulas are the same, so treat that name as unverified and use the name your own sources use.

Direct answer: The N from G*Power is the number you need to analyse, not the number to recruit. Inflate it for expected attrition: divide your target by (1 minus the dropout proportion). If you need 100 completers and expect 20% dropout, recruit 100 ÷ 0.80 = 125. Survey studies do the same for the expected non-response rate.

Evidence: Hickey et al. (2018) note that real studies lose participants to withdrawal, loss to follow-up, and missing data, so the recruited sample must exceed the calculated analytic sample. In the example, 100 completers with 20% dropout means recruiting 125, because the loss is counted on the people recruited, not on those who finish. Serdar et al. (2021) similarly advise building an attrition allowance into the recruitment target rather than discovering the shortfall mid-study.

Direct answer: Report enough that a reader could reproduce the calculation: the primary outcome and what difference you considered meaningful, the alpha level, the target power, the assumed effect size with its source, the test used, and the final N including the attrition allowance. Reporting these in the Methods is now a baseline expectation, not a bonus.

Evidence: The CONSORT 2010 statement (Schulz et al. 2010) requires randomised trials to report how the sample size was determined. Yet Kang (2021) and Serdar et al. (2021) both cite reviews showing that only about a third of sample-size calculations in high-impact journals are reported in enough detail to reproduce so doing it well is a genuine quality signal.

Direct answer: If you cannot reach the ideal N, do not invent a "post-hoc power" figure to defend it, reviewers see through that. Instead, design honestly within your limits: pre-register a feasibility or pilot study, report confidence intervals rather than chasing significance, and state the limitation plainly. A transparent small study is far more publishable than an over-claimed one.

Evidence: Hickey et al. (2018) caution explicitly against post-hoc power calculations, which are circular once the data are in. Cohen (1992) and Serdar et al. (2021) point researchers toward reporting effect sizes with confidence intervals, which remain informative even when a sample is modest, the route many early-career Vietnamese researchers take into conference proceedings and Q2 journals.