Sample Size

Sample size is the number of participants, observations, or units included in a study. For studies that test for an effect, an adequate sample size, determined through power analysis, is essential for ensuring that a study has sufficient statistical power to detect a meaningful effect while maintaining acceptable Type I and Type II error rates. The required sample size depends on the expected effect size, the desired power, the significance level, the variability of the outcome, and the study design.

Sample size directly determines a study's ability to produce reliable, interpretable results. An underpowered study with too few participants is unlikely to detect a true effect, producing null results that are uninformative and contributing to research waste. An unnecessarily large study wastes resources, delays completion, and may expose more participants to research procedures than needed. Funding agencies, ethics committees, and journal reviewers commonly expect a justified sample size calculation as evidence of rigorous study planning. Too small a sample leaves estimates imprecise, with wide confidence intervals; a larger sample reduces this random error but cannot remove systematic error (bias), and how far conclusions generalize depends on how the sample was selected, not only on its size.

Sample size calculation begins with specifying the statistical test to be used, the expected effect size, the significance level (typically alpha = 0.05), and the desired power (typically 80% or 90%). Software tools (G*Power, R, Stata, SAS) compute the minimum sample size that satisfies these constraints.

The expected effect size is often the most challenging parameter to specify. Sources include pilot studies, published research on similar interventions, and the minimum clinically important difference (the smallest effect that would change clinical practice). Effect sizes from small pilot studies are imprecise and may overestimate the true effect, so they should not set the sample size on their own; the minimum clinically important difference is a safer basis. Using an inflated effect size to justify a small, inexpensive study is a common pitfall.

Several design features affect the required sample size. Clustered designs (where participants are grouped within clusters such as hospitals or schools) require larger samples because of the intraclass correlation, quantified by the design effect. Repeated measures designs can reduce the required sample size by using within subject correlations. Studies with high expected attrition must inflate the initial enrollment to maintain adequate power at the time of analysis.

For descriptive studies (such as prevalence estimation), sample size is determined by the desired precision of the estimate (width of the confidence interval) rather than by power to detect an effect. For qualitative studies, sample size is often guided by data saturation rather than statistical power, although saturation is not the only rationale.

Calculate sample size during the study planning phase, before data collection begins. Include the calculation and its assumptions in the study protocol, grant application, and ethics submission. Report the sample size achieved versus the target in the published paper. When interpreting published studies, consider whether the achieved sample size was adequate for the stated aims. If a study reports null results with a small sample, assess whether the study was sufficiently powered to detect a clinically meaningful effect.

A common error is calculating sample size using an unrealistically large effect size to justify a smaller, cheaper study. Another mistake is failing to inflate for anticipated dropout, resulting in a final analyzable sample that is smaller than required. Researchers sometimes neglect to account for the design effect in clustered studies, producing substantially underpowered analyses. Using a post hoc power calculation to interpret null results is uninformative and should be avoided. Finally, rounding down instead of up when the formula produces a non integer can reduce power below the target.

A team plans a two arm, parallel group randomized trial of a new rehabilitation protocol for stroke patients. Based on a previous trial, they expect a moderate effect size (Cohen's d = 0.45) on the primary outcome (Functional Independence Measure score at 12 weeks). At alpha = 0.05 and power = 0.90, the required sample size is 105 per group. Anticipating 20% attrition, they plan to enroll 132 per group, for a total of 264 participants. The power analysis is performed using G*Power and confirmed using the pwr package in R.