Sample Size

Definition

Sample size is the number of observations or participants included in a statistical study. It directly influences the precision of estimates, the width of confidence intervals, and the statistical power to detect true effects. An inadequate sample size risks both false negatives (missing real effects) and unstable estimates.

Why It Matters

Determining sample size before data collection is one of the most critical steps in research design. Under-powered studies waste resources and may produce misleading null results. Over-powered studies are ethically questionable and inefficient. Power analysis provides a principled way to balance these concerns by linking sample size to expected effect size, significance level, and desired power.

Example

A researcher expects a new therapy to reduce depression scores by a medium effect size (Cohen's d = 0.5). Using a power analysis with α = 0.05 and desired power = 0.80, she calculates that she needs 64 participants per group. Recruiting only 30 participants per group would yield power of approximately 0.45, meaning she has less than a coin-flip chance of detecting the effect if it truly exists.

Related Terms

• Statistical Power
• Effect Size
• Confidence Interval
• P-Value

Software Notes

• SPSS: Analyze > Power Analysis (requires the Power Analysis module) or use G*Power (free external software) for t-tests, ANOVA, regression, and proportions.
• R: pwr.t.test(d = 0.5, sig.level = 0.05, power = 0.80) from the pwr package. For more complex designs: power.t.test() in base R, or simr for mixed models.
• Stata: power twomeans 0 0.5, sd(1) power(0.8) for two-group mean comparisons. power oneproportion and power twoproportions are available for categorical outcomes.