Sample size and statistical power in medical research
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Sample Size
The sample size of a study is a critical design element, not chosen arbitrarily. It should be large enough to detect the smallest effect that is clinically meaningful, while avoiding unnecessary recruitment that may waste resources or expose participants to risk.Sample size is influenced by:
- The expected effect size (i.e. the magnitude of difference deemed clinically important)
- The variability of the outcome
- The significance level (α): usually 0.05, representing a 5% risk of a type I error
- The desired statistical power: typically set at 80% or 90%.
An insufficient sample size increases the risk of failing to detect a true effect (type II error), undermining the study's validity.
Statistical power
Power is the probability of correctly rejecting the null hypothesis when it is false i.e. detecting a true effect if one exists.Mathematically:
- Power = 1 − β
A study with 80% power (β = 0.2) has a 1 in 5 chance of missing a real difference, assuming one exists. This threshold is widely accepted in clinical research as a reasonable balance between sensitivity and feasibility.
Factors that increase power
Power can be increased by:- Larger sample size
- Lower variability in the data
- Larger expected effect size
- Higher significance level (α): though this increases the chance of a type I error
There is a fundamental trade-off between α and β: reducing one typically increases the other.
Confidence intervals and power
A wide confidence interval around an effect estimate suggests greater uncertainty and may indicate insufficient power. In contrast, narrow intervals are associated with larger, more precise samples.Examining confidence intervals can help interpret the adequacy of power, especially in studies with negative or inconclusive results.