Definition · Plain-language
Sample size
Sample size is the number of observations or participants included in a study — a key determinant of how reliably the data can detect a real effect and represent the wider population.
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What determines the right sample size
An appropriate sample size is calculated a priori, before data are collected, using a power analysis. Four quantities are linked: the significance level α (the accepted false-positive rate, often 0.05), the desired power (the probability of detecting a real effect, commonly set at 0.80), the smallest effect size worth detecting, and the variability of the outcome. Holding the others fixed, smaller expected effects and greater variability both require larger samples, while a stricter α or higher power also pushes the number up. Specialised software or formulae solve for the required n.
Underpowered and overpowered studies
A sample that is too small leaves a study underpowered: it lacks the precision to detect an effect that truly exists, inflating the rate of Type II errors (false negatives) and producing wide, uninformative confidence intervals. At the other extreme, an excessively large sample can drive the p-value below the threshold for differences so small they carry no practical meaning, so that statistical significance is achieved without practical importance. The aim is a sample large enough to detect effects that matter, but not so large that it wastes resources or over-emphasises trivial findings.
Size is not the same as representativeness
A large sample is not automatically a good one. If the sampling method is biased, increasing the number of participants only produces a precisely measured but systematically wrong estimate. Representativeness — how well the sample mirrors the target population — depends on the sampling strategy, such as random or stratified sampling, not on size alone. A modest, well-drawn random sample can support better inferences than a huge convenience sample. Sound studies therefore plan both an adequate size and an unbiased sampling method before collecting data.
Key facts
At a glance
- Definition: the number of observations or participants in a study
- Determined by: power, expected effect size, α and variability
- Set when: a priori, via power analysis before data collection
- Common targets: power ≈ 0.80, α ≈ 0.05 (conventions)
- Too small: underpowered → Type II errors (missed real effects)
- Caveat: large size ≠ representative; sampling method drives bias
Common misconceptions
What people often get wrong
Often heard: A bigger sample is always better and removes bias from a study.
Actually: Size improves precision, not validity. A biased sampling method gives a wrong answer no matter how large the sample; representativeness depends on how participants are selected, not on how many there are.
Often heard: Sample size can be decided after seeing the results.
Actually: The required size should be set a priori through a power analysis. Choosing or extending the sample based on interim results inflates false-positive rates and undermines the validity of the test.
Often heard: If a result is not significant, the effect simply does not exist.
Actually: A non-significant result can mean the study was underpowered — too small to detect a real effect. Absence of evidence is not evidence of absence; the effect size and confidence interval must be examined.
Going deeper
