Frequentist statistics · BEGINNER LESSON
Statistical power
Statistical power is the long-run probability that a statistical test correctly rejects the null hypothesis when a specific alternative is true. In simple terms, it measures how likely a study is to detect an effect that really exists, given the test, sample size, effect size, and significance level.
What it is and what is measured
Statistical power is a probability: the chance that a statistical test will reject the null hypothesis when the alternative hypothesis is true. The null hypothesis is the default claim of no effect or no difference, and the alternative hypothesis is the claim that an effect or difference exists. Power is usually written as 1 − β, where β is the Type II error rate, meaning a false negative.
[1] Improving statistical reporting in psychology [2] Statistical Power in Musculoskeletal Research: A Meta-Review of ... [3] Small Samples, Big Problems, Statistical Tests in Nematology ...
How it works in practice
In the frequentist framework, researchers choose a fixed significance level, often α = 0.05, before collecting data. They then do an a priori power analysis, which is a sample size calculation made before the study begins. This analysis uses the planned statistical test, the effect size of interest, the chosen alpha level, and the desired power. If the sample is too small, power drops and the study is less likely to detect the target effect.
[1] Improving statistical reporting in psychology [2] Statistical Power in Musculoskeletal Research: A Meta-Review of ... [3] Small Samples, Big Problems, Statistical Tests in Nematology ...
Why it matters
Higher power reduces the chance of missing a real effect and is often targeted at about 0.80, meaning the study would detect the planned effect in 8 out of 10 similar repetitions. Power is therefore used during study design to choose a sample size that is adequate for the intended analysis and to reduce underpowered research.
[1] Improving statistical reporting in psychology [2] Statistical Power in Musculoskeletal Research: A Meta-Review of ... [3] Small Samples, Big Problems, Statistical Tests in Nematology ...
Limitations and cautions
Power does not prove that a result is true. A rejected null hypothesis is a decision to act as though the alternative is true, not a confirmation of truth. Power also depends on the exact test, sample size, assumed effect size, and alpha level, so biased or uncertain effect-size estimates can make sample size planning unreliable. If multiple tests are planned, the analysis can become more complicated.
[1] Improving statistical reporting in psychology [2] Statistical Power in Musculoskeletal Research: A Meta-Review of ... [3] Small Samples, Big Problems, Statistical Tests in Nematology ...
SEE THE IDEA
How statistical power is determined
The researcher chooses the statistical test, such as a t-test, correlation, or ANOVA.
Sample size, expected effect size, and alpha level are set before data collection.
These inputs are used to estimate the probability of detecting the target effect.
If the test result falls in the rejection region, the null hypothesis is rejected.
Planned test and design inputs feed a power analysis, which guides how much data to collect before making a decision.
Power is not observed directly; it is planned from the study design and the effect researchers want to detect.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.