Statistical Power#
The probability of detecting a true effect when one exists.
Important
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What it is#
Statistical power is the probability that a test correctly detects a real effect — that it rejects the null hypothesis when the null is genuinely false. Formally it is \(1 - \beta\), where \(\beta\) is the Type II error (false-negative) rate.
What it depends on#
Power rises with larger effect sizes, bigger samples, a looser significance level \(\alpha\), and lower variance. Researchers conventionally target 0.80 — an 80% chance of catching a true effect — and solve for the sample size that achieves it via power analysis.
Why it matters#
An underpowered study is likely to miss true effects and produces findings that don’t replicate; power is the guard against false negatives, the complement of the \(\alpha\) that guards against false positives. Too much power on a huge sample flips the risk — flagging trivial effects as significant, which is why effect size is reported alongside significance.
Theme: Statistical Inference & Power · All terminology
Hint
Mind map — connected ideas
Power Analysis · Confidence Intervals (CIs) · Statistical Tests · Population Proportion · Correlation · Chi-square (χ²) Test
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More in Statistical Inference & Power
A Priori Power Analysis · Chi-square (χ²) Test · Clopper–Pearson Interval · Compromise Power Analysis · Confidence Intervals (CIs) · Effect Size (δ) · Hypothesis Testing · Kolmogorov–Smirnov (KS) Test · Minimum Detectable Lift (MDL) · P-Value (probability value) · Post Hoc Power Analysis · Power (1 – β) · Power Analysis · Sample size
See also
Source article Adapted (context, re-expressed) in our own words from: Statistical Power (insightful-data-lab.com).