Power of a Test

Statistics · Axiom Academy

Understanding the probability of correctly detecting a true effect Statistical power is the probability that a hypothesis test will correctly reject a false null hypothesis. In other words, it's the probability of detecting an effect when one truly exists. Where β (beta) is the probability of a Type II error (failing to reject H₀ when it is false). This animation illustrates the relationship between the null hypothesis distribution, alternative hypothesis distribution, and statistical power. Four main factors influence the power of a statistical test: This animation demonstrates how sample size affects power by showing the sampling distributions become narrower with larger samples. 3. Why Power Matters in Research Statistical power is crucial for designing and interpreting research studies: Increased risk of Type II errors (missing real effects) Wasted resources on inconclusive studies Publication bias toward false negatives Difficulty replicating findings Greater confidence in detecting true effects More efficient use of research resources Improved reproducibility of results Stronger evidence for decision-making This animation shows the trade-off between Type I error (α) and Type II error (β), and how power relates to both. 4. Power Analysis and Sample Size Planning Power analysis helps researchers determine the sample size needed to detect an effect of a given size with adequate power. Desired power level (typically 0.80) Significance level α (typically 0.05)

This is the written version of the interactive lesson above. See the full Statistics course.