Statistical Power, explained.
Statistical power is the probability that a specified test rejects its null hypothesis when a particular alternative is true.
Why it happens
Two-sided Normal z tests use known standard deviation one and critical values ±1.96. A nonzero generating mean shifts the sampling distribution; expected power and realised rejection counts are displayed separately.
Statistical power is the probability that a specified test rejects its null hypothesis when a particular alternative is true.
Read the result
Expected power and the rejection fraction from a hundred studies answer related but different questions; finite simulation counts fluctuate.
A worked example
An effect that a small study can miss
Set a positive standardised mean difference and inspect expected two-sided z-test power.
Increase sample size while preserving the generating effect and the fixed rejection threshold.
Set the effect to zero and interpret rejections as false positives rather than successful detection of a real shift.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two-sided Normal z tests use known standard deviation one and critical values ±1.96. A nonzero generating mean shifts the sampling distribution; expected power and realised rejection counts are displayed separately.
Where this idea is useful
A practical use
Plan a study around a meaningful effect size before collecting data, rather than explaining an inconclusive result through significance alone.
A common misconception
“A non-significant test proves the effect is zero.”
A test can fail to reject despite a nonzero effect, particularly when the sampling distribution is broad relative to that effect.
What this explanation leaves out
- Known-variance independent Normal tests and a chosen alternative are assumed; significant results do not establish importance or study quality.
Does high power make an estimate unbiased?
Power concerns rejection probability under a specified alternative. It does not repair selection bias, confounding, measurement error or an inappropriate model.
What effect size would matter before you decide how much evidence to collect?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.