Lesson 2 of 7 · 12 min

Type I and Type II errors, significance and power

A test can go wrong in two ways, rejecting a true null (Type I) or missing a false one (Type II); the significance level caps the first, and power measures how well the test avoids the second.

In short

  • Type I error: rejecting a true null, a false positive. Its probability is the significance level α\alpha.
  • Type II error: failing to reject a false null, a false negative. Its probability is β\beta.
  • Confidence level = 1−α1 - \alpha. Power = 1−β1 - \beta, the probability of correctly rejecting a false null.
  • With the sample size fixed, cutting α\alpha raises β\beta and lowers power. Only a larger sample reduces both errors at once.
  • Choose α\alpha by weighing what each mistake would cost.

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Type I and Type II errors, significance and power · Hypothesis Testing