Lesson 2 of 7 · All lessons in this module
- The six steps and stating the hypotheses
- Type I and Type II errors, significance and powerVideo lesson
- Critical values, p-values and the decision ruleVideo lesson
- Testing a single mean
- Two means: independent vs paired samplesVideo lesson
- Testing variances: chi-square and FVideo lesson
- Parametric vs nonparametric tests
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 .
- Type II error: failing to reject a false null, a false negative. Its probability is .
- Confidence level = . Power = , the probability of correctly rejecting a false null.
- With the sample size fixed, cutting raises and lowers power. Only a larger sample reduces both errors at once.
- Choose by weighing what each mistake would cost.
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