Lesson 34 of 1524
One-way ANOVA
Compare three or more means in one test. The null says they are all equal.
Practice this chapterOne-way ANOVA asks whether several group means differ. The null hypothesis says every group mean is equal. The alternative says at least one differs. It does not, by itself, say which one.
The F statistic is the variance between groups divided by the variance within groups. Only a large F is evidence against the null, so the test is right-tailed. Between-groups degrees of freedom are k − 1, one less than the number of groups.
The F ratio
F = (between-group variance) / (within-group variance)
A large ratio means the groups differ by more than the scatter inside them.
Worked example
Four groups are compared. What is the between-groups degrees of freedom?
- 1Between-groups degrees of freedom depend on how many groups there are, not on how many observations are inside each group.
- 2Here k = 4.
- 3df between = k − 1 = 4 − 1 = 3.
- 4One group mean can be the baseline. Each of the other three groups can differ from it, so there are three free comparisons among four means.
Result: 3
Why. Four group means leave three degrees of freedom between groups, because k − 1 = 3. The within-groups degrees of freedom are a different count. They use the number of observations, and this question does not give that number.
A significant F says the means are not all equal. It does not name the pair that differs. That needs a follow-up comparison.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.