← All apps

One-way ANOVA

Three groups are sampled from normal populations with a common standard deviation. Compare the spread between the group means with the spread within each group.

Population means

μ₁

μ₂

μ₃

Population and sample

Standard deviation σ

Sample size per group n

Show

Sample means Grand mean Within-group deviations (MSW) Between-group deviations (MSB)

Try this

Keep the means equal. How large does F typically get?
Move one mean away from the others. How do MSB and F respond?
Now increase σ. Why does F drop, even though the means haven't changed?

Between-group variance (MSB)

Within-group variance (MSW)

F = MSB / MSW