Testing hypotheses in one-way ANOVA
We have I independent SRSs, from I populations or treatments.
The ith population has a normal distribution with unknown mean µi.
All I populations have the same standard deviation σ, unknown.
The ANOVA F statistic tests:
When H0 is true, F has the F distribution with I − 1 (numerator) and N − I (denominator) degrees of freedom.
H0: = = … = I
Ha: not all the i are equal.