Checking our assumptions
The ANOVA F-test requires that all populations have the same standard deviation . Since is unknown, this can be hard to check.
Practically: The results of the ANOVA F-test are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation.
(Equal sample sizes also make ANOVA more robust to deviations from the equal rule)
Each of the I populations must be normally distributed (histograms or normal quantile plots). But the test is robust to normality deviations for large enough sample sizes, thanks to the central limit theorem.