![]() ![]() When the means are not significantly different, the variance of the sample means will be small, relative to the mean of the sample variances. The strategy behind an ANOVA test relies on estimating the common population variance in two different ways: 1) through the mean of the sample variances - called the variance within samples and denoted $s^2_w$, and 2) through the variance of the sample means - called the variance between samples and denoted $s^2_b$. ![]() In the case where one is dealing with $k \ge 3$ samples all of the same size $n$, the calculations involved are much simpler, so let us consider this scenario first. The null hypothesis is that all population means are equal, the alternative hypothesis is that at least one mean is different.
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