The sample means for each of k treatment groups were identical (yes, this is very unlikely), 0 would be the observed value of the anova test statistic also called ANOVA.
Analysis of variance (ANOVA) is a statistical method for examining differences in means.
It consists of a number of statistical models and the accompanying estimating techniques (such as the "variation" within and between groups). Ronald Fisher, a statistician, created ANOVA.
The rule of total variance, on which the ANOVA is based, divides the observed variance in a given variable into components owing to various causes of variation.
ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the ANOVA is employed to determine whether two or more means differ from one another.
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