Changes

where <math>\bar{Y}_{i\cdot}</math> denotes the [[average|sample mean]] in the ''i''-th group, <math>n_i</math> is the number of observations in the ''i''-th group,<math>\bar{Y}</math> denotes the overall mean of the data, and <math>K</math> denotes the number of groups.

where <math>Y_{ij}</math> is the ''j''^th observation in the ''i''^th out of <math>K</math> groups and <math>N</math> is the overall sample size. This ''F''-statistic follows the [[F-distribution|''F''-distribution]] with degrees of freedom <math>d_1=K-1</math> and <math>d_2=N-K</math> under the null hypothesis. The statistic will be large if the between-group variability is large relative to the within-group variability, which is unlikely to happen if the [[expected value|population means]] of the groups all have the same value.