Both MSTR and MSE estimatevariation in the data (2 )
If the group means are equal, the ratio MSTR/MSE should be close to 1. (statistically, H0 is true)
If the means are unequal (i.e., H0 is not true), the ratio should be significantly larger than 1, since MSTR would tend to over-estimate 2.
The ratio F = MSTR/MSE
Hence, reject H0 if F = MSTR/MSE is too large
F follows an F distribution with numerator d.f. a - 1, and denominator d.f. N - a.
F is too large, if it is larger than a critical value, F,a-1,N-a.