The table below shows the sum of squares in an ANOVA table.
Source of Variation
Degrees of Freedom
Sum of Squares
Mean Squares (MS)
SSW MSW df_
Within
SSW
~Zzo-Xy' df = k = 1
MSB MSW
Between
SSB -Ze-8)
df, = k
SSB MSB df,
Total
SST = Ze-Yy df, = n - [
Show that MSW and MSB are chi-square distributions with k - 1 and n = k degrees of freedom respectively, and as a result, F MSB / MSW has an F distribution with the degrees of freedom mentioned above.