14.4 The sum of squares

\[SS_{tot}=\sum_{k=1}^G\sum_{i=1}^{N_k}(Y_{ik}-\bar{Y})^2\] ### Between-group sum of squares \[SS_{b}=\sum_{k=1}^G\sum_{i=1}^{N_k}(Y_{k}-\bar{Y})^2\] \[=\sum_{k=1}^G{N_k}(\bar{Y}_{k}-\bar{Y})^2\] \[SS_w+SS_b=SS_{tot}\] ## The F-test

\[df_b=G-1\] \[df_w=N-G\] \[MS_b=\frac{SS_b}{df_b}\] \[MS_w=\frac{SS_w}{df_w}\]

\[F=\frac{MS_b}{MS_w}\]