Show that [S S_{T}=S S_{text {Treat }}+S S_{E},] where $S S_{T}=sum_{i=1}^{k} sum_{j=1}^{n_{i}}left(y_{i j}-bar{y} . ight)^{2}, S S_{text

Show that

\[S S_{T}=S S_{\text {Treat }}+S S_{E},\]

where $S S_{T}=\sum_{i=1}^{k} \sum_{j=1}^{n_{i}}\left(y_{i j}-\bar{y} .\right)^{2}, S S_{\text {Treat }}=\sum_{i=1}^{k} n_{i}\left(\overline{y_{i}}-\bar{y} . .\right)^{2}$, and $S S_{E}=$ $\sum_{i=1}^{k} \sum_{j=1}^{n_{i}}\left(y_{i j}-\bar{y}_{i}\right)^{2}$.