TABLE IV.

USS mean squares and means for Model 1.

Statistic	Definition
$S_T^2$	$\frac{n_S{r}_H{\sum }_i{\left({\overline{Y}}_{i^{\ast \ast }}-{\overline{Y}}_{\ast \ast \ast }\right)}^2}{(n_T-1)}$
$S_S^2$	$\frac{n_T{r}_H{\sum }_j{\left({\overline{Y}}_{{\ast }_j\ast }-{\overline{Y}}_{\ast \ast \ast }\right)}^2}{(n_S-1)}$
$S_{TS}^2$	$\frac{r_H{\sum }_i{\sum }_j{\left(Y_{{\mathit{ij}}^{\ast }}-{\overline{Y}}_{i^{\ast \ast }}-{\overline{Y}}_{{\ast }_j\ast }+{\overline{Y}}_{\ast \ast \ast }\right)}^2}{(n_T-1)(n_S-1)}$
$S_E^2$	$\frac{{\sum }_i{\sum }_j{\sum }_k{\left(Y_{\mathit{ijk}}-{\overline{Y}}_{{\mathit{ij}}^{\ast }}\right)}^2}{N-n_T{n}_S}$
${\overline{Y}}_{{\mathit{ij}}^{\ast }}$	$\frac{{\sum }_k{Y}_{\mathit{ijk}}}{r_{\mathit{ij}}}$
${\overline{Y}}_{i^{\ast \ast }}$	$\frac{{\sum }_j{\overline{Y}}_{{\mathit{ij}}^{\ast }}}{n_s}$
${\overline{Y}}_{{\ast }_j\ast }$	$\frac{{\sum }_i{\overline{Y}}_{{\mathit{ij}}^{\ast }}}{n_T}$
${\overline{Y}}_{\ast \ast \ast }$	$\frac{{\sum }_i{\sum }_j{\overline{Y}}_{{\mathit{ij}}^{\ast }}}{n_T{n}_S}$
rH	$\frac{n_T{n}_S}{{\sum }_i{\sum }_{j}1∕r_{\mathit{ij}}}$