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Table 2. Estimates of size for nominal $\alpha=0.05$ tests  \\ for data
from the beta-binomial($\rho$) distribution.
\begin{tabular}{clccccccccccc} \hline\hline
Number of     &    &\multicolumn{3}{c}{$\rho=0.0$}&
&\multicolumn{3}{c}{$\rho=0.2$}& &\multicolumn{3}{c}{$\rho=0.8$} \\ \cline{2-13}
strata     &$n_{ij},m_{ij}=$&  5   & 5-10 & 5-15 &&    5 & 5-10 & 5-15  && 5   & 5-10  & 5-15 \\ \hline
k=5  & $T_{MH}$ &.056  & .054 & .042 && .141 & .175 & .261  &&.340 & .437  & .493 \\
     & $T_{L}$  &.022  & .022 & .016 && .020 & .019 & .033  &&.017 & .023  & .023 \\
     & $T_{DD}$ &.046  & .038 & .032 && .051 & .050 & .066  &&.044 & .049  & .043 \\
     & $T_{P}$  &.057  & .052 & .039 && .050 & .050 & .064  &&.041 & .047  & .036 \\
     & $T_{U}$  &.058  & .058 & .040 && .051 & .051 & .067  &&.045 & .048  & .040 \\ \hline

k=15 & $T_{MH}$ &.047  &.065  &.032  && .154 &.215  &.238   &&.325 & .432  & .482 \\
     & $T_{L}$  &.049  &.051  &.037  && .045 & .051 &.039   &&.040 & .038  & .038 \\
     & $T_{DD}$ &.037  &.050  &.022  && .086 &.095  &.104   &&.119 & .133  & .131 \\
     & $T_{P}$  &.045  &.060  &.032  && .045 &.057  &.049   &&.054 & .047  & .052 \\
     & $T_{U}$  &.048  &.060  &.037  && .048 &.061  &.051   &&.055 & .049  & .057 \\ \hline

k=25 & $T_{MH}$ &.043  &.059  &.046  &&.157  &.203  &.234   &&.344 & .411 & .491\\
     & $T_{L}$  &.047  &.045  &.058  &&.047  &.052  &.048   &&.045 & .040 &.043  \\
     & $T_{DD}$ &.024  &.029  &.024  &&.049  &.057  &.064   &&.081 & .091 &.093 \\
     & $T_{P}$  &.044  &.057  &.044  &&.049  &.055  &.053   &&.047 & .050  &.054 \\
     & $T_{U}$  &.042  &.059  &.043  &&.047  &.053  &.052   &&.049 & .048  &.053 \\ \hline\hline
\end{tabular}
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