\begin{table}%t2
\par
\caption {Summary of the results obtained for the three field models$^a$.
\label{Table_summary1}}
%\centerline
 {\begin{tabular}{l l|r c c|r c c|r c c}
\hline\hline%\\[-3mm]
%\noalign{\smallskip}
& & \multicolumn{3}{c|}{Ring model \ ($\nu=1$)} 
& \multicolumn{3}{c|}{Axisymmetric model \ ($\nu=2$)} 
& \multicolumn{3}{c}{Bisymmetric model \ ($\nu=3$)} \\%[-3mm]
%\noalign{\smallskip}
\hline%\\[-3mm]
%%\cline{3-5} \cline{7-9} \cline{11-13} \\\noalign{\smallskip}
$i$ & $n_i$ & $\chi^2_{\rm min}$ 
& $
[ \chi^2_{\rm min} \le n_i - \nu 
]$
& $
[ \chi^2_{\rm min} \le \chi^2_{\rm crit} (0.1) 
]$
& $\chi^2_{\rm min}$ 
& $
[ \chi^2_{\rm min} \le n_i - \nu 
]$
& $
[ \chi^2_{\rm min} \le \chi^2_{\rm crit} (0.1) 
]$
& $\chi^2_{\rm min}$ 
& $
[ \chi^2_{\rm min} \le n_i - \nu 
]$
& $
[ \chi^2_{\rm min} \le \chi^2_{\rm crit} (0.1) 
]$ \\
%[-3mm] %\\[-3mm]
%\noalign{\smallskip}
\hline%\\%[-3mm]
%\noalign{\smallskip}
4   & 4 & 5.03 &        & $\ast$ &  2.91 &        & $\ast$ & 3.08 &        & \\
4.5 & 6 & 3.17 & $\ast$ & $\ast$ &  3.11 & $\ast$ & $\ast$ & 1.75 & $\ast$ & $\ast$ \\
5   & 5 & 25.37&        &        & 18.65 &        &        & 1.79 & $\ast$ & $\ast$ \\
5.5 & 5 & 14.52&        &        & 14.43 &        &        & 4.95 &        & \\
6   & 6 & 8.84 &        & $\ast$ &  5.06 &        & $\ast$ & 5.48 &        & $\ast$ \\
6.5 & 5 & 20.29&        &        & 17.93 &        &        &13.55 &        & \\
7   & 6 & 9.57 &        &        &  5.81 &        & $\ast$ & 3.37 &        & $\ast$ \\
7.5 & 4 & 19.31&        &        & 19.30 &        &        & 7.44 &        & \\
8   & 4 & 52.53&        &        &  3.04 &        & $\ast$ & 0.82 &        & $\ast$ 
\\
\hline
\end{tabular}}
\par
\smallskip
 $^a\ $ When a value of $\chi^2_{\rm min}$ satisfies the first or second 
        consistency condition, \\ an asterisk is plotted in the corresponding column.
\end{table}