\begin{table}%t4
\par
\caption {\label{tab4}The Kendaull's $\tau$ test results for the correlations plotted in 
Fig.~\ref{fig2}.}
%\centerline
 {\begin{tabular}{ccc}
\hline
\hline
 & $\tau/$$P_{\rm null}^{a}$ & $\tau^{b}$/$P_{\rm null}$  \\
\hline
$\bar{\Gamma}$ vs. $\nu_{\rm bf}$   & 0.20/0.32 & 0.21/0.30 \\
$\bar{\Gamma}$ vs. BH mass          & 0.11/0.58 & 0.10/0.62 \\
$\bar{\Gamma}$ vs. $\nu_{\rm norm}$ & 0.53/$8.2\times 10^{-3}$ 
& 0.54/$7.3\times 10^{-3}$ \\
\hline 
\end{tabular}}
\par
\smallskip
$^{a}$ $P_{\rm null}$ depends on both the size of the sample
and the value of $\tau$. 
$^{b}$ Results in the case we use $\bar{\Gamma}_{\rm 20\%}$
instead of $\bar{\Gamma}_{\rm obs}$.
\end{table}