\begin{table}%t3 
\caption{\label{Tab4}\label{tab3}Correlation tests of various substructure measures using the 31~galaxy 
    clusters in the \rexcess\ sample.}
\small
%\centering
\par
\begin{tabular}{l r r r r r}
\hline
\hline\noalign{\smallskip}
\multicolumn{1}{l}{Correlation} & 
\multicolumn{1}{c}{$\tau$} & 
\multicolumn{1}{c}{$P$} & \multicolumn{1}{c}{$\rho$} &
\multicolumn{1}{c}{$P$} & \multicolumn{1}{c}{Figure} \\
(1)       &     (2)        &   (3)         &    (4)          &  (5)       & (6)  \\
\hline 
$P_3/P_0-w\ (R_{500})$     & 0.80 & 0.43 & 0.21 & 0.25 & 2\\
$P_3/P_0-w\ (R_{500})$\tablefootmark{a}   & 1.22 & 0.22 & 0.29 & 0.12 & 2\\
$P_3/P_0-w\ (0.9R_{500})$  & 1.63 & 0.10 & 0.29 & 0.10 & --\\
$P_3/P_0-w\ (0.8R_{500})$  & 2.20 & 0.03 & 0.37 & 0.044 & --\\
$P_3/P_0-w\ (0.7R_{500})$  & 2.13 & 0.03 & 0.38 & 0.035 & A.5\\
$P_3/P_0-w\ (0.6R_{500})$  & 1.38 & 0.17 & 0.25 & 0.17 & --\\
$P_3/P_0-w\ (0.5R_{500})$  & 0.36 & 0.72 & 0.01 & 0.99 & --\\ 
$M_{500}-w$    & 0.24 & 0.81 &--0.04 & 0.81 & 11 \\
$M_{500}-P_3/P_0$ & 0.39 & 0.69 &-0.06 & 0.73 & 11 \\
$L_1-w$       & 0.49 & 0.63 & --0.09 & 0.63 & 12\\
$L_1-P3/P0$   & 1.48 & 0.14 & --0.22 & 0.22 & 12\\
$M_{500}-L_{\rm rat}$    & 0.03 & 0.97 & --0.04 & 0.84 & 14\\
$L_1-L_{\rm rat}$\tablefootmark{b} & 1.41 & 0.16 & 0.245 & 0.18 & 14\\
$L_2-L_{\rm rat}$ & 0.43 & 0.67 & 0.055 & 0.76 & 14\\
$n_{e0} - P3/P0$         & 1.54 & 0.12 & --0.30 & 0.10 & 13\\
$t_{\rm cool} - P3/P0$       & 1.86 & 0.06 &  0.34 & 0.06 & 13\\
$n_{e0} - w$                & 2.57 & 0.01 & --0.52 & 0.004 & --\\
$t_{\rm cool}- w$                & 2.62 & 0.009 & 0.50 & 0.006 & --\\
\hline
\end{tabular}
\tablefoot{Column (1) lists the correlation tested, (2) gives the parameter of Kendall's $\tau$ test and (3) the corresponding probability of a null-correlation, (4) gives the result for Spearman's rank test  $\rho$ and (5) the corresponding probability and (6) gives the figure number that shows the correlation. For the correlation analysis the ASURV software package (Isobe et~al. \cite{Isobe1986}) was used. 
\tablefoottext{a}{Same correlation as in the first row but excluding the outlier object RXC~J2157.4-0747.} 
\tablefoottext{b}{$L_1$ is the \mbox{X-ray} luminosity in the $R_{500}$ aperture in the [0.1$-$2.4]~keV band and $L_2$ refers to the core excised luminosity (values given in Pratt et~al. \cite{Pratt2009a}).}}
\end{table}