Table 1 Non-equalized and group-equalized versions of the correlation indices (r) and the indicator value indices (IndVal)

Correlation (r)

\(r_{\phi } = \frac{{N \times n_{p} - n \times N_{p} }}{{\sqrt {\left( {N \times n - n^{2} } \right) \times \left( {N \times N - N_{p}^{2} } \right)} }}\)

\(r_{\phi }^{g} = \frac{{N \times n_{p}^{g} - n^{g} \times N_{p}^{g} }}{{\sqrt {\left( {N \times n^{g} - n^{g2} } \right) \times \left( {N \times N_{p}^{g} - N_{p}^{g2} } \right)} }}\)

\(r_{ind} = \frac{{N \times a_{p} - a \times N_{p} }}{{\sqrt {\left( {N \times c \times a - a^{2} } \right) \times \left( {N \times N_{p} - N_{p}^{2} } \right)} }}\)

\(r_{ind}^{g} = \frac{{N \times a_{p}^{g} - a^{g} \times N_{p}^{g} }}{{\sqrt {\left( {N \times c \times a^{g} - a^{g2} } \right) \times \left( {N \times N_{p}^{g} - N_{p}^{g2} } \right)} }}\)

Indicator value (IndVal)

\(IndVal_{pa} = A_{pa} \times B_{pa} = \frac{{n_{p} }}{n} \times \frac{{n_{p} }}{{N_{p} }}\)

\(IndVal_{pa}^{g} = A_{pa}^{g} \times B_{pa} = \frac{{{{n_{p} } \mathord{\left/ {\vphantom {{n_{p} } {N_{p} }}} \right. \kern-\nulldelimiterspace} {N_{p} }}}}{{\sum\limits_{k = 1}^{k} {{{n_{k} } \mathord{\left/ {\vphantom {{n_{k} } {N_{k} }}} \right. \kern-\nulldelimiterspace} {N_{k} }}} }} \times \frac{{n_{p} }}{{N_{p} }}\)

\(IndVal_{ind} = A_{ind} \times B_{pa} = \frac{{a_{p} }}{a} \times \frac{{n_{p} }}{{N_{p} }}\)

\(IndVal_{ind}^{g} = A_{ind}^{g} \times B_{pa} = \frac{{{{a_{p} } \mathord{\left/ {\vphantom {{a_{p} } {N_{p} }}} \right. \kern-\nulldelimiterspace} {N_{p} }}}}{{\sum\limits_{k = 1}^{k} {{{a_{k} } \mathord{\left/ {\vphantom {{a_{k} } {N_{k} }}} \right. \kern-\nulldelimiterspace} {N_{k} }}} }} \times \frac{{n_{p} }}{{N_{p} }}\)