Table 2 Calculation of the general similarity index for more than two groups

Let case 1 be a study comparing traits preference in a species “A” by farmers from three different socio-cultural groups (1, 2 and 3) and whose preferred traits are elicited as follows:

A1: [a, b, c, d, e]; A2: [a, d, e, f, h] and A3: [b, g, h, j].

The objective is to calculate the general multi-group similarity index of preferred traits among these three socio-cultural groups.

For this example, T = 3, a₁ = 5, a₂ = 5 and a₃ = 4, a₁₂ = 3, a₁₃ = 1, a₂₃ = 1, a₁₂₃ = 0

\( {\mathbf{C}}_{\mathbf{S}}^{\mathbf{3}} \)=\( \frac{T}{T-1}\ \left(\frac{\sum \limits_{\boldsymbol{i}<\boldsymbol{j}}{\boldsymbol{a}}_{\boldsymbol{i}\boldsymbol{j}}-\sum \limits_{\boldsymbol{i}<\boldsymbol{j}<\boldsymbol{k}}{\boldsymbol{a}}_{\boldsymbol{i}\boldsymbol{j}\boldsymbol{k}}}{\sum \limits_{\boldsymbol{i}}{\boldsymbol{a}}_{\boldsymbol{i}}}\right) \) = \( \frac{3}{3-1}\ \left(\frac{\left[{a}_{12}+{a}_{13}+{a}_{23}\ \right]-{a}_{123}}{a_1+{a}_2+{a}_3}\right) \)= \( \frac{3}{3-1}\ \left(\frac{\left[3+1+1\right]-0}{5+5+4}\right) \)

\( {\mathbf{C}}_{\mathbf{S}}^{\mathbf{3}}=\frac{3}{2}\left(\frac{5}{14}\right) \)

\( {\mathbf{C}}_{\mathbf{S}}^{\mathbf{3}} \)=\( \frac{15}{28} \)

The similarity index of preferred traits among these three socio-cultural groups is 0.53, which reflects a moderate preference similarity.