I came across this:
"Therefore, board gender diversity and board racial diversity are calculated using Blau's index of heterogeneity $(1 - \sum p_{i}^2)$, where $p_i$ is the proportion of group members in each of the $i$ categories."
I'd like to know, if the category just includes $2$ (male and female) then how can I calculate Blau's Index? How can I calculate $p_i$?
For example, if ten men and ten women in total, what is the index?
Sorry, English is not my first language.
Blau's Index calls for adding the squared proportion of individuals in each category, summing them up, then subtracting from 1. In the example of two individuals, half (.5) are male and half (.5) are female. .52 is .25. Add .25 and .25 to obtain .5. Subtract this from 1 and you have a diversity index of .5. The proportions are the same when there are ten females and ten males so the answer would be the same. However, different proportions such as 3 females and 7 males do result in a different answer. .32 is .09 and .72 is .49. Added together we have .58 to subtract from 1 and a diversity index of .42. Pi represents each category's proportion with each proportion (.5 and .5 or .3 and .7 in the respective examples).