Legends

• paygap = the ratio of median salaries of one group divided by the median of the salaries of the other group
• NA = numbers are too small, please look at individuals;
• nothing = no bias detectable;
• . = maybe there is some bias, but the numbers are low, check individuals;
• * = you should check for bias;
• ** = bias is probably there;
• *** = most certainly there is bias

So, there will be more stars if the probability of a bias is higher: this can be due to a higher bias and/or due to a larger sample size.

The column headers of the pay-gap matrices are abbreviated as follows:

• grade = the salary grade as used in the company
• jobID = a unique identifier of the job category (can be abbreviated)
• sal_F = the median salary of the females (F)
• sal_oth = the median salary of the other groups (non F). The tool is open to use more than one gender.
• age_F = the median age of the females (or age_Pol could be the median age of the team members with Polish citizenship)
• age_oth = the median age of the other groups take together (e.g. the median age of non females)
• paygap = the ratio of median salary earned by the selected group (e.g. females) divided by the median of the other people. If this is lower than \(1\), then median female earns less than the median non-female.
• conf. = the confidence level that this paygap is significant.

The Diversity Index

We express diversity as a number between zero and one. Our calculation is based on @debrouwer2020 and more in particular section 36.3.1 ``The Business Case: a Diversity Dashboard’’. Details can be found in the book. The method is:

• The diversity is \(0\) if only one of the groups is present, and is \(1\) if both groups are equitably present.
• This calculation is similar to the established concept of entropy in physics.
• More than two categories can be used (e.g. one is not limited to two genders)
• We calibrate the probabilities so that they show maximum entropy (or diversity) for the percentages that naturally occur (see next slide).

The diversity index illustrated for the case where there are only two possible classes, and where the prior priorities are respectively 50/50 (top) and 70/30 (bottom). The index reaches a maximum at a distribution equal to the prior probabilities.

Hence, the diversity indexes show how diverse our workforce is. They are calculated similar to entropy: \(I = -\frac{1}{\log(N)} \sum_i^N {p_i \log p_i}\), where there are \(N\) possible and mutually exclusive states \(i\). They range from \(0\) to \(1\).

The confidence level and p-value

The p-value is the probability that we make a mistake by assuming that there is no paygap.

It is calculated by splitting the data on a variable in binary factors (e.g. Females and others) and then checking how likely it is that a random person from the first group earns less than a random person from the second group. This is done by a method known as Mann-Whitney U test.

The Mann–Whitney U test (aka. Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X. If we assume that the distributions are symmetric, it boils down to a test that the medians are different.

More information: see Wikipedia