I am trying to formalize an observed trend. To simplify what I am trying to do, suppose a dataset of salesmen selling items A, B, C, D. In the year 1950, the proportion of each sold is (0.2, 0.2, 0.1, 0.5), however this shifts to (0.4, 0.1, 0.1, 0.4) in 2000 (or some other statistically significant shift) – now this can be shown with a chi-square test. Important to note, the group of salesmen in 1950 is not the same as in 2000.
Now what I would like to show is that taking into account the shift in product sales, we witness a specialization in certain products, ie whereas in 1950 salesmen would sell all products fairly equally, in 2000, salesmen increasingly focus on certain products (for example, whereas in 1950 an average salesperson may have a distribution of sales more or less representative of the sales overall – 0.2, 0.2, 0.1, 0.5; a 2000 salesperson may have 0.9 of A and 0.03 of each of the others).
I was wondering how one would go about this? Would it be appropriate to compare the top 10% of sales people in each product and show increasing discrepency in how they sell when compared to a normalized supposed salesperson? Is there a more standard way of doing this?
Any help would be very much appreciated.