How diverse? (IQV, Shannon, Gini-Simpson)

In brief

One number for how evenly or concentrated answers are spread over the categories. It appears under the frequency table for category columns.

What for

Choice of subject, home languages, career wish: are the answers spread over all possibilities or clustered in a few?

Requirements

A column with categories (text, value labels). The order of the categories does not matter.

Reading the result

• IQV from 0 (all in one answer) to 1 (even). Shannon H with evenness J; e to the power of H says: this many equally frequent answers would be equally diverse.
• k is the number of possible answers (from the value labels), otherwise of the occupied ones; the sentence names it. "Only occupied" changes it. J and IQV depend on k.

Reporting the result

Shannon H = 1.28, evenness J = .92; IQV = .93; N = 100, with 4 possible answers

Limits

Many rare answers raise H without being more even. With fewer than 50 cases H is a little too small. No test, no confidence interval; "More numbers" shows Gini-Simpson and 1/Σp².

Source

Agresti, A., & Agresti, B. F. (1978). Statistical analysis of qualitative variation. Sociological Methodology, 9, 204-237.