### Introduction

Occasionally it is useful to cite measures in papers other than simple probabilities or differences in probability. When we do, we should estimate confidence intervals on these measures. There are a number of ways of estimating intervals, including bootstrapping and simulation, but these are computationally heavy.

For many measures it is possible to derive intervals from the Wilson score interval by employing a little mathematics. Elsewhere in this blog I discuss how to manipulate the Wilson score interval for simple transformations of *p*, such as 1/*p*, 1 *–* *p*, etc.

Below I am going to explain how to derive an interval for grammatical diversity, *d*, which we can define as **the probability that two randomly-selected instances have different outcome classes**.

Diversity is an effect size measure of a vector of *k* values. If all values are the same, the data is evenly spread, and the score will be at its maximum. If all values except for one are zero, the chance of picking two different instances will be zero. Continue reading