ABSTRACT
There are a number of circumstances in which the readers might want to estimate confidence intervals on variables other than probabilities or proportions. In this chapter, the author discusses the problem of citing and plotting a non-probabilistic property with a confidence interval. Sometimes expressing something as a proportion or probability does not make sense. The author discusses how the Wilson interval can be applied to other quantities – like sentence length. Scatter refers to the distribution of observed values. Confidence concerns the projected distribution of resampled means. The author needs a confidence interval that estimates the reproducibility of the observed mean length. He knows how to calculate intervals on a Binomial proportion, which might be ‘the number of utterances per word’ or (perhaps more meaningfully) the proportion of words that are utterance-initial. The general theorem applies the Wilson interval to functions of Binomial proportions.
