3 Ordinal Data Analysis

Suppose that instead of making measurements on a continuous scale, we are able to discriminate only a few ordered categories with our measuring instrument. This situation is commonly encountered when assessing the presence or absence of disease, or responses to a single item on a questionnaire. Although it is possible to calculate a covariance matrix from these data, the correlations usually will be biased. The degree of bias depends on factors such as the number of categories and the number of observations in each category, and usually results in an underestimate of the true liability correlation in the population. In this section we describe methods for summarizing ordinal data.