Measures and tests of heaping in discrete quantitative distributions

Heaping is often found in discrete quantitative data based on subject responses to openended interview questions or observer assessments. Heaping occurs when subjects or observers prefer some set of numbers as responses (e.g. multiples of 5) simply because of the features of this set. Although heaping represents a common type of measurement error, apparently no prior general measure of heaping exists. We present simple measures and tests of heaping in discrete quantitative data, illustrate them with data from an epidemiologic study, and evaluate the bias of these statistics. These techniques permit formal measurement of heaping and facilitate comparisons of the degree of heaping in data from different samples, substantive domains, and data collection methods.