On measurements and their quality: Paper 3: Post hoc pooling and errors of discreteness

This is the third in a short series of papers on measurement theory and practice with particular relevance to research in nursing, midwifery, and healthcare. In this paper I demonstrate how the decisions we make regarding the post hoc treatment of our measurements impact the quality of our data and influence the validity of the inferences we draw from them. I address two variations of this practice, pooling data over response options found on self-report measures, and transforming measurements of continuous variables, such as age, into ranges or ordered categories. The problems inherent in this practice are examined using concepts from information theory. Pooling more precise measurements into less precise ones creates errors of discreteness that introduce unpredictable (positive or negative) bias in our results.