Rescaling Ordinal Data to Interval Data in Educational Research

Abstract

Many statistical procedures used in educational research are described as requiring that dependent variables follow a normal distribution, implying an interval scale of measurement. Despite the desirability of interval scales, many dependent variables possess an ordinal scale of measurement in which the differences among values composing the scale are unequal in terms of what is being measured, permitting only a rank ordering of scores. This means that data possessing an ordinal scale will not satisfy the assumption of normality needed in many statistical procedures and may produce biased statistical results that threaten the validity of inferences. This article shows how the measurement technique known as item response theory can be used to rescale ordinal data to an interval scale. The authors provide examples of rescaling using student performance data and argue that educational researchers should routinely consider rescaling ordinal data using item response theory.

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