Three Tales of Change

When could it be safe to report ordinal scores instead of linear measures? In this study, preschool gains measured with ordinal scores were compared with residualized gain scores, as well as Rasch model measures of linear change (logits) to clarify respective implications for objectivity, precision, validity, and meaningfulness. Results showed that ordinal scores and linear gains were highly correlated (~.90), and specific conditions were identified such as pre-test score distributions, pre-test variability, and overall test targeting that determine complementarity of ordinal scores and linear scale values for reporting achievement gains. Several properties of ordinal score gains were discussed, including negative correlation between gain and pre-test, unreliability of gains, and usefulness of residualized gains. This report concludes by supporting interchangeability of ordinal scores and objective, linear measures when appraisal of complementarity is supervised by principles of mathematical logic.