Computing weighted Success, failure, and absence rates in education: an application of a general theory of rate comparison

his paper proposes a methodological framework for computing weighted success, failure, and absence rates in education as an application of a general theory of rate comparison. The study shows that the classical success rate is structurally a relative proportion computed on variable local bases. While descriptively valid within each entity, its comparative interpretation becomes problematic when entity sizes differ. In heterogeneous cohorts, identical percentages may correspond to very different quantitative contributions, and ranking divergences emerge from the measurement architecture rather than from performance inconsistencies. To address this limitation, the paper introduces a normalization framework based on a common structural reference — the cohort average enrollment (EM). By defining weighted entity-level rates (TPRi, TPEi, TPAi), local proportions are transformed into directly comparable structural contributions expressed within a shared measurement space. The framework establishes a micro–macro coherence theorem demonstrating that the arithmetic mean of entity-level weighted rates is exactly equal to the cohort weighted mean. Numerical applications show that divergences between relative and weighted rankings increase with structural heterogeneity and disappear under homogeneity conditions. The proposed approach does not replace classical relative rates; it clarifies their domain of validity and provides a complementary metric suitable for comparison, evaluation, and governance in heterogeneous educational contexts. More broadly, the article contributes to a general theory of rate computation and comparison, highlighting that the choice of denominator determines the conditions of comparability across domains such as education, economics, finance, health, and public policy.