Two Provinces of Thirty-Eight: When a Correlation Is an Artefact of Its Outliers

Abstract

A correlation of 0.4893 between provincial primary and tertiary-age school participation in Indonesia falls to 0.0178 when two of the thirty-eight provinces are removed. This article uses that case to show how a cheap and rarely reported diagnostic identifies such failures. Using Central Statistics Agency figures for 2025 and 2023 covering all thirty-eight provinces, it computes both Pearson and Spearman correlations for four relationships in Indonesian education data. Three behave normally: participation at ages sixteen to eighteen against ages nineteen to twenty-three gives 0.7337 and 0.6615, primary against upper secondary completion gives 0.6725 and 0.6067, and the two dimensions of the national literacy index give 0.9462 and 0.8807. The fourth does not: primary against tertiary-age participation gives 0.4893 against a Spearman value of 0.0734, a gap of 0.4159. Deleting single observations confirms the diagnosis, with Papua Pegunungan alone moving the coefficient by 0.1489 and Papua Tengah by 0.1003; removing both leaves 0.0178. The article argues that a Pearson-Spearman gap of this size is a sufficient signal to investigate, that the appropriate response is to report both coefficients and the influential observations rather than to delete them, and that the influential provinces are usually the substantively important ones.