High inter-measure correlation can conceal systematic, non-random measurement divergence.

Evidence

Nevertheless, we have seen that a high correlation can mask clear and significant differences that exist between the family resemblance and essentialist measure structures. These differences are neither random nor due to measurement error. They are systematic and coherent in character. The ceiling effect of the necessary condition structure has multiple ramifications, in terms of reduced means, reduced variances, systemically lower values, and extensive disagreement on categorization. — Gary Goertz, Social Science Concepts, 824

Categorization

• DEEPTHINKING: Undercuts the common practice of validating measures by correlation alone — a genuinely destabilizing point for anyone building indices.