Sex Differences in Piaget's Water Level Tasks: A Systematic Review and Multiverse Meta-Analysis

Jean Piaget developed the water level tasks (WLTs) to investigate emerging Euclidean spatial concepts of horizontality invariance in children, expecting universal mastery by about age nine. However, it has been shown that even adults have difficulties solving these tasks, with men on average outperforming women. While this effect has repeatedly been replicated, its generalizability remains unclear. Here, we meta-analytically synthesized the retrievable evidence for sex differences in WLT performance (1964-2025, 267 samples, N = 38,000+). Potential effect moderators were examined via subgroup analysis, precision-weighted meta-regression, and (multiverse-style) specification-curve and combinatorial meta-analysis, accounting for numerous reasonable decisions regarding which data to meta-analyze (data multiverse) and how to synthesize them (model multiverse). Results showed medium-to-large-sized male advantages in WLT performance (d = 0.50; 95% CI [0.47, 0.54]) that increased with age. Effect sizes declined across publication years, particularly among adolescents, and were smaller in more recent birth cohorts. Multiverse-style meta-analyses revealed a remarkable generality of this effect across sample characteristics, test variants, and analytic approaches, with 94% of 13,204 models yielding nominally significant male advantages. These findings indicate moderate-to-large, robust, yet cross-temporally declining sex differences in WLT performance, challenging Piaget's idea of a universal understanding of horizontality invariance by late childhood.