Complex span and the n-back lack convergent validity as measures of working memory: Reply to Wilhelm et al. (2025)

In our target article, "Which Working Memory Are We Talking About? N-Back vs. Complex Span Tests," we analyzed data from 1,272 participants and demonstrated that complex span and n-back tasks lack convergent validity as measures of working memory. Evidence for their dissociation included 1) exploratory factor analyses revealing two distinct factors with near-zero cross-loadings, 2) confirmatory factor analyses showing these factors share one-fifth of their reliable variance, and 3) both factors correlating more strongly with fluid intelligence than with each other. Structural equation modeling demonstrated that n-back and complex span factors each explained significant unique variance in fluid intelligence (24% and 14% respectively), beyond their jointly explained variance (30%). These findings align with previous meta-analytic results and support a theoretical framework where complex span tasks emphasize information maintenance while n-back tasks require rapid disengagement from outdated information. Our analyses extended beyond method-specific effects by replicating these results at the broader construct level with additional measures of updating and working memory capacity. In their commentary, Wilhelm et al.'s alternative single-factor model suggests a near-perfect association between working memory and fluid intelligence (β = .97). Their model relies on inconsistently applied correlated error terms selected through a data-driven approach. Notably, modification indices suggest improvements to their model that would bring it closer to our two-factor structure, consisting of clusters of measures representing working memory capacity on one hand and updating on the other. Recognizing these distinctions advances our understanding of cognitive abilities and helps avoid the jingle fallacy.