On the Illusion of the Normal Distribution

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The normal distribution is often treated in psychology as a useful approximation to the empirical world. This talk argues that this thinking shapes or "warps" psychologists' intuitions around uncertainty. Much of psychological science treats the covariance (or correlation) matrix as if it captured the dependence structure of the data. In copula terms, this amounts to an implicit commitment to elliptical copulas, where dependence is governed by a correlation matrix (with the Gaussian copula functioning as the default). In this talk, I present three claims.

First, the adoption of Gaussian thinking in the social sciences has more to do with epistemic and historical reasons than scientific ones. Gauss’ error/least-squares logic, Quetelet’s “social physics,” and Galton’s correlation-based view of variation helped turn the normal curve into a model of the world rather than a local approximation.

Second, many psychological data-generating processes violate the mechanisms that make this Gaussian or elliptical worldview plausible. Common measures are discrete, bounded, and subject to ceiling or floor effects, and the Central Limit Theorem (CLT) can converge too slowly to justify normal approximations in realistic sample sizes. More importantly, even when univariate marginals look acceptable, dependence can depart sharply from ellipticity via mixtures, selection, and tail dependence.

Third, many common workflows in psychology (e.g., regression, latent variable modeling, corrections for range restriction or attenuation, etc..) inherit this elliptical-copula scaffold because they operationalize structure primarily through covariances. Through simulations that break ellipticity while holding Pearson correlations constant, I show how standard analyses can remain numerically stable yet scientifically misleading, and I outline practical diagnostics and alternatives when dependence itself is the scientific target.