Multivariate Versus Univariate Conceptions of Sex Differences: Let the Contest Begin

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Richard A. Lippa

The following guest post is written by Professor of Psychology, Richard A. Lippa. Dr. Lippa is a professor at California State University, Fullerton and is also a peer reviewer for PLoS ONE. In the following opinion piece, he comments on the paper, The Distance Between Mars and Venus: Measuring global sex differences in personality, which published in PLoS ONE today.

In their paper, “The Distance Between Mars and Venus: Measuring global sex differences in personality,” Del Giudice, Booth, and Irwing offer an interesting new perspective on sex differences and a useful critique of Hyde’s gender similarities hypothesis [1]. At core, Del Giudice and his colleagues ask: What is the proper metric to use when assessing sex differences in multivariate domains? They nominate the Mahalanobis D statistic—the multivariate generalization of the d statistic—as the best metric to assess sex differences in multi-trait individual differences domains such as personality, cognitive abilities, and interests, and they show empirically that, while on-average sex differences in traits from a given domain (e.g., personality) may be relatively small, the multivariate effect size (D) can simultaneously be quite large.

By way of analogy, consider sex differences in body shape. The Hyde “gender similarities” approach would assess specific traits—e.g., shoulder-waist ratios, waist-hip ratios, torso-to-leg-length ratios, etc.—and then average the d values across these traits, to arrive at the likely conclusion that men and women are more similar than different in body shape. In contrast, the Del Giudice, Booth, and Irwing multivariate approach would more likely generate the conclusion that sex differences in human body shape are quite large, with men and women having distinct multivariate distributions that overlap very little.

Which conclusion is correct? Although there are no God-given prescriptions for proper metrics of effect size, my guess is that lay people would agree more with the Mahalonobis D than with the “mean d” result—i.e., if asked to classify actual human body outlines as “male” or “female,” lay people would likely achieve extremely high levels of accuracy by intuitively aggregating across various body-shape dimensions and making “multivariate,” configural judgments, despite the fact that ds for some individual body traits might be low.

In advocating the use of the Mahalanobis D statistic, Del Giudice, Booth, and Irwing seem, to me, to be advocating the notion that sex differences in various domains are often multivariate and configural in nature. Such a multivariate approach is especially important in research that explores how well sex differences in personality, cognitive abilities, and interests predict sex differences in real-life criteria, such as participation in STEM (science, technology, engineering, and math) fields, susceptibility to mental and physical illnesses, and the tendency to engage in antisocial behaviors.

For example, to adequately explain men’s and women’s different participation in STEM fields, researchers need to consider sex differences in a variety of cognitive ability domains: various visuospatial skills, math abilities, mechanical aptitudes, and so on. A still more complete account would focus on sex differences in interests and personality as well. Men’s interests are, on average, considerably more thing-oriented and less people-oriented than women’s interest are, and women exceed men some on personality traits (e.g., agreeableness, warmth) that may not always find satisfying expression in STEM fields [2, 3].

This discussion of predicting real-life criteria leads to the two additional methodological recommendations made by Del Giudice, Booth, and Irwing: When assessing sex differences in psychological traits, researchers should ensure that (1) trait measures are reliable, and (2) traits are measured at the proper level of specificity. Regarding point (1): Although many gender researchers may not have the statistical expertise or inclination to compute latent factor measures, they nonetheless need to recognize that unreliable trait measures can attenuate sex differences and they must statistically correct for the unreliability of measures, when possible [4].

One nice feature of Del Guidice, Booth, and Irwing’s recommendations is that they can be put to an empirical test. This can be illustrated by research on how well sex differences in personality account for sex differences in antisocial behavior [5]. Del Giudice, Booth, and Irwing suggest that, because of their finer resolution, Big Five facet scores will predict sex differences in antisocial behavior better than Big Five factor scores. This is a testable proposition. They also suggest that when researchers predict sex differences in antisocial behavior from personality measures, they need to employ a multivariate approach to personality. Research shows that sex differences in a number of personality traits—e.g., components of agreeableness, conscientiousness, and neuroticism—contribute to sex differences in antisocial behavior [5]. Thus, the large sex differences in antisocial behavior that are apparent in everyday life probably reflect large multivariate sex differences in personality (in keeping with Del Guidice, Booth, and Irwing’s approach). Clearly, the power of the multivariate approach to predict sex differences in criteria such as antisocial behavior is open to empirical investigation.

It is ironic that while the “gender similarities hypothesis” has gained currency among some psychologists, many biological and medical researchers appear to be moving in the opposite direction, increasingly emphasizing the importance of sex differences in various physiological and disease processes [6]. Would biological and medical researchers entertain the Hydean proposition that “males and females are similar on most, but not all, biological variables”?  On some level, this assertion seems to be true but, as Del Giudice, Booth, and Irwing note, its truth value depends critically on the specific domain of sex differences under study and on the metric of similarity and difference that researchers use. In practical terms, Hyde’s vague “gender similarities hypothesis” will probably provide cold comfort to men and women seeking sound and specific medical advice concerning their heart disease, autoimmune disorders, or medication levels. In biology and medicine, as in psychology, I believe it will prove useful to take a multivariate approach to sex-linked traits in various domains, to acknowledge that some sex differences are small while others are large, and to keep one’s eye on the criteria that need to be predicted rather than on broad ideological statements.

Del Giudice, Booth, and Irwing’s title employs the much-used “Mars and Venus” metaphor, suggesting a seemingly astronomical separation between the sexes. This is undoubtedly an exaggeration, reflecting a kind of poetic license. Hyde prefers to speak of the distance between North Dakota and South Dakota. However, her metaphor may, inadvertently, reflect a truth she is unwilling to acknowledge: that if you travel from the multivariate “centroid” of one state to the other, you’ll still have a mighty long way to walk.


1. Hyde JS (2005). The gender similarities hypothesis. Amer Psychologist 60: 581-592.
2.Lippa RA (2005). Gender, nature, and nurture. Mahwah, NJ: Lawrence Erlbaum Associates.
3.Su R, Rounds J, Armstrong PI (2009). Men and things, women and people: A meta-analysis of sex differences in interests. Psych Bull, 135, 859-884.
4.Lippa RA (2006). The gender reality hypothesis. Amer. Psychologist 61: 639-640.
5.Moffit TE, Caspi A, Rutter M, Silva PA (2001). Sex differences in antisocial behavior. Cambridge, England: Cambridge University Press.
6.Blair ML (2007). Sex-based differences in physiology: What should we teach in the medical curriculum? Adv Physiol Educ, 31, 23-25.

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