Back to Post-publication discussions

Are We Comparing Apples or Squared Apples? The Proportion of Explained Variance Exaggerates Differences Between Effects

Submission status

Submission Editor
Emil O. W. Kirkegaard

Marco Del Giudice

Are we comparing apples or squared apples? The proportion of explained variance exaggerates differences between effects


This brief note addresses a known problem whose implications are still not widely appreciated: using the proportion of explained variance as an index of effect size does not just distort the real-world magnitude of individual effects, but also exaggerates the differences between effects, which may lead to strikingly incorrect judgements of relative importance. Luckily, a meaningful and interpretable “effect ratio” can be easily calculated as the square root of the ratio between proportions of explained variance. In a variety of practical examples, effect ratios tell a different story than variance components, and suggest a different perspective on certain canonical results (e.g., regarding the role of the shared environment in the development of psychological traits). This simple but highly consequential point should be understood more widely, to help researchers avoid fallacious interpretations of empirical findings.

explained variance, variance components, effect size, correlation



Typeset Pdf

Typeset Paper

Reviewers ( 0 / 0 / 2 )
Kevin Quinn: Accept
Anon Anonsen: Accept

Wed 05 May 2021 21:43


Author has updated the submission to version #8


All has been quiet for a while, so to save the reviewers' time, I uploaded an update (#8): I added this paragraph about the breeder's equation to clarify that directly comparing heritabilities can be meaningful in some contexts:

"As an important caveat to the above paragraphs, I wish to stress that there are contexts in which directly comparing heritabilities has a natural, meaningful interpretation. For example, the response of a trait under selection can be predicted with the breeder’s equation R=h^2 S, where S is the selection differential (i.e., the within-generation change in the trait mean), R is the response to selection (i.e., the between-generation change in the trait mean), and h2 is the narrow-sense heritability. In this particular context, the effect of interest—that is, the response to selection—is directly proportional to the heritability; for instance, doubling the heritability of a trait will double its response to the same amount of selection. More generally, I am emphatically not suggesting that the heritability is a meaningless quantity. The point is that the real-world effect of additive genetic factors on a trait (in terms of the trait’s original units) is not quantified by the heritability but by its square root."


Replying to Forum Bot

Author has updated the submission to version #8



The submission was accepted for publication.


Author has updated the submission to version #10