The fraternal birth-order effect as a statistical artefact: convergent evidence from probability calculus, simulated data, and multiverse meta-analysis

The fraternal-birth order effect (FBOE) is a research claim which states that each older brother increases the odds of homosexual orientation in men via an immunoreactivity process known as the maternal immune hypothesis. Importantly, older sisters supposedly either do not affect these odds, or affect them to a lesser extent. Consequently, the fraternal birth-order effect predicts that the association between the number of older brothers and homosexual orientation in men is greater in magnitude than any association between the number of older sisters and homosexual orientation. This difference in magnitude represents the main theoretical estimand of the FBOE. In addition, no comparable effects should be observable among homosexual vs heterosexual women. Here, we triangulate the empirical foundations of the FBOE from three distinct, informative perspectives, complementing each other: first, drawing on basic probability calculus, we deduce mathematically that the body of statistical evidence used to make inferences about the main theoretical estimand of the FBOE rests on incorrect statistical reasoning. In particular, we show that throughout the literature researchers ascribe to the false assumptions that effects of family size should be adjusted for and that this could be achieved through the use of ratio variables. Second, using a data-simulation approach, we demonstrate that by using currently recommended statistical practices, researchers are bound to frequently draw incorrect conclusions. And third, we re-examine the empirical evidence of the fraternal birth-order effect in men and women by using a novel specification-curve and multiverse approach to meta-analysis (64 male and 17 female samples, N = 2,778,998). When analyzed correctly, the specific association between the number of older brothers and homosexual orientation is small, heterogenous in magnitude, and apparently not specific to men. In addition, existing research evidence seems to be exaggerated by small-study effects.