Preprints are early versions of research articles that have not been peer reviewed. They should not be regarded as conclusive and should not be reported in news media as established information.
Two-Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships with Quadratic Regressions
preprintposted on 25.10.2018, 18:28 by Uri Simonsohn
Many psychological theories predict U-shaped relationships: the effect of x is positive for low values of x, but negative for high values, or vice-versa. Despite implying merely a change of sign, hypotheses about U-shapes are tested almost exclusively via quadratic regressions, imposing an arbitrary functional form assumption that can lead to a 100% false-positive rate, e.g., concluding with certainty that y=log(x) is U-shaped. Estimating two regression lines, one for low and one high values of x, allows testing for a sign change without a functional form assumption. To set the breakpoint between the lines, I introduce the Robin Hood algorithm. It delivers higher power to detect U-shapes than all other breakpoint setting alternatives considered. The paper includes simulations and re-analyses of published results. The two-line test can be performed at http://webstimate.org/twolines
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in Advances in Methods and Practices in Psychological Science