Two Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships With Quadratic Regressions

By Uri Simonsohn. Advances in Methods and Practices in Psychological Science, 2018

320 citations recorded by the source corpus.

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-shaped functions are tested almost exclusively via quadratic regressions, an approach that imposes an arbitrary functional-form assumption that in some scenarios can lead to a 100% rate of false positives (e.g., the incorrect conclusion that y = log(x) is U shaped). Estimating two regression lines, one for low and one for high values of x, allows testing for a sign change without a functional-form assumption. I introduce the Robin Hood algorithm as a way to set the break point between the lines. This algorithm delivers higher power to detect U shapes than all the other break-point-setting alternatives I compared with it. The article includes simulations demonstrating the performance of the two-lines test and reanalyses of published results using this test. An app for running the two-lines test is available at http://webstimate.org/twolines.

Subfields: Food Science, Social Psychology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6486fee0a71bc2767af665d2f2c717c3b0a8d2d1

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Citations in the corpus

When Putting Work Off Pays Off: The Curvilinear Relationship between Procrastination and Creativity (2020, unknown): “These conditions can be examined with the two-lines test (Simonsohn, 2018).”
The Dunning-Kruger effect is (mostly) a statistical artefact: Valid approaches to testing the hypothesis with individual differences data (2020, methodology): “Finally, it may be useful to consider novel methods to test for curvilinearity in regression (e.g., Simonsohn, 2018), as opposed to the well-known polynomial (quadratic) regression approach adopted in this investigation.”
Job autonomy and psychological well-being: A linear or a non-linear association? (2021, methodology): “Accordingly, the spline model follows the recommendations of Simonsohn (2018), by estimating whether the slopes of the individual splines that describe the association between the independent and the dependent variable are positive or negative for different levels of the independent variable.”
Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects (2021, methodology): “An opposite incorrect conclusion of an increasing trend could be made if y first increases gradually but then decreases steeply (Simonsohn, 2018, Figures 2, 3).”