The outset of the problem In one of my project, I’d like to show that there is a U-shape relationship between two variables. The traditional way to do this would be to fit a quadratic model and test whether the quadratic term is different from zero. However, Simonsohn (2018) among other correctly points out that evidence for a quadratic fit is not enough and there might be situations where the quadratic term is not zero but there is no true u-shape.
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The problem While analysing the data from our U-shape experiments (see pre-registration for context: https://osf.io/kcr2q), we ran into a peculiar problem. As expected, we did find that memory performance can be described as a U-shape function of how expected a certain object is in certain location. However, we also predicted that the memory advantage for highly incongruent item/locations pairings as well as for highly congruent pairings are driven by different processes.
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