Dichotomization, Partial Correlation, and Conditional Independence

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50 Years of Test (Un)fairness: Lessons for Machine Learning (2018, background): “…π 1 and threshold x ∗ 2 for group π 2 of the test score R given the target variable Y . notion of equal opportunity for those with a given value of Y , an in terms of the correlation ρ AR between the demographic variable holds for every subgroup, then ρ AR = ρ AY / ρ RY [63]. that ρ AR = ρ AY .”
A researcher's guide to regression, discretization, and median splits of continuous variables (2015, background): “(2015), Irwin and McClelland (2003), Lemon (2009), Maxwell and Delaney ), Royston et al. (2006), Streiner (2002), Vargha et al. (1996) 09), Hunter and Schmidt (1990), Lagakos (1988), Morgan and Elashoff (1986) Callum et al. (2002) collinearity is absent should not be accepted as sufficient…”
Spotlights, Floodlights, and the Magic Number Zero: Simple Effects Tests in Moderated Regression (2012, unknown): “…is a substantial loss of statistical power from dichotomizing a single predictor variable (e.g., Irwin and McClelland 2001, 2003; Jaccard et al. 2006; MacCallum et al. 2002), and dichotomizing in multiple predictor models creates spurious effects (Maxwell and Delaney 1993; Vargha et al. 1996).”