The probabilistic revolution in physics

A researcher's guide to regression, discretization, and median splits of continuous variables

“…Though the null hypothesis significance testing paradigm is the dominant statistical paradigm in academic training and reporting in the biomedical and social sciences (see, for example, Gigerenzer (1987), Gill (1999), Morrison and Henkel (1970), Sawyer and Peter (1983)), this paradigm has received no small degree of criticism over the decades (see, for example, Cohen (1994), Gigerenzer (2004), McShane and Gal (in press), Meehl (1978), Rosnow and Rosenthal (1989), Rozenboom (1960)) and many have argued for a greater focus on effect sizes, their variability, and the uncertainty in estimates of them (see, for example, Cohen (1990), Fidler, Thomason, Cumming, Finch, and Leeman (2004), Gelman (2015), Iacobucci (2005), Kelley and Preacher (2012)). Without entering into this debate here, we note that preserving the continuous nature of the variable and analyzing the data via linear regression is superior to dichotomizing the variable and analyzing the data via ANOVA on both dimensions: the former performs as well or better on Type I and Type II error as discussed above and yields more efficient estimates of effect sizes (Cox, 1957;Gelman & Park, 2009;Lagakos, 1988;Morgan & Elashoff, 1986).…”