Some behavioral researchers occasionally wish to conduct a median split on a continuous variable and use the result in subsequent modeling to facilitate analytic ease and communication clarity. Traditionally, this practice of dichotomization has been criticized for the resulting loss of information and reduction in power. More recently, this practice has been criticized for sometimes producing Type I errors for effects regarding other terms in a model, resulting in a recommendation of the unconditional avoidance of median splits. In this paper, we use simulation studies to demonstrate more thoroughly than has been shown in the literature to date when median splits should not be used, and conversely, to provide nuance and balance to the extant literature regarding when median splits may be used with complete analytical integrity. For the scenario we explicate, the use of a median split is as good as a continuous variable. Accordingly, there is no reason to outright reject median splits, and oftentimes the median split may be preferred as more parsimonious.

The objective of this study was to investigate the effects of bovine respiratory disease (BRD) complex on economically important production traits with the use of health records in combination with lung lesion scores obtained at slaughter. Records from 5,976 animals were used in this study from cattle that were managed in Midwestern feedlots. Average daily gain for 3 different feeding periods (acclimation, on-test, and overall test) along with final BW were evaluated as performance measures. Hot carcass weight, LM area, subcutaneous fat cover, and marbling score were collected at slaughter. All calves were monitored by experienced feedlot personnel and treated according to the specific health protocol of each feedlot. Incidence of BRD was observed at a rate of 8.17%, and lung lesions at slaughter were present in 61.9% of cattle from a subpopulation (n = 1,665). From this group of cattle, the overall incidence of BRD, which was defined as cattle that had lung lesions, that were treated for BRD in the feedlot, or both, was 64.4%. Incidence of BRD in the feedlot decreased ADG during both the acclimation period (0.37 +/- 0.03 kg) and the overall test period (0.07 +/- 0.01 kg). Incidence of BRD also had significant effects on HCW and marbling score with reduction of 8.16 +/- 1.38 kg and 0.13 +/- 0.04, respectively, in treated cattle. The adverse effects on production traits tended to increase as the number of treatments increased. Potential decrease in performance and carcass merit observed in this study were associated with a decline of $23.23, $30.15, and $54.01 in carcass value when comparing cattle never treated with cattle treated once, twice, or 3 or more times, respectively. The presence of lung lesions did not have a significant effect on any of the traits; however, there was an association between the presence of active bronchial lymph nodes and less productivity of feedlot cattle.

There seems to be confusion among researchers regarding whether it is good practice to center variables at their means prior to calculating a product term to estimate an interaction in a multiple regression model. Many researchers use mean centered variables because they believe it's the thing to do or because reviewers ask them to, without quite understanding why. Adding to the confusion is the fact that there is also a perspective in the literature that mean centering does not reduce multicollinearity. In this article, we clarify the issues and reconcile the discrepancy. We distinguish between Bmicro^and Bmacro^definitions of multicollinearity and show how both sides of such a debate can be correct. To do so, we use proofs, an illustrative dataset, and a Monte Carlo simulation to show the precise effects of mean centering on both individual correlation coefficients as well as overall model indices. We hope to contribute to the literature by clarifying the issues, reconciling the two perspectives, and quelling the current confusion regarding whether and how mean centering can be a useful practice.

In this rebuttal, we discuss the comments of Rucker, McShane, and Preacher (2015) and McClelland, Lynch, Irwin, Spiller, and Fitzsimons (2015). Both commentaries raise interesting points, and although both teams clearly put a lot of work into their papers, the bottom line is this: our research sets the record straight that median splits are perfectly acceptable to use when independent variables are uncorrelated. The commentaries do a good job of furthering the discussion to help readers better develop their own preferences, which was the purpose of our paper. In the final analysis, neither of the commentaries pose any threat to our findings of the statistical robustness and valid use of median splits, and accordingly we can reassure researchers (and reviewers and journal editors) that they can be confident that when independent variables are uncorrelated, it is totally acceptable to conduct median split analyses.

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