The median split: Robust, refined, and revivedby Dawn Iacobucci, Steven S. Posavac, Frank R. Kardes, Matthew J. Schneider, Deidre L. Popovich

Journal of Consumer Psychology

About

Year
2015
DOI
10.1016/j.jcps.2015.06.014
Subject
Applied Psychology / Marketing

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Journal of Consumer Psychology 25, 4 (20Introduction

In Iacobucci, Posavac, Kardes, Schneider, and Popovich (2015), we had documented the enormous popularity of median splits, in consumer research, psychology, and numerous other fields. We had acknowledged the traditional concerns regarding median splits regarding the loss of information and resulting power. More importantly, we sought to investigate the extent to which the more recently expressed concern about median splits held true, that using median splits may give rise to Type I errors. Our approach was more comprehensive than that of the literature to date because we designed full simulation studies rather than relying on an anecdotal data set.

We found that in the presence of multicollinearity, median splits could indeed result in Type I errors, though the effects were often negligible. The results of our studies were clean and unambiguous; in the absence of multicollinearity, median splits do not create misleading results. We made it clear that the findings were not attributable to the use of an ANOVA vs. the regression model, but rather due to the presence or absence of multicollinearity. If a researcher is running an experiment, such as a typical factorial (or other orthogonal design), then letting a median split serve as a factor is completely legitimate.

In our Discussion section, we mentioned that median splits were not likely to have caused problems in published articles ? The authors are grateful to the Editor, the original submission Area Editor and the Research Dialog Area Editor, and the teams of commentators for their respective roles in this Research Dialog.(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. ? 2015 Society for Consumer Psychology. Published by Elsevier Inc. All rights reserved.

Keywords: Median split; Median-split; Dichotomization; CategorizationIn this rebuttal, we discuss the comments of Rucker, McShane, andAbstract

Preacher (2015) and McClelland, Lynch, Irwin, Spiller, and FitzsimonsDawn Iacobucci a,?, Steven S.

Matthew J. Schneider a Vanderbilt University, b Lindner College of Business, University c Medill School of Journalism, Northwe d Rawls College of Business, Texas Te

Received 17 June 201

Available on? Corresponding author.

E-mail addresses: Dawn.Iacobucci@owen.vanderbilt.edu (D. Iacobucci),

Steve.Posavac@owen.vanderbilt.edu (S.S. Posavac), Frank.Kardes@uc.edu (F.R. Kardes), mattschneids@gmail.com (M.J. Schneider),

Deidre.Popovich@ttu.edu (D.L. Popovich). http://dx.doi.org/10.1016/j.jcps.2015.06.014 1057-7408/? 2015 Society for Consumer Psychology. Published by Elsevier Inc. AArticle refined, and revived? osavac a, Frank R. Kardes b,

Deidre L. Popovich d hville, TN 37203, USA

Cincinnati, Cincinnati, OH 45221, USA n University, Evanston, IL 60201, USA

University, Lubbock, TX 79409, USA ccepted 26 June 2015 3 July 2015 15) 690?704and we explained why. We also explained that our statistical results hold for naturally occurring or experimenter-created groups. We demonstrated that our results held even in the presence of extremely non-normal distributions (e.g., quadratic, ll rights reserved.

Type II error. Although we see some of the issues raised in

Rucker et al.'s commentary differently, we feel that they make a number of well-reasoned arguments regarding Type II error that help to increase the sophistication of the discussion regarding median splits.

Type I and Type II errors

If this discussion is to revolve around Type I and Type II 691umer Psychology 25, 4 (2015) 690?704natural log, bimodal, and uniform). We also entertained the notion of two median splits in a single study, that while such a practice might not seem advisable, in truth, it may well be less problematic than one might first think.

Finally, in our paper, we stated repeatedly and quite clearly that we were not intending to persuade researchers who like their continuous variables to begin dichotomizing. Rather, our study provides support for researchers who like working with median splits due to the beauty of their parsimony, and the ease with which they may be communicated. The findings of

Iacobucci et al. (2015) support those researchers in their preferences for median splits.

Although we suspect that the commentaries as a whole would have added more value if a psychologist or consumer researcher favorable to median splits wrote one of the commentaries, the upside of our having received commentaries written by two teams with a track record of opposition to median splits is that readers can be confident that any possible objection to our results has been generated. Thus, taken together, we are delighted with the commentaries by Rucker,

McShane, and Preacher (2015) and McClelland, Lynch, Irwin,

Spiller, and Fitzsimons (2015), and this opportunity to clarify and reify the fact that median splits are a perfectly valid, and extremely useful analytical tool for researchers. The commentaries offer a range of opinions, from concepts that are absolutely correct on one hand (e.g., Rucker et al.'s points that, all other things being equal, Type I and Type II errors rise and fall in opposition, and that regressions in and of themselves do not support causal statements, or McClelland et al.'s remarks that a median split is known to reduce power), to erroneous on the other (e.g., McClelland et al.'s claim that our simulations were incomplete or incorrect with technical errors, and their false equivalence logical fallacy when appealing to the ESP literature). The styles of the two commentaries are rather different, with the first being deeper and focused, whereas the second is broader. We address the arguments in each commentary in turn, concurring and clarifying as appropriate.