Tis Not, Tis Not – Tis So, Tis So : Rebuttal of Rebuttal by Iacobucci, Posavac, Kardes, Schneider, and Popovich (2015) on the Appropriateness of Median Splits

Iacobucci, Posovac, Kardes, Schneider, and Popavich (2015a) published a defense of median splits. We (McClelland, Lynch, Irwin, Spiller, and Fitzsimons 2015) and Rucker, McShane, and Preacher (2015) published criticism of each of the key conclusions from Iacobucci et al. Iacobucci et al. (2015b) then prepared a rebuttal. Iacobucci et al. believe that we have misunderstood their points, and we believe that they have misunderstood ours. Iacobucci et al. were given the last word in the pages of Journal of Consumer Psychology. We will use this SSRN outlet to say why the claims in their rejoinder are either incorrect or miss the point of our criticisms. First when only significant results are published, the fraction of published findings that are type 1 errors are a direct function of power divided by type 1 error rate. Second, Iacobucci et al. stress that their simulations were intended to apply to the case of zero multicollinearity; but in the real world with random assignment of subjects to conditions, the correlation between the median split variable and the treatment dummy can be substantial, particularly with small sample sizes. Third, they are incorrect to assert that in a moderated regression model with predictors X, Z, and X*Z it is not possible to get an effect of X or X*Z that is significant using median splits but not significant using continuous X. Finally, they ignore our point that the median split will bias the parameter estimate of the interaction in cases where it is in fact non-zero. We stand by every point in our original critique