I’ve always thought a physicist considering the non uncommon practice in the social sciences of doing median splits or using discrete cutoffs of a continuous variable would think our practices are crazy and unscientific. Last fall I had the opportunity to observe a confirmation of my hypothesis when a Nobel-prize winning physicist sat on the honors committee of one our psychology students. She was studying reading disability and as is not uncommon in that field, defined the reading disabled as those below the 10th percentile.
The physicist gently but firmly pointed out that surely that was a bad idea and that it would obviously be better to leave a continuous variable as a continuous variable.
So, resist the temptation to split. Leave your continuous variables continuous.
Irwin, J.R., & McClelland, G.H. (2003)
MacCallum R.C., Zhang, S., Preacher, K.J., & Rucker, D.D. (2002).
both provide a lot of the earlier references. I know of no published article using statistical arguments to support splitting continuous variables.
If the relationship is nonlinear, then dividing into two groups, whether the extreme third tails or median splits, precludes any possibility of detecting the nonlinearity. Furthermore, Maxwell & Delaney (Psych Bulletin, 1993, 113, 181-190) demonstrate that obscuring nonlinearity in that way can produce a spurious interaction. Why anyone continues to split data after that article is beyond me, but subsequent articles like the recent MacCollum et al. article in Psych Methods (indeed a gem) remain necessary. Irwin & McClelland (Journal of Marketing Research, forthcoming) squashes another false belief that perhaps median splits are a good idea when the predictor variables are very skewed, non-normal distributions. Even in those situations, splitting the data remains a bad idea.
Gary has also provided a nice visual showing the effect of dichotomization -- check it out at
Dale Glaser added:
Cohen’s oft-cited article: Cohen, J. (1983) The cost of dichotomization. Applied Psychological Measurement, 7, 249-253.
Werner W. Wittmann [firstname.lastname@example.org] contributed:
Both strategies are bare nonsense ( "blanker Unsinn" in the language of your ancestors). Other have said that already, but I have a different reason from a