Bivariate median splits and spurious statistical significance.

Abstract

Despite pleas from methodologists, researchers often continue to dichotomize continuous predictor variables. The primary argument against this practice has been that it underestimates the strength of relationships and reduces statistical power. Although this argument is correct for relationships involving a single predictor, a different problem can arise when multiple predictors are involved. Specifically, dichotomizing 2 continuous independent variables can lead to false statistical significance. As a result, the typical justification for using a median split as long as results continue to be statistically significant is invalid, because such results may in fact be spurious. Thus, researchers who dichotomize multiple continuous predictor variables not only may lose power to detect true predictor-criterion relationships in some situations but also may dramatically increase the probability of Type I errors in other situations. For many years, behavioral statisticians have chided psychological researchers for artificially dichotomizing continuous variables. Despite many such methodological pleas (e.g., Cohen, 1983,1990; Humphreys, 1978; McNemar, 1969, pp. 444449), the ubiquitous median split has retained its popularity in many areas of psychology. Indeed, some well-known psychological theories such as the Type A/Type B personality distinction, the reflection/impulsivity distinction, and the models of sex roles discussed by Bern (1977) and Spence and Helmreich (1978) are based on forming dichotomies from continuous scores obtained from psychological instruments. Studies have demonstrated that dichotomization is not just an abstract methodological issue but can in fact greatly impact the interpretation of empirical results (e.g., Block, Block, & Harrington, 1974; Lubinski, Tellegen, & Butcher, 1983; Spence, 1983; Tellegen & Lubinski, 1983). Why have researchers continued to ignore methodologists' advice not to dichotomize their measures? Certainly one obvious reason is that data analysis procedures are generally somewhat simpler for dichotomous measures than for continuous measures. A common defense on the part of researchers is that as long as they can obtain statistical significance with a dichotomous measure, why should they have to bother with the more complicated statistical technique likely to be required by using a continuous measure? Underlying this argument is an implicit assumption that the effect of artificially dichotomizing a continuous measure is necessarily to lower the power of obtaining statistical significance. In fact, various methodologists have noted that dichotomizing a continuous measure in effect throws away information because individuals within a subgroup are treated as if they were identical with respect to the attribute in question, when there is evidence to the contrary. This loss of information typically re

Cites (31)

1. Statistical power analysis for the behavioral sciences
   1990 · Computers, Environment and Urban Systems
2. Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
   Lachenbruch, Peter A., Cohen, Jacob · 1989 · Journal of the American Statistical Association
3. Multiple regression: testing and interpreting interactions
   1992 · Choice Reviews Online
4. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
   Cohen, Patricia, Cohen, Patricia, West, Stephen G., Aiken, Leona S. · 2014 · Psychology Press eBooks
5. Untitled work
   1991
6. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences.
   Tufte, Edward R., Cohen, Jacob, Cohen, Patricia · 1979 · Journal of the American Statistical Association
7. Journal of the Royal Statistical Society (B)
   Fildes, Robert · 1993 · International Journal of Forecasting
8. Interaction Effects in Multiple Regression.
   Richardson, S. C., Jacard, J., Turrisi, R., Wan, C. K. · 1991 · The Statistician
9. Masculinity & femininity: Their psychological dimensions, correlates, and antecedents
   JANET TAYLOR SPENCE, Robert L. Helmreich · 1978 · Medical Entomology and Zoology
10. The Cost of Dichotomization
    Cohen, Jacob · 1983 · Applied Psychological Measurement

Show all 31 references

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