The Cost of Dichotomization
Open accessAbstract
Assuming bivariate normality with correlation r, dichotomizing one variable at the mean results in the reduction in variance accounted for to .647r²; and dichotomizing both at the mean, to .405r². These losses, in turn, result in reduction in statistical power equivalent to discarding 38% and 60% of the cases under representative conditions. As dichotomization departs from the mean, the costs in variance accounted for and in power are even larger. Consequences of this practice in measurement applications are considered. These losses may not be quite so large in real data, but since methods are available for making use of all the original scaling information, there is no reason to sustain them.
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Grouping continuous data loses information and may reduce statistical power, especially when dichotomization is used.
“However, grouping loses information and may reduce statistical power [ 87 ] especially when dichotomization is used [ 82 , 85 , 88 ].”
From Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): Explanation and Elaboration (2007) · cites this paper as [87]
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Ek, A., Sorjonen, K., Eli, K., Lindberg, L., Nyman, J., Marcus, C., & Nowicka, P. (2016) · PLoS ONE · doi:10.1371/journal.pone.0147257 · Cited by 154 · see citing works
Managing heteroscedasticity in general linear models.
Rosopa, P., Schaffer, M. M., & Schroeder, A. (2013) · Psychological methods · doi:10.1037/a0032553 · Cited by 153 · see citing works
Li, M., Kennedy, E. B., Byrne, N., Gérin-Lajoie, C., Katz, M. R., Keshavarz, H., Sellick, S., & Green, E. (2017) · Psycho-Oncology · doi:10.1002/pon.4286 · Cited by 151 · see citing works
Mohammed, S. H., Habtewold, T., Birhanu, M. M., Sissay, T. A., Tegegne, B., Abuzerr, S., & Esmaillzadeh, A. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-028238 · Cited by 148 · see citing works
Abar, C. C., Jackson, K. M., Colby, S. M., & Barnett, N. (2014) · Journal of Youth and Adolescence · doi:10.1007/s10964-014-0143-6 · Cited by 148 · see citing works
“were in support of our hypothesis and were particularly striking given the known reduction in predictive power associated with dichotomizing continuous predictors (Cohen 1983).”
ResultSulpizio, S., Maschio, N. D., Mauro, G. D., Fedeli, D., & Abutalebi, J. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.116306 · Cited by 158 · see citing works
“The dichotomization of a continuous variable (e.g., proficiency or use) is in fact well-known to potentially reduce the amount of variance that can be explained, resulting in loss of statistical power and reliability (e.g., Baayen, 2004; Cohen, 1983).”
The Latent Structure of Social Anxiety Disorder: Consequences of Shifting to a Dimensional Diagnosis
Ruscio, A. (2010) · Journal of Abnormal Psychology · doi:10.1037/a0019341 · Cited by 147 · see citing works
“Assessing the full social anxiety continuum may additionally increase power to detect causal relationships and to account for temporal fluctuations in symptoms (cf. Cohen, 1983).”
BackgroundMethodInfluentialMeyer, R. D., Dalal, R. S., & Bonaccio, S. (2009) · Journal of Organizational Behavior · doi:10.1002/job.602 · Cited by 145 · see citing works
“…because both allow meta-analysts to simultaneously test multiple, continuously distributed moderators, whereas subgroup analysis requires that continuously distributed moderators be artificially divided into two or more sub-groups, thereby reducing statistical power (Chaplin, 1991; Cohen, 1983).”
BackgroundChambers, C. G., & Cooke, H. (2009) · Journal of Experimental Psychology. Learning, Memory and Cognition · doi:10.1037/a0015901 · Cited by 143 · see citing works
“…is clearly a nondiscrete phenomenon in the real world, its treatment as a categorical variable is likely to entail a loss of power in statistical inference (e.g., the effect of dichotomizing continuous measures can be equivalent to eliminating one third of the original data; see Cohen, 1983).”
BackgroundJust a Game? Unjustified Virtual Violence Produces Guilt in Empathetic Players
Hartmann, T., Toz, E., & Brandon, M. (2010) · Media Psychology · doi:10.1080/15213269.2010.524912 · Cited by 142 · see citing works
“Following recommendations from related methodological literature (Bissonnette, Ickes, Berstein, & Knowles, 2006; Cohen, 1983; Irwin & McClelland, 2003), we favored a moderated regression over an Analysis of Variance (ANOVA) in order to avoid dichotomization of the empathy variable based on a median…”
MethodIsHak, W. W., Mirocha, J., James, D., Tobia, G., Vilhauer, J., Fakhry, H., Pi, S., Hanson, E., Nashawati, R., Peselow, E. D., et al. (2015) · Acta Psychiatrica Scandinavica · doi:10.1111/acps.12301 · Cited by 140 · see citing works
“A number of authors had criticized categorizing continuous variables (51, 52).”
BackgroundMalhotra, M. K., Singhal, C., Shang, G., & Ployhart, R. E. (2014) · Journal of Operations Management · doi:10.1016/j.jom.2014.01.003 · Cited by 144 · see citing works
“Further, compared with the full sample, power is lower for each sub-group (Cohen, 1983).”
BackgroundRelationship between parental feeding styles and eating behaviours of Dutch children aged 6-7.
Sleddens, E., Kremers, S., de Vries, N. D., & Thijs, C. (2010) · Appetite · doi:10.1016/j.appet.2009.09.002 · Cited by 139 · see citing works
Norris, C. J., Creem, D., Hendler, R. A., & Hedy Kober, A. (2018) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2018.00315 · Cited by 154 · see citing works
“In summarizing the issues with median splits, Aiken and West (1991, p. 4) state that: ‘‘Median splits of continuous variables throw away information, reducing the power of the statistical test: they make it much more difficult to detect significant effects when in fact they do exist (Cohen, 1983).’’”
BackgroundMarelli, M., & Luzzatti, C. (2012) · Journal of Memory and Language · doi:10.1016/j.jml.2012.01.003 · Cited by 127 · see citing works
Rotondi, M., & Donner, A. (2012) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2011.10.019 · Cited by 132 · see citing works
“First, we note that given a fixed number of raters, combining k categories into i!k categories will generally result in a greater required sample size, consistent with the wellknown reduction of efficiency associated with the categorization of continuous variables [25].”
Strøm, H. K., Adolfsen, F., Fossum, S., Kaiser, S., & Martinussen, M. (2014) · Substance Abuse Treatment, Prevention, and Policy · doi:10.1186/1747-597x-9-48 · Cited by 128 · see citing works
“Studies that report categorical or dichotomous data lose one-third to two-thirds of the information on the variance of the sample [74].”
BackgroundPrimer on Risk Assessment and the Statistics Used to Evaluate Its Accuracy
Helmus, L., & Babchishin, K. (2017) · Criminal Justice and Behavior · doi:10.1177/0093854816678898 · Cited by 125 · see citing works
“In the social sciences, Cohen (1988) is often regarded as a credible source of heuristics for interpreting effect sizes.”
BackgroundInfluentialLi, Y., Wei, Z., Jie, Z., Zhang, C., & Liu, Y. (2012) · International Journal of Production Economics · doi:10.1016/j.ijpe.2012.11.008 · Cited by 119 · see citing works
- Authors
- Cohen, J.
- Affiliations
- New York University (US)
- Corresponding author
- Cohen, Jacob
- Venue
- Applied Psychological Measurement
- Publisher
- SAGE Publications
- Published
- 1983-06
- Volume
- 7
- Issue
- 3
- Pages
- 249-253
- ISSN
- 0146-6216 (ISSN-L)
- 1552-3497
- OpenAlex
- W1987838173
- Cited by
- 1,564
- References
- 0
- Citations by year
- 2026: 67 · 2025: 59 · 2024: 59 · 2023: 50 · 2022: 63 · 2021: 66 · 2020: 74 · 2019: 68 · 2018: 91 · 2017: 78 · 2016: 66 · 2015: 79 · 2014: 86 · 2013: 53 · 2012: 60
- FWCI
- 3.58
- Type
- journal article
- Language
- en
- Open access
- green
- purl.umn.edu
- Locations
- Applied Psychological Measurement (publishedVersion)
- University of Minnesota Digital Conservancy (University of Minnesota) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- dichotomization, variable reduction, bivariate normal distribution, correlation, variance accounted for, statistical power, measurement loss, scale reduction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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