Cited by 1,564Psychometric Methodologies and TestingStatistical Methods and ApplicationsStatistical Methods and Bayesian Inference

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The Cost of Dichotomization

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Cohen, Jacob·1983·Applied Psychological Measurement

DOI 10.1177/014662168300700301

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Abstract

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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Cohen, J., 1977, Statistical power analysis for the behavioral sciences
Cohen, J., 1983, Applied multiple regression/ correlation analysis for the behavioral sciences
10.1037/h0036539 · DOI
10.1037/13596-000 · DOI

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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
DOI: 10.1177/014662168300700301
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
Licence: journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
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

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The Cost of Dichotomization

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