Optimal dichotomization of bimodal Gaussian mixtures

Yan-ni Jhan, Wan-cen Li, Shin-hui Ruan, Jia-jyun Sie and Iebin Lian ()
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Yan-ni Jhan: National Changhua University of Education
Wan-cen Li: National Changhua University of Education
Shin-hui Ruan: National Changhua University of Education
Jia-jyun Sie: National Changhua University of Education
Iebin Lian: National Changhua University of Education

Statistical Papers, 2024, vol. 65, issue 5, No 25, 3285-3301

Abstract: Abstract Despite criticism for loss of information and power, dichotomization of variables is still frequently used in social, behavioral, and medical sciences, mainly because it yields more interpretable conclusions for research outcomes and is useful for decision making. However, the artificial choice of cut-points can be controversial and needs proper justification. In this work, we investigate the properties of point-biserial correlation after dichotomization with underlying bimodal Gaussian mixture distributions. We propose a dichotomous grouping procedure that considers the largest standardized difference in group mean while minimizing information loss.

Keywords: Categorization; Information loss; Distributional method; Bimodality; 62F07; 62P10; 62E15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01521-1

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