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The Law of Categorical Judgment (Corrected) and the Interpretation of Changes in Psychophysical Performance

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Title: The Law of Categorical Judgment (Corrected) and the Interpretation of Changes in Psychophysical Performance
Language: English
Authors: Rosner, Burton S., Kochanski, Greg
Source: Psychological Review. Jan 2009 116(1):116-128.
Availability: American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002-4242. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org/publications
Peer Reviewed: Y
Physical Description: PDF
Page Count: 13
Publication Date: 2009
Document Type: Journal Articles
Reports - Descriptive
Descriptors: Probability, Rating Scales, Criteria, Value Judgment
DOI: 10.1037/a0014463
ISSN: 0033-295X
Abstract: Signal detection theory (SDT) makes the frequently challenged assumption that decision criteria have no variance. An extended model, the Law of Categorical Judgment, relaxes this assumption. The long accepted equation for the law, however, is flawed: It can generate negative probabilities. The correct equation, the Law of Categorical Judgment (Corrected), is derived; the SDT rating model is a special case. An example shows how to invert the Law of Categorical Judgment (Corrected) numerically, thereby extracting estimates of signal and criterion density parameters and their confidence limits from rating data. The SDT rating model predicts linear z-transformed operating characteristics (zROCs), whereas the new equation can produce nonlinear zROCs. For single-criterion experiments (e.g., yes/no, two-alternative forced choice), however, the corrected law yields identical d' values and linear zROCs whether criterion variance is nonzero or zero. Performance differences observed in such experiments can always be attributed equally well to altered perceptual sensitivity or to modified criterion variance. The Law of Categorical Judgment (Corrected) offers to resolve this ambiguity through rating experiments. (Contains 3 figures and 2 tables.)
Abstractor: As Provided
Number of References: 47
Entry Date: 2009
Accession Number: EJ827125
Database: ERIC
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  Data: American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002-4242. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: order@apa.org; Web site: http://www.apa.org/publications
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  Data: Signal detection theory (SDT) makes the frequently challenged assumption that decision criteria have no variance. An extended model, the Law of Categorical Judgment, relaxes this assumption. The long accepted equation for the law, however, is flawed: It can generate negative probabilities. The correct equation, the Law of Categorical Judgment (Corrected), is derived; the SDT rating model is a special case. An example shows how to invert the Law of Categorical Judgment (Corrected) numerically, thereby extracting estimates of signal and criterion density parameters and their confidence limits from rating data. The SDT rating model predicts linear z-transformed operating characteristics (zROCs), whereas the new equation can produce nonlinear zROCs. For single-criterion experiments (e.g., yes/no, two-alternative forced choice), however, the corrected law yields identical d' values and linear zROCs whether criterion variance is nonzero or zero. Performance differences observed in such experiments can always be attributed equally well to altered perceptual sensitivity or to modified criterion variance. The Law of Categorical Judgment (Corrected) offers to resolve this ambiguity through rating experiments. (Contains 3 figures and 2 tables.)
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