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: | |
| 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 |
| 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.) |
|---|---|
| ISSN: | 0033-295X |
| DOI: | 10.1037/a0014463 |
