Sources of bias in the Goodman–Kruskal gamma coefficient measure of association: Implications for studies of metacognitive processes.
Abstract
In many cognitive, metacognitive, and perceptual tasks, measurement of performance or prediction accuracy may be influenced by response bias. Signal detection theory provides a means of assessing discrimination accuracy independent of such bias, but its application crucially depends on distributional assumptions. The Goodman-Kruskal gamma coefficient, G, has been proposed as an alternative means of measuring accuracy that is free of distributional assumptions. This measure is widely used with tasks that assess metamemory or metacognition performance. The authors demonstrate that the empirically determined value of G systematically deviates from its actual value under realistic conditions. A distribution-specific variant of G, called G-sub(c), is introduced to show why this bias arises. The findings imply that caution is needed when using G as a measure of accuracy, and alternative measures are recommended.
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Masson and Rotello (2009) showed in an extensive simulation study that G is sensitive to the tendency to use higher or lower confidence ratings (bias), and this may lead to erroneous conclusions, such as interpreting a difference in G between groups as reflecting a true underlying difference in metacognitive sensitivity despite possible differences in bias.
“In an extensive simulation study, Masson and Rotello (2009) showed that G was similarly sensitive to the tendency to use higher or lower confidence ratings (bias), and that this may lead to erroneous conclusions, such as interpreting a difference in G between groups as reflecting a true underlying difference in metacognitive sensitivity despite possible differences in bias.”
From How to measure metacognition (2014) · cites this paper as Masson and Rotello (2009)
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- Authors
- Masson, M. E. J., & Rotello, C. M.
- Affiliations
- University of Victoria (CA)
- University of Massachusetts Amherst (US)
- Venue
- Journal of Experimental Psychology: Learning, Memory, and Cognition
- Published
- 2009
- Volume
- 35
- Issue
- 2
- Pages
- 509-527
- ISSN
- 0278-7393 (ISSN-L)
- 1939-1285
- OpenAlex
- W2008182492
- Cited by
- 173
- References
- 57
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 6 · 2023: 14 · 2022: 6 · 2021: 13 · 2020: 9 · 2019: 11 · 2018: 8 · 2017: 12 · 2016: 11 · 2015: 15 · 2014: 18 · 2013: 9 · 2012: 7
- FWCI
- 12.20
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Experimental Psychology Learning Memory and Cognition (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Natural Sciences and Engineering Research Council (7910-03)
- National Institutes of Health (MH60274)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Reliability and Agreement in Measurement
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory Processes and Influences
- Keywords
- response bias, metacognition, metamemory, signal detection theory, discriminatory accuracy, distributional assumptions, bias correction
- MeSH terms
- Association, Culture, Data Interpretation, Statistical, Decision Making, Discrimination, Psychological, Humans, Judgment, Paired-Associate Learning, Psychometrics, Mental Recall, ROC Curve, Reproducibility of Results, Models, Statistical, Bias, Signal Detection, Psychological, Recognition, Psychology
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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