A probability-based measure of effect size: Robustness to base rates and other factors.
Abstract
Calculating and reporting appropriate measures of effect size are becoming standard practice in psychological research. One of the most common scenarios encountered involves the comparison of 2 groups, which includes research designs that are experimental (e.g., random assignment to treatment vs. placebo conditions) and nonexperimental (e.g., testing for gender differences). Familiar measures such as the standardized mean difference (d) or the point-biserial correlation (rpb) characterize the magnitude of the difference between groups, but these effect size measures are sensitive to a number of additional influences. For example, R. E. McGrath and G. J. Meyer (2006) showed that rpb is sensitive to sample base rates, and extending their analysis to situations of unequal variances reveals that d is, too. The probability-based measure A, the nonparametric generalization of what K. O. McGraw and S. P. Wong (1992) called the common language effect size statistic, is insensitive to base rates and more robust to several other factors (e.g., extreme scores, nonlinear transformations). In addition to its excellent generalizability across contexts, A is easy to understand and can be obtained from standard computer output or through simple hand calculations.
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The short-term effect size corresponds to a 58.4% chance that a randomly selected score of a student who received the intervention is greater than the score of a randomly selected student who did not.
“This effect size corresponds to a 58.4% chance that a randomly selected score of a student who received the intervention is greater than the score of a randomly selected student who did not”
From Targeted school‐based interventions for improving reading and mathematics for students with or at risk of academic difficulties in Grades K‐6: A systematic review (2021) · cites this paper as Ruscio, 2008
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- Authors
- Ruscio, J.
- Affiliations
- The College of New Jersey (US)
- Corresponding author
- Ruscio, John
- Venue
- Psychological Methods
- Published
- 2008
- Volume
- 13
- Issue
- 1
- Pages
- 19-30
- ISSN
- 1082-989X (ISSN-L)
- 1939-1463
- OpenAlex
- W2012259509
- Cited by
- 398
- References
- 29
- Citations by year
- 2026: 27 · 2025: 44 · 2024: 46 · 2023: 42 · 2022: 34 · 2021: 31 · 2020: 35 · 2019: 33 · 2018: 26 · 2017: 18 · 2016: 14 · 2015: 11 · 2014: 7 · 2013: 9 · 2012: 8
- FWCI
- 4.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Methods (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Keywords
- effect size, standardized mean difference, point-biserial correlation, heteroscedasticity, robustness, two-group comparison
- MeSH terms
- Mental Disorders, Humans, Models, Psychological, Models, Statistical, Effect Modifier, Epidemiologic, Sample Size
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.
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