A paradox in the interpretation of group comparisons.
Abstract
It is common practice in behavioral research, and in other areas, to apply the analysis of covariance in the investigation of preexisting natural groups. The research worker is usually interested in some criterion variable (y) and would like to make allowances for the fact that his groups are not matched on some important independent variable or control variable (x). The situation is such that observed differences in the dependent variable might logically be caused by differences in the independent variable, and the research worker wishes to rule out this possibility. It is widely recognized that ideally the research worker should assign cases or individuals at random to the groups that are to be studied by analysis of covariance. In behavioral research and in many other areas, such random assignment is usually difficult or impossible—as, for example, in a com-
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
An ANCOVA controlling for pre-intervention differences would indicate a benefit of the intervention for the treatment group despite no improvement from the intervention (Lord's paradox).
“An ANCOVA controlling for pre-intervention differences would indicate a benefit of the intervention for the treatment group despite no improvement from the intervention (i.e., Lord's paradox, Lord, 1967; see also Wright, 2006).”
From Do growth mindset interventions impact students’ academic achievement? A systematic review and meta-analysis with recommendations for best practices. (2023) · cites this paper as Lord, 1967
Cited by
Sorted by citations
Bias in cross-sectional analyses of longitudinal mediation
Maxwell, S. E., & Cole, D. A. (2007) · Psychological Methods · doi:10.1037/1082-989x.12.1.23 · Cited by 3,401 · see citing works
Latent Variable Modeling of Differences and Changes with Longitudinal Data
McArdle, J. J. (2009) · Annual Review of Psychology · doi:10.1146/annurev.psych.60.110707.163612 · Cited by 1,952 · see citing works
Why IQ is not a covariate in cognitive studies of neurodevelopmental disorders
DENNIS, M., FRANCIS, D. J., CIRINO, P. T., SCHACHAR, R., BARNES, M. A., & FLETCHER, J. M. (2009) · Journal of the International Neuropsychological Society · doi:10.1017/s1355617709090481 · Cited by 875 · see citing works
Van Breukelen, G. J. P. (2006) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2006.02.007 · Cited by 765 · see citing works
Macnamara, B. N., & Burgoyne, A. P. (2023) · Psychological Bulletin · doi:10.1037/bul0000352 · Cited by 415 · see citing works
The Perils of Partialling: Cautionary Tales from Aggression and Psychopathy
Lynam, D. R., Hoyle, R. H., & Newman, J. P. (2006) · Assessment · doi:10.1177/1073191106290562 · Cited by 402 · see citing works
Gola, H., Engler, H., Sommershof, A., Adenauer, H., Kolassa, S., Schedlowski, M., Groettrup, M., Elbert, T., & Kolassa, I.-T. (2013) · BMC Psychiatry · doi:10.1186/1471-244x-13-40 · Cited by 225 · see citing works
Valente, M. J., & MacKinnon, D. P. (2017) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705511.2016.1274657 · Cited by 173 · see citing works
CONSIDERATIONS FOR STUDIES OF TEST BIAS
LINN, R. L., & WERTS, C. E. (1971) · Journal of Educational Measurement · doi:10.1111/j.1745-3984.1971.tb00898.x · Cited by 113 · see citing works
What does It take to Show that a Cognitive Training Procedure is Useful?
Jacoby, N., & Ahissar, M. (2013) · Progress in Brain Research · doi:10.1016/b978-0-444-63327-9.00004-7 · Cited by 30 · see citing works
Kane, M. J., Core, T. J., & Hunt, R. R. (2010) · Psychonomic Bulletin & Review · doi:10.3758/pbr.17.2.206 · Cited by 23 · see citing works
- Authors
- Lord, F. M.
- Affiliations
- Educational Testing Service (US)
- Corresponding author
- Lord, Frederic M.
- ORCID
- Lord, Frederic M.
- Venue
- Psychological Bulletin
- Published
- 1967
- Volume
- 68
- Issue
- 5
- Pages
- 304-305
- ISSN
- 0033-2909 (ISSN-L)
- 1939-1455
- OpenAlex
- W2055127135
- Cited by
- 627
- References
- 0
- Citations by year
- 2026: 25 · 2025: 10 · 2024: 11 · 2023: 13 · 2022: 16 · 2021: 17 · 2020: 30 · 2019: 28 · 2018: 17 · 2017: 25 · 2016: 18 · 2015: 20 · 2014: 20 · 2013: 20 · 2012: 16
- FWCI
- 13.28
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Bulletin (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- covariance analysis, group comparison, random assignment, control variables, confounding, statistical interpretation, behavioral research
- MeSH terms
- Behavior, Humans, Psychological Tests, Sex Factors, Statistics as Topic
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 ›
Are you an author, or do you see a problem with this page? Request a review
