The DOI matches its Crossref record.
The $\chi^2$ Test of Goodness of Fit
Open accessAbstract
This paper contains an expository discussion of the chi square test of goodness of fit, intended for the student and user of statistical theory rather than for the expert. Part I describes the historical development of the distribution theory on which the test rests. Research bearing on the practical application of the test--in particular on the minimum expected number per class and the construction of classes--is discussed in Part II. Some varied opinions about the extent to which the test actually is useful to the scientist are presented in Part III. Part IV outlines a number of tests that have been proposed as substitutes for the chi square test (the $\omega^2$ test, the smooth test, the likelihood ratio test) and Part V a number of supplementary tests (the run test, tests based on low moments, subdivision of chi square into components).
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Boateng, G. O., Neilands, T. B., Frongillo, E. A., Melgar-Quiñonez, H. R., & Young, S. L. (2018) · Frontiers in Public Health · doi:10.3389/fpubh.2018.00149 · Cited by 5,925
Assessing heterogeneity in meta-analysis: Q statistic or I² index?
Huedo-Medina, T. B., Sánchez-Meca, J., Marín-Martínez, F., & Botella, J. (2006) · Psychological Methods · doi:10.1037/1082-989x.11.2.193 · Cited by 4,256
Some Methods for Strengthening the Common χ 2 Tests
Cochran, W. G. (1954) · Biometrics · doi:10.2307/3001616 · Cited by 3,718
Self-citationEgo depletion and the strength model of self-control: a meta-analysis
Hagger, M. S., Wood, C., Stiff, C., & Chatzisarantis, N. L. D. (2010) · Psychological Bulletin · doi:10.1037/a0019486 · Cited by 2,265
A checklist for testing measurement invariance
van de Schoot, R., Lugtig, P., & Hox, J. (2012) · European Journal of Developmental Psychology · doi:10.1080/17405629.2012.686740 · Cited by 2,064
Metadata
- Authors
- Cochran, W. G.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1952-09
- Volume
- 23
- Issue
- 3
- Pages
- 315-345
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2018913979
- Cited by
- 1,106
- References
- 0
- FWCI
- 7.52
- Type
- journal article
- Language
- en
- Open access
- bronze
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The $\chi^2$ Test of Goodness of Fit. https://app.cochat.ai/papers/10.1214/aoms/1177729380
- The paper
- Cochran, W. G. (1952). The $\chi^2$ Test of Goodness of Fit. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177729380
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
