The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Significance Tests in Discrete Distributions
Abstract
In discrete distributions, it has often been recommended that an auxiliary random experiment should be carried out so as to make the size of the test equal to the significance level. In certain experimental situations, this procedure would be time-consuming and even embarrassing to the statistician. An alternative criterion of significance is suggested, the mid or median probability. To avoid computations P(χ), the probability of the square root of a chi-square variable, can be used in the binomial, Poisson and hypergeometric distributions as an approximation to the mid probability. In statistical control of counting experiments or where experiments are being repeated P(χ) rather than P(χ c ), the probability of χ corrected for continuity, gives acceptable approximations to size of significance levels. Some computations are given for the multinomial distribution which show that here P(χ2) gives acceptable approximations.
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
Cites
Contingency Tables Involving Small Numbers and the χ2 Test
Yates, F. (1934) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.2307/2983604 · Cited by 1,281
The Logic of Inductive Inference
Fisher, R. A. (1935) · Journal of the Royal Statistical Society · doi:10.2307/2342435 · Cited by 1,265
124: The Logic of Inductive Inference.
Fisher, R. A. (1935) · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · Cited by 881
Compounding Probabilities from Independent Significance Tests
Wallis, W. A. (1942) · Econometrica · doi:10.2307/1905466 · Cited by 113
ON QUESTIONS RAISED BY THE COMBINATION OF TESTS BASED ON DISCONTINUOUS DISTRIBUTIONS
PEARSON, E. S. (1950) · Biometrika · doi:10.1093/biomet/37.3-4.383 · Cited by 80
Statistical control of counting experiments
Lancaster, H. O. (1952) · Biometrika · doi:10.1093/biomet/39.3-4.419 · Cited by 55
Self-citationTHE X2 DISTRIBUTION FOR THE BINOMIAL AND POISSON SERIES, WITH SMALL EXPECTATIONS
Cochran, W. G. (1936) · Annals of Eugenics · doi:10.1111/j.1469-1809.1936.tb02140.x · Cited by 38
FURTHER NOTES ON THE χ2 DISTRIBUTION
Neyman, J., & Pearson, E. S. (1931) · Biometrika · doi:10.1093/biomet/22.3-4.298 · Cited by 21
Cited by
Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
Agresti, A., & Coull, B. A. (1998) · The American Statistician · doi:10.1080/00031305.1998.10480550 · Cited by 3,223
Simonsohn, U., Simmons, J. P., & Nelson, L. D. (2020) · Nature Human Behaviour · doi:10.1038/s41562-020-0912-z · Cited by 651
Confidence intervals for a binomial proportion
Vollset, S. E. (1993) · Statistics in Medicine · doi:10.1002/sim.4780120902 · Cited by 477
Fagerland, M. W., Lydersen, S., & Laake, P. (2013) · BMC Medical Research Methodology · doi:10.1186/1471-2288-13-91 · Cited by 403
Exact inference for categorical data: recent advances and continuing controversies
Agresti, A. (2001) · Statistics in Medicine · doi:10.1002/sim.738 · Cited by 162
Metadata
- Authors
- Lancaster, H. O.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1961-06
- Volume
- 56
- Issue
- 294
- Pages
- 223-234
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2042732005
- Cited by
- 272
- References
- 8
- FWCI
- 1.74
- Type
- journal article
- Language
- en
- Open access
- closed
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: Significance Tests in Discrete Distributions. https://app.cochat.ai/papers/10.1080/01621459.1961.10482105
- The paper
- Lancaster, H. O. (1961). Significance Tests in Discrete Distributions. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1961.10482105
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.
