The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Tests for departure from normality. Empirical results for the distributions of b2 and √b1
Abstract
This paper is a preliminary to a detailed survey of the relative powers of a number of omnibus and directional tests of nonnormality. The probability integrals of √b1 and b2, the standardized third and fourth moment statistics, are found for random samples from a normal distribution. Main attention is given to b2. Extensive computer simulation and curve fitting have been used to provide charts of probability levels out to the 0.1% point, for 20 ≤ n ≤ 200. For √b1, the parameters of Johnson's symmetrical SU approximation are tabled for values of n between 8 and 1000. An illustration is given of two ‘omnibus’ tests applying the charts and table, involving the joint use of √b1 and b2.
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
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
An analysis of variance test for normality (complete samples)
SHAPIRO, S. S., & WILK, M. B. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.591 · Cited by 23,480
Biometrika Tables for Statisticians
Savage, I. R., Pearson, E. S., & Hartley, H. O. (1967) · Mathematics of Computation · doi:10.2307/2004190 · Cited by 1,435
Self-citationA Comparative Study of Various Tests for Normality
Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968) · Journal of the American Statistical Association · doi:10.1080/01621459.1968.10480932 · Cited by 1,185
An Approximate Analysis of Variance Test for Normality
Shapiro, S. S., & Francia, R. S. (1972) · Journal of the American Statistical Association · doi:10.1080/01621459.1972.10481232 · Cited by 1,166
Expected values of normal order statistics
HARTER, H. L. (1961) · Biometrika · doi:10.1093/biomet/48.1-2.151 · Cited by 353
Transformation to normality of the null distribution of g1
D'AGOSTINO, R. B. (1970) · Biometrika · doi:10.1093/biomet/57.3.679 · Cited by 351
Self-citationCONTRIBUTIONS TO THE THEORY OF TESTING STATISTICAL HYPOTHESES
Neyman, J., & Pearson, E. S. (1967) · University of California Press eBooks · doi:10.1525/9780520339897-010 · Cited by 127
Self-citationPearson, E. S. (1938) · Biometrika · doi:10.1093/biomet/30.1-2.134 · Cited by 124
Self-citationSimulation Probability Points of b 2 for Small Samples
D’Agostino, R. B., & Tietjen, G. L. (1971) · Biometrika · doi:10.1093/biomet/58.3.669 · Cited by 55
Self-citation
Cited by
A Test for Normality of Observations and Regression Residuals
Jarque, C. M., & Bera, A. K. (1987) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1403192 · Cited by 3,179
A Suggestion for Using Powerful and Informative Tests of Normality
D'agostino, R. B., Belanger, A., & D'agostino, R. B. (1990) · The American Statistician · doi:10.2307/2684359 · Cited by 1,809
Self-citationEstimating log models: to transform or not to transform?
Manning, W. G., & Mullahy, J. (2001) · Journal of Health Economics · doi:10.1016/s0167-6296(01)00086-8 · Cited by 1,790
Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding
Hundman, K., Constantinou, V., Laporte, C., Colwell, I., & Soderstrom, T. (2018) · Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining · doi:10.1145/3219819.3219845 · Cited by 1,771
On the meaning and use of kurtosis.
DeCarlo, L. T. (1997) · Psychological Methods · doi:10.1037//1082-989x.2.3.292 · Cited by 1,755
Metadata
- Authors
- D'AGOSTINO, R., & PEARSON, E. S.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1973
- Volume
- 60
- Issue
- 3
- Pages
- 613-622
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2091406001
- Cited by
- 606
- References
- 11
- FWCI
- 4.30
- 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: Tests for departure from normality. Empirical results for the distributions of b2 and √b1. https://app.cochat.ai/papers/10.1093/biomet/60.3.613
- The paper
- D'AGOSTINO, R., & PEARSON, E. S. (1973). Tests for departure from normality. Empirical results for the distributions of b2 and √b1. Biometrika. https://doi.org/10.1093/biomet/60.3.613
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.
