The DOI matches its Crossref record; 3 of the 4 references it cites were found in a registry or an index.
Statistical Tests Based on Permutations of the Observations
Open accessOverview
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.
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?
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“In the scenario of large-scale problems, the distribution of eigenvalues tends to converge to a normal distribution 42 .”
From Toward a linear-ramp QAOA protocol: evidence of a scaling advantage in solving some combinatorial optimization problems (2025) · cites this paper as [42]
Experimental — accuracy not yet measured
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
Statistical Methods for Research Workers
Fisher, R. A. (1945) · American Journal of Clinical Pathology · doi:10.1093/ajcp/15.11.552b · Cited by 10,883
Fisher, R. A. (1936) · BMJ · doi:10.1136/bmj.1.3923.554-a · Cited by 4,980
Random Variables and Probability Distributions
Nussbaum, E. M. (2014) · Routledge eBooks · doi:10.4324/9780203122860-10 · Cited by 439
Research works printed but not linked: 10
- [1][1] A. WALD AND J. WoLFOwITz, Annals of Math. Stat., Vol. 14 (1943), p. 378. -
- [2][2] HENRY ScHEFFÉ, Annals of Math. Stat., Vol. 14 (1943), p. 305. -
- [3][3] H. HoTELLING AND M. R. PABST, Annals of Math. Stat., Vol. 7 (1936), p. 29. -
- [4][4] E. J. G. PITmAN, Supp. Jour. Roy. Stat. Soc., Vol. 4 (1937), p. 225. -
- [5][5] E. J. G. PitmaN, Supp. Jour. Roy. Stat. Soc., Vol. 4 (1937), p. 119. -
- [6][6] E. J. G. PITMAN, Biometrika, Vol. 29 (1938), p. 322. -
- [7][7] B. L. WELcí, Biometrika, Vol. 29 (1937), p. 21. -
- [10][10] H. HoTELLING, Annals Math. Stat., Vol. 2 (1931), p. 359. -
- [11][11] H. CRAmÉR AND H. WoLD, Journal London Math. Soc., Vol. 11 (1936), pp. 290–4. -
- [12][12] J. RADoN, Sitzungsberichte Akademie Wien, Vol. 122 (1913), pp. 1295–1438. -
Cited by
Sorted by citations
Items 201–260 of 260
Toothaker, L. E. (1972) · Journal of Statistical Computation and Simulation · doi:10.1080/00949657208810004
The summer meeting in Wellesley
Hollcroft, T. R. (1944) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1944-08207-4
A Repeated-Measures Permutation Procedure for Analyzing Semantic Differential Data
Berry, K. J., & Mielke, P. W. (1995) · Psychological Reports · doi:10.2466/pr0.1995.77.2.355
Cao, D. (2025) · Library, Museums and Press - UDSpace (University of Delaware) · doi:10.58088/11rn-6q51
Nonexistence of blue's under a randomization model for the randomized block design
Kaiser, L. D. (1989) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(89)90065-7
On the error bound in a combinatorial central limit theorem
Ng, I. F. (2015)
Likelihood-Based Tests and Confidence Regions
Boos, D., & Stefanski, L. (2013) · Springer texts in statistics · doi:10.1007/978-1-4614-4818-1_3
Parallel Sequential Estimation of Quantiles During Steady State Simulation
Eickhoff, M., Pawlikowski, K., & McNickle, D. C. (2012) · UC Research Repository (University of Canterbury) · doi:10.26021/2275
Comparing Attributes by a Probabilistic and Statistical Association II
Lerman, I. C. (2016) · Advanced information and knowledge processing · doi:10.1007/978-1-4471-6793-8_6
Comparing Attributes by Probabilistic and Statistical Association I
Lerman, I. C. (2016) · Advanced information and knowledge processing · doi:10.1007/978-1-4471-6793-8_5
Empirical power of four statistical tests in one way layout
H., L. J. M. (2014) · International Mathematical Forum · doi:10.12988/imf.2014.47128
Contributions to the theory of rank order tests
Dwass, M. (1952) · NCSU Libraries Repository (North Carolina State University Libraries)
On the Asymptotic Distribution of Linear Combinations of Interchangeable Random Variables.
Blom, G. (1959) · MATHEMATICA SCANDINAVICA · doi:10.7146/math.scand.a-10577
Hoeffding, W. (1950) · NCSU Libraries Repository (North Carolina State University Libraries)
AUC Regression for Multiple Comparisons With the Jonckheere Trend Test
Buros, A. F., Tubbs, J. D., & Zyl, J. S. V. (2017) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2017.1322135
Empirical Sampling from Permutation Space with Unique Patterns
Odiase, J. I. (2012) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1335845340
An improvement of a non-uniform bound for combinatorial central limit theorem
Sumritnorrapong, P., Neammanee, K., & Suntornchost, J. (2018) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2018.1459711
Stein meets Malliavin in normal approximationPreprint
Chen, L. H. Y. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1407.5172
A Bernstein type inequality for sums of selections from three dimensional arrays
Banerjee, D., & Sordello, M. (2019) · Statistics & Probability Letters · doi:10.1016/j.spl.2019.06.010
Determination of Validation Errors Precisely Using Bootstrapped Latin Partitions
Harrington, P. D. B. (2019) · Encyclopedia of Analytical Chemistry · doi:10.1002/9780470027318.a9695
Advances in the theory of non-parametric tests in statistical inference
Janko, J. (1949) · Časopis pro pěstování matematiky a fysiky · doi:10.21136/cpmf.1949.123049
Exact Permutation/Randomization Tests Algorithms
Ghosh, S. (2020) · Journal of Statistical Theory and Practice · doi:10.1007/s42519-020-00131-6
A Model-Free Approach for Testing Association
Chatterjee, S., Chowdhury, S., & Basu, S. (2021) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12467
Multiple Comparison Methods in Zero-dose Control Trials
Zyl, J. S. V., & Tubbs, J. D. (2021) · Journal of Data Science · doi:10.6339/jds.201804_16(2).0005
Generalized Permutation Framework for Testing Model Variable SignificancePreprint
Wu, Y., Spaide, T., Nakamichi, K., Gelder, R. V. V., & Lee, A. Y. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.13952
Weiss, L. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat01344
Practical Graph Isomorphism for Graphlet Data Mining in Protein Structures
Henneges, C., Behle, C., & Zell, A. (2012) · Studies in computational intelligence · doi:10.1007/978-3-642-27534-0_23
Welsh, A. H. (1996) · Wiley series in probability and statistics · doi:10.1002/9781118165423.refs
Berry, K. J., Johnston, J. E., & Mielke, P. W. (2014) · Springer eBooks · doi:10.1007/978-3-319-02744-9_3
Berry, K. J., Johnston, J. E., & Mielke, P. W. (2014) · Springer eBooks · doi:10.1007/978-3-319-02744-9_2
Berry, K. J., Johnston, J. E., & Mielke, P. W. (2014) · Springer eBooks · doi:10.1007/978-3-319-02744-9_4
Boos, D. D., & Stefanski, L. A. (2012) · Springer texts in statistics · doi:10.1007/978-1-4614-4818-1_10
Boos, D. D., & Stefanski, L. A. (2012) · Springer texts in statistics · doi:10.1007/978-1-4614-4818-1_11
Boik, R. J. (2011) · Elsevier eBooks · doi:10.1016/b978-0-444-51862-0.50032-0
Pesarin, F., & Salmaso, L. (2010) · Wiley series in probability and statistics · doi:10.1002/9780470689516.refs
Berry, K. J., Johnston, J. E., & Mielke, P. W. (2018) · Springer eBooks · doi:10.1007/978-3-319-98926-6_6
Agung, I. G. N. (2008) · doi:10.1002/9780470823699.refs
(1997) · Wiley series in probability and statistics · doi:10.1002/9781118150719.ch46
Serfling, R. J. (1980) · Wiley series in probability and statistics · doi:10.1002/9780470316481.refs
Sen, P. K. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat02806
Permutation Tests in Clinical Trials
Zucker, D. M. (2014) · doi:10.1002/9781118596333.ch31
Noether and Related Conditions
Smith, P. J. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess1790
Weiss, L. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess2876
Sen, P. K. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess7032
Hallin, M. (2001) · Encyclopedia of Environmetrics · doi:10.1002/9780470057339.var016
Permutation Tests in Clinical Trials
Zucker, D. M. (2006) · Wiley Encyclopedia of Clinical Trials · doi:10.1002/9780471462422.eoct058
Noether and Related Conditions
Smith, P. J. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess1790.pub2
(1982) · IEEE Transactions on Information Theory · doi:10.1109/tit.1982.1056541
Anticoncentration and Berry–Esseen bounds for random tensors
Dodos, P., & Tyros, K. (2023) · Probability Theory and Related Fields · doi:10.1007/s00440-023-01211-x
The principle and state-of-art applications of permutation tests
Li, J. (2023) · Highlights in Science Engineering and Technology · doi:10.54097/hset.v61i.10258
Non–uniform bound of normal approximation for Combinatorial random sums
Nonsoong, P., & Neammanee, K. (2016) · doi:10.58837/chula.the.2016.1682
On the Term “Randomization Test”
Hemerik, J. (2024) · The American Statistician · doi:10.1080/00031305.2024.2319182 · Cited by 1
Marc Hallin: A Commented Bibliography (from 1972 to 2023)
Barigozzi, M., Hörmann, S., & Paindaveine, D. (2024) · Springer eBooks · doi:10.1007/978-3-031-61853-6_1
Chan, J. C. C., & Kroese, D. P. (2025) · Springer texts in statistics · doi:10.1007/978-1-0716-4132-3_11
A Multivariate Two-Sample Location Test Based on Empirical Distribution Functions
Mathur, S., & Sakate, D. M. (2025) · Sankhya B · doi:10.1007/s13571-025-00375-x
Salmaso, L., & Pesarin, F. (2020) · Wiley series in probability and statistics · doi:10.1002/9781119438199.ref
Theory of One‐Dimensional Permutation Tests
Salmaso, L., & Pesarin, F. (2020) · Wiley series in probability and statistics · doi:10.1002/9781119438199.ch2
(1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478482
Stratified permutational Berry–Esseen bounds and their applications to statistics
Tian, P., Yang, F., & Ding, P. (2026) · Bernoulli · doi:10.3150/26-bej1988
Metadata
- Authors
- Wald, A., & Wolfowitz, J.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1944-12
- Volume
- 15
- Issue
- 4
- Pages
- 358-372
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2038298134
- Cited by
- 260
- References
- 4
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 4 · 2023: 7 · 2022: 2 · 2021: 8 · 2020: 6 · 2019: 8 · 2018: 6 · 2017: 3 · 2016: 5 · 2015: 8 · 2014: 18 · 2013: 4 · 2012: 18
- FWCI
- 3.53
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- permutation tests, nonparametric tests, rank tests, asymptotic distribution, asymptotic normality, asymptotic efficiency
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
