Alhakim, Abbas; Hooper, William A non-parametric test for several independent samples. (English) Zbl 1216.62066 J. Nonparametric Stat. 20, No. 3, 253-261 (2008). Summary: We introduce a large sample nonparametric test for the hypothesis of equal distributions of three or more independent samples. The test can be considered as a generalisation of the two sample run tests of A. Wald and J. Wolfowitz [Ann. Math. Stat. 11, 147–162 (1940; Zbl 0023.24802)] in that it sorts the data and replaces the values with the ‘label’ of the sample from which they come, thus transforming the problem to a question about the randomness of the resulting pooled sample. The test statistic and its asymptotic null distribution are derived using the central limit theorem of finite Markov chains. Simulation results and comparisons with the standard \(k\)-sample Kruskal-Wallis and Kolmogorov-Smirnov tests are given. One particular strength of the test is that it is capable of distinguishing between different distributions having the same mean in a few cases when the Kruskal-Wallis test is completely paralysed. Cited in 1 Document MSC: 62G10 Nonparametric hypothesis testing 62E20 Asymptotic distribution theory in statistics 65C60 Computational problems in statistics (MSC2010) 60F05 Central limit and other weak theorems Keywords:chi-square statistic; Kruskal-Wallis; \(k\)-sample problem; overlapping Markov chains PDF BibTeX XML Cite \textit{A. Alhakim} and \textit{W. Hooper}, J. Nonparametric Stat. 20, No. 3, 253--261 (2008; Zbl 1216.62066) Full Text: DOI References: [1] DOI: 10.1214/aoms/1177731909 · Zbl 0023.24802 · doi:10.1214/aoms/1177731909 [2] DOI: 10.1073/pnas.88.6.2297 · Zbl 0756.60103 · doi:10.1073/pnas.88.6.2297 [3] DOI: 10.1073/pnas.93.5.2083 · Zbl 0849.60002 · doi:10.1073/pnas.93.5.2083 [4] DOI: 10.1073/pnas.94.8.3513 · Zbl 0873.11047 · doi:10.1073/pnas.94.8.3513 [5] DOI: 10.1007/s00440-003-0321-z · Zbl 04576229 · doi:10.1007/s00440-003-0321-z [6] Alhakim A., Markov Process. Related Fields 10 pp 629– (2004) [7] DOI: 10.1007/BF03019651 · JFM 40.0283.01 · doi:10.1007/BF03019651 [8] Kolmogorov A. N., Grundbegriffe der Wahrscheinlichkeitsrechnung (1933) · JFM 59.1154.01 · doi:10.1007/978-3-642-49888-6 [9] Von Mises R., Probability, Statistics and Truth,, 2. ed. (1957) [10] DOI: 10.1038/scientificamerican0575-47 · doi:10.1038/scientificamerican0575-47 [11] Kemeny J., Finite Markov Chains (1960) · Zbl 0089.13704 [12] Manoukian E. B., Mathematical Nonparametric Statistics (1960) · Zbl 0705.62038 [13] Hájek J., Theory of Rank Tests (1999) · Zbl 0944.62045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.