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May, 1979 An Alternative to the Friedman Test with Certain Optimality Properties
S. Schach
Ann. Statist. 7(3): 537-550 (May, 1979). DOI: 10.1214/aos/1176344675


R. L. Anderson proposed a $\chi^2$-type rank statistic for the nonparametric analysis of a randomized blocks design. In this paper the asymptotic distribution of the test statistic is derived under a sequence of alternatives contiguous to the null hypothesis. Using Bahadur's concept of local approximate slope, it is shown that the test is optimal within a large class of rank tests including the tests proposed by Friedman and by Page. The results are extended to BIB designs. Ties are considered.


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S. Schach. "An Alternative to the Friedman Test with Certain Optimality Properties." Ann. Statist. 7 (3) 537 - 550, May, 1979.


Published: May, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0413.62027
MathSciNet: MR527489
Digital Object Identifier: 10.1214/aos/1176344675

Primary: 62G10
Secondary: 62G20

Keywords: Bahadur efficiency , contiguous alternatives , efficiency , Friedman test , nonparametric analysis of complete and balanced incomplete block designs , Page test , ties

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 3 • May, 1979
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