The Annals of Statistics

An Alternative to the Friedman Test with Certain Optimality Properties

S. Schach

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Abstract

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.

Article information

Source
Ann. Statist., Volume 7, Number 3 (1979), 537-550.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344675

Digital Object Identifier
doi:10.1214/aos/1176344675

Mathematical Reviews number (MathSciNet)
MR527489

Zentralblatt MATH identifier
0413.62027

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

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

Citation

Schach, S. An Alternative to the Friedman Test with Certain Optimality Properties. Ann. Statist. 7 (1979), no. 3, 537--550. doi:10.1214/aos/1176344675. https://projecteuclid.org/euclid.aos/1176344675


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