## The Annals of Statistics

### An Alternative to the Friedman Test with Certain Optimality Properties

S. Schach

#### 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

#### 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