# ENBIS: European Network for Business and Industrial Statistics

Forgotten your password?

Not yet a member? Please register

## ENBIS-8 in Athens

*21 – 25 September 2008*Abstract submission: 14 March – 11 August 2008

### Location-scale rank testing with application in quality control

*23 September 2008, 11:30 – 11:35*

#### Abstract

- Submitted by
- Marco Marozzi
- Authors
- Marco Marozzi, Paolo Cozzucoli
- Affiliation
- Università della Calabria
- Abstract
- The comparison of two samples is one of the most important problems in statistical testing. If it is assumed that parent distributions may differ only in location, there are many parametric and nonparametric tests. There are many tests also for the scale problem. It is well-known that under normal distributions the t test and the F test are the uniformly most powerful unbiased tests for the location and scale problem respectively, at least for one-sided alternatives; and that the t test is alfa robust for nonnormal distributions (except for very heavy-tailed ones), whereas the F test is non alfa robust (see, among others, Tiku et al. 1986 and Wilcox 2005). Therefore it may be useful to act within the rank setting, without requiring the assumption of normality. Moreover, even if the usual two-sample problem tests for a location shift, in quality control and industrial statistics situations in which location and scale shifts should be simultaneously detected arise often.

The best known and most used rank test for the location-scale problem is the Lepage (1971) test. There is also another rank test, due to Cucconi (1968) that is earlier but neither known in the literature nor applied in practice. The test is of interest since, contrary to the other location-scale tests, it is not a quadratic form of a test on location and a test on scale and it is easier to be computed than that of Lepage, and other tests. It should be noted that the power of the Lepage test, contrary to that of the Cucconi test, has been widely studied, even recently. For this reason power and size of the Cucconi test are studied, and comparisons with the Lepage test are assesed. Applications of the tests to real data sets in the context of quality control and industrial statistics are discussed.

Cucconi, O. (1968) Un nuovo test non parametrico per il confronto tra due gruppi campionari, Giornale degli Economisti, XXVII, 225-248.

Lepage, Y. (1971) A combination of Wilcoxon’s and Ansari-Bradley’s statistics, Biometrika, 58, 213-217.

Tiku, M. L., Tan, W. Y. and Balakrishnan, N. (1986) Robust inference, Marcel Dekker: New York.

Wilcox, R. R. (2005) Introduction to robust estimation and hypothesis testing, Academic Press: San Diego.