Chiang Mai Journal of Science

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The twoway layout is often used in trials even if only one factor is studied. For example blocking can be used to reduce the between subject variability in the comparisons between treatments or in a clinical trial many medical centers have to take part in order to recruite a sufficient number of patients. This paper is concerned with the statistical analysis of data arising from such trials when assumptions like normality do not necessarily apply.

Nonparametric analysis of the twoway layout based on ranks was first described by Friedman 1937

[1], but he did not take interaction effects into account and used separate ranking in the different blocks.           The purpose of this paper is to study nonparametric tests of interaction effects based on joint ranking of       all observations. For main effects such a test has been proposed by Mehra and Sarangi 1967
[2]. The proposed test for interaction effects is based on joint ranking of all subjects after removing possible       block and treatment effects. By simulation experiments the validity of the significance level of the test           when using a finite sample version of the asymptotic distribution of the test statistic is manifested and         thepower against different alternatives illustrated.

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