Page 94 - Contributed Paper Session (CPS) - Volume 2

CPS1442 Uzuke C.A. et al.

Two-way median test
Uzuke, C. A., Oyeka I. C. A
Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria

Abstract
This paper proposes a two way median test to analyse data when the
assumptions of normality and homogeneity of variance are not satisfied as in
parametric two analysis of variance. In this case the criterion variable is
numeric with out replication and the study is based on the overall median of
the data when pulled together. The proposed method is illustrated with some
data. A comparison with the Friedman two way analysis of variance showed
that the proposed two way median test is more powerful than the Friedman
two way analysis of variance test.

Keywords
Median test; Friedman’s ANOVA; P-value; Chi-square test of independence

1. Introduction
In the conventional two way parametric analysis of variance (ANOVA) test
involving two factors A and B, Daniel, (1990); Esinga et al, (2017), interest is
often in testing the null hypothesis that the levels of factor A and the levels of
factor B do not differ statistically in their effects on the criterion variable of
interest which is usually assumed to be continuous Dixon, (1990). Factors A
and B may both be fixed, both random, or one fixed and the other random. If
in addition there are more than one observation per cell, interest may also be
in testing for the absence of any interaction effects between factors A and B.
Here we present a non-parametric alternative to the two-way parametric
ANOVA test in the case when they are only one observation per cell, which
means there are no replications. We assume that the factor A has levels and
factor B has levels and that the criterion variable being studied is numeric
measured on at least the ordinal scale Siegel & Castellan (1988); Zar, (1999).
The method is based on the median test and makes provision for the possible
presence of ties between the observations and their assumed common
median.

2. Methodology
In the non-parametric Friedmans’ two-way ANOVA by ranks, Zar, (1999) it
is usually assumed that this data set if treated as a parametric two-way ANOVA

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