Science Journal Of Mathematics and Statistics, Volume
2013 (2013), July 2013
© Author(s) 2013. This work is distributed under the Creative Commons Attribution 3.0 License.
Ties Adjusted Two Way Analysis Of Variance Tests with Unequal Observations Per Cell
Author: Oyeka I.C.A
Department of Industrial Mathematics and Applied Statistics, Ebonyi State University Abakaliki,Nigeria.
Accepted 2 June, 2013; Available Online 15 July 2013
This paper proposes a non-parametric statistical method for the analysis of factor
effects in a two factor analysis of variance type model with unequal observations or
replications per cell or treatment combination. It is here, for simplicity assumed that
there are no interactions between the factors of interest or that such interactions have
been removed by appropriate data transformation. The proposed test statistics are
intrinsically and structurally adjusted for the possible presence of ties between
observations in each cell or treatment combination, thereby obviating the need to
require the sampled populations to be continuous or even numeric. The populations
may be measurements on as low as the ordinal scale. The method enables the
researcher test for the statistical significance of not only the effect of each factor level
but also for the equally of several factor level effects.
The proposed method which is generally more robust than the corresponding classical 'F' test that may be used for the same purpose is illustrated with some sample data and shown to be as expected more powerful than an alternative ties-unadjusted method which is shown to have reduced degrees of freedom, for the same sample size.
Keyword:intrinsically and structurally adjusted, ties-unadjusted, level of factor A, level of factor A, replication