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

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