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A study of simple unbalanced factorial designs that use type ii and type iii sums of squares

Lewsey, J.D. and Gardiner, W.P. and Gettinby, G. (1997) A study of simple unbalanced factorial designs that use type ii and type iii sums of squares. Communications in Statistics - Simulation and Computation, 26 (4). pp. 1315-1328. ISSN 0361-0918

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Abstract

Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.