Annals of the Institute of Statistical Mathematics

, Volume 22, Issue 1, pp 159–169

# On non-orthogonal main effect plans for asymmetrical factorials

• G. M. Saha
• S. Mohanty
Article

## Summary

Following the lines of Raktoe and Federer [19] a unified approach for constructing main effect plans in any$$k_1^{n_1 } \times k_2^{n_2 } \times \cdots \times k_r^{n_r }$$ factorials wherek i's are the numbers of equispaced levels of each of then i factors, andk i's are not necessarily primes or prime powers and need not satisty any relations among themselves, is presented. The method consists of, first, dividing the totality of treatment combinations, omitting, of course, some, if necessary, in to pairs such that the differences within the pairs are clear of ‘even’ effects and the sums are clear of ‘odd’ effects, and then, depending on the number of error d.f. wanted, selecting a suitable sub-set of these pairs which lead to the solution of the estimates of main effects. A general class of non-orthogonal main effect plans for 2 m ×2 n factorials is proposed. Information matrices and their inverses for such plans are worked out. An example followed by discussions and comparison statements is presented.

## Keywords

Treatment Combination SAHA Prime Power Incidence Matrix Fractional Factorial Design
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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