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On the Use of the Factor-Sparsity Assumption to Get an Estimate of the Variance in Saturated Designs

Joachim Kunert
Technometrics
Vol. 39, No. 1 (Feb., 1997), pp. 81-90
DOI: 10.2307/1270775
Stable URL: http://www.jstor.org/stable/1270775
Page Count: 10
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On the Use of the Factor-Sparsity Assumption to Get an Estimate of the Variance in Saturated Designs
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Abstract

In unreplicated multifactor designs, it is customary to nominate some factor interactions as not active-that is, to assume that they have no influence on the response-and to use the corresponding sums of squares to calculate an estimate of the variance. This estimate usually is based on very few degrees of freedom. An estimate of the variance is needed if one wants to find out which of the factors are really important. In many cases, especially in screening designs, it can be assumed that most factors and interactions are 0. When the design is orthogonal, then this assumption, called factor sparsity, is often used to get alternative estimates that are based on more degrees of freedom. There are several proposals for such estimators. This article uses approximations to discuss the respective advantages and disadvantages of four of them. I also show that such estimates of variance proposed for orthogonal designs can be extended to the nonorthogonal case. A method of analysis for nonorthogonal data is proposed. The method is applied to a dataset with missing values. It is shown that the improved estimate of the variance yields a more reliable analysis.

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