Finding Significant Effects for Unreplicated Fractional Factorials Using thenSmallest Contrasts

Abstract

Pooling nonsignificant effects to estimate the experimental error variance is considered unsatisfactory because it leads to an underestimation of the variance. Hence, the t statistic based on this variance estimate is inflated and should be used with caution. Instead, several graphical methods, such as the normal probability plot and the Bayes plot, have been suggested to determine active factors. Here a t test based on a less biased estimate of the experimental error variance is considered. Specifically, one uses the sums of squares associated with the n effects that are smallest in absolute value and treats them as a Type II right censored sample. It is shown that the t statistic based on this new variance estimate is much more reliable than the standard t statistic. Using five data sets, it is shown that this method is robust with respect to the number of chosen effects and results in conclusions similar to those obtained using normal probability plots or Bayes plots.

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