Pere Grima Cintas

Experimentation order in factorial designs with 8 or 16 runs

Abstract Randomizing the order of experimentation in a factorial design does not always achieve the desired effect of neutralizing the influence of unknown factors. In fact, with some very reasonable assumptions, an important proportion of random orders afford the same degree of protection as that obtained by experimenting in the design matrix standard order. In addition, randomization can induce a big number of changes in factor levels and thus make experimentation expensive and difficult. This paper discusses this subject and suggests experimentation orders for designs with 8 or 16 runs that combine an excellent level of protection against the influence of unknown factors, with the minimum number of changes in factor levels.

Selecting Significant Effects in Factorial Designs Taking Type II Errors into Account

When analysing the effects of a factorial design, it is customary to take into account the probability of making a Type I error (the probability of considering an effect significant when it is non-significant), but not to consider the probability of making a Type II error (the probability of considering an effect as non-significant when it is significant). Making a Type II error, however, may lead to incorrect decisions regarding the values that the factors should take or how subsequent experiments should be conducted. In this paper, we introduce the concept of minimum effect size of interest and present a visualization method for selecting the critical value of the effects, the threshold value above which an effect should be considered significant, which takes into account the probability of Type I and Type II errors. Copyright