Fundamentals of Statistical Experimental Design and Analysis

7Other Experimental Designs

Introduction

Over the years, the need to develop experimental designs that efficiently address important issues in the face of various constraints on experimental materials, protocols, and costs has led to the creation of new experimental designs. We have seen some examples:

1. The shoe research manager needed to compare three tread designs in a situation where it was advantageous (for reasons of statistical precision) to use blocks (boys) that had only two experimental units (feet) in each block. Balanced incomplete block designs, developed for agricultural needs, provided a clever and efficient way to do that.
2. Industrial processes posed new problems that agriculturally motivated designs did not address adequately. Industrial processes often involve a large number of process variables, in which case running an experiment with a full factorial set of treatment combinations is often prohibitive because of cost or time requirements. This constraint led to experiments with all factors at only two or three levels. Then, when there are enough factors that full factorial treatment combinations still become excessive, research led to the selection of cleverly selected fractions of the set of all possible factor combinations. There is no free lunch, though. We usually pay a cost for fractionalization in that the design then cannot detect interactions that might be important. If subject-matter context supports assuming certain interactions are negligible, this ...