Statistical Thinking, 3rd Edition

APPENDIX EMore on Design of Experiments

Experiment, and it will lead you to the light.

—Cole Porter

Chapter 8 discussed the use of statistically designed experiments to collect data for building models, focusing on experiments involving three variables. As you use this approach, you may encounter situations in which you have four or more variables to study. This appendix presents some designs that enable you to investigate the effects of four or more variables and provides guidance on how to analyze the results. The designs discussed are summarized in Table E.1 and shown in detail in Tables E.2 to E.7. The references at the end of this appendix present further details on the use and analysis of these designs.

Table E.1 shows the number of variables that each design is typically used to study. The designs in Tables E.5, E.6, and E.7 are used to study multiple numbers of factors. These designs should be used to estimate the effects of “L” factors using the first L columns of the designs. For example, the first 10 columns of Table E.7 should be used to estimate the linear (main) effects of 10 factors.

ANALYSIS OF TWO-LEVEL EXPERIMENTS

Two-level factorial designs are analyzed either by computing the factor effects as discussed in Chapter 8 or by using regression analysis to compute coefficients (i.e., Effect = 2 × Regression coefficient of the factor) as discussed in Chapter 8. The effects or regression coefficients are subsequently analyzed by hypothesis tests or normal probability ...