What we give up to do Exploratory Designs 1

Hicks Tire Wear Example data 2

Linear Model 3

ANOVA with Main Effects 4

It’s an orthogonal design so… The Type III tests on top match the Type I tests below. Main Effects Are not confounded with each other. 5

We are primarily interested in Brand, but what about interactions? If we put in even one interaction, then there are no df for error and this Interaction is completely confounded with Brand. 6

Notice One cannot estimate and test Interaction terms since we do not have enough d.f. Interaction terms are confounded with error and other terms. As we shall see later with Fractional Factorials, they are likely confounded with each other too. 7

Brand is the only Fixed Effect for Inference 8

Tukey HSD on Tire Wear LS Means 9

Residuals vs. Predicted 10

Normal Plot of Residuals 11

Normality Test 12

Hicks Graeco-Latin Square Example 13

Basic ANOVA with Main Effects 14

Only Time is close to significance so… 15

Since this is a screening design….. Which variables might we investigate further? How might we collect more data? What about diagnostics on the model we fit? 16

Residuals Vs. Predicted Plot 17

Normality Plot 18

Normality Test 19

What happened with our Diagnostics? With Diagnostics we use Residuals as surrogates for Experimental Error in our Model The Diagnostics are based on the assumption that our Residuals are independently distributed This assumption was never true in an absolute sense However, if the df for Error is “large” relative to the Model df, it is close enough to “true” so that our Diagnostics make sense Remember, these designs are meant to screen factors for further study 20