Study Questions, Chapter 15

1. Why do we call these designs 2^k designs?

Because they are multiple-factor designs, and each factor has 2 levels. Here, "k" refers to the number of factors.

2. Higher-order designs are _______________________, often used in __________ ______________ experiments.

exploratory

factor screening

3. If there are replicates (Gs instead of Ss), what do we use as our MSE?

We use our ordinary estimate of sigma-squared, the sum of squared residuals.

4. If there are no replicates, what is the problem?

Our ordinary estimate of sigma-squared equals zero

5. What can we do about it (four methods)?

remove small effects, use as error term

remove interactions, use as error term

remove the one smallest factor and all its interactions - "hidden replication"

hidden replication but with more than one factor

6. In that case, what extra assumption(s) do we have to make?

That the effects that have been pooled together into creating the error term really are zero.

7. How can we graphically assess effect sizes? How does this help us?

Make a quantile plot of q vs. sorted effect sizes

The central, linear part contains effects thought to be noise-only, and candidates for pooling into the error term

The outliers, negative and positive, are the potentially significant effects that should be tested