1. Stat 470-11 Today: More Chapter 3

2. Assessing Effect Significance For replicated experiments, can use regression to determine important effects Can also use a graphical procedure The graphical procedure can be used for replicated and replicated factorial experiments

3. Normal and Half-Normal Probability Plots Graphical method for assessing which effects are important are based on normal probability plots (a.k.a normal qq-plots) Let be the sorted (from smallest to largest) effect estimates Plot, where represents the cumulative distribution function of the standard normal (N(0,1)) distribution

4. Normal and Half-Normal Probability Plots That is, we plot the percentiles of our sample of effects versus the corresponding percentiles of the standard normal If no effect is important then the sample of effects appear to be a random sample from a normal distribution…we observe: Otherwise:

5. Normal and Half-Normal Probability Plots Why does this work?

6. Normal and Half-Normal Probability Plots Half-Normal Plots

7. Example: Epitaxial Growth Layer Experiment

8. Analysis of Location and Dispersion Effects The epitaxial growth layer experiment is a 2 4 factorial design Have looked at ways to analyze response of a factorial experiment –Plotting effects on a normal probability plot –Regression Can also model the dispersion:

9. Example: Original Growth Layer Experiment

11. Model Matrix for a single replicate:

12. Example: Original Growth Layer Experiment Effect Estimates and QQ-Plot:

13. Example: Original Growth Layer Experiment Regression equation for the mean response:

14. Example: Original Growth Layer Experiment Dispersion analysis:

15. Example: Original Growth Layer Experiment Regression equation for the ln(s 2 ) response:

16. Example: Original Growth Layer Experiment Suggested settings for the process: