1. The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs
Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina

2. Part I. Full Factorial Designs
Introduction
Analysis Tools
Example
Violin Exercise
2k Designs

3. How many combinations of factor levels are there?
24 Designs Introduction
Suppose the effects of four factors, each having two levels, are to be investigated.
How many combinations of factor levels are there?
With 16 runs, one per each treatment combination, we can estimate:
four main effects - (A,B,C,D)
six two-way interactions - (AB,AC,AD,BC,BD,CD)
four three-way interactions - (ABC,ABD,ACD,BCD)
one four-way interaction (ABCD).
15 effects = 2^4 - 1

4. 24 Designs Analysis Tools - Design Matrix
No cube plot for now.

5. 24 Designs Analysis Tools - Design Matrix Signs Table

6. 24 Designs Analysis Tools - Signs Table
Effects are divided by 8

7. 24 Designs Analysis Tools - Fifteen Effects Paper

8. Response: Computer throughput (kbytes/sec), (large y’s are desirable)
24 Designs Example 4*
Response: Computer throughput (kbytes/sec), (large y’s are desirable)
Factors: A, B, C and D were various performance tuning parameters such as
number of buffers
size of unix inode tables for file handling *Data courtesy of Greg Dobbins

9. 24 Designs Example 4 - Experimental Report Form

10. 24 Designs Example 4 - Signs Table U-Do-It
Fill Out the Signs Table to Estimate the Factor Effects
If enough people are in class, we stop here and have each class member compute an effect, share effects then sort them. Think about a scale if using plotting paper, then plot effects.

11. 24 Designs Example 4 - Completed Signs Table
Try to sort effects here by hand

12. 24 Designs Example 4 - Effects Normal Probability Plot
Factors A and C Stand Out
Choose Hi Settings of Both A and C since the response is throughput
The large negative effects are on the WRONG side of the line—they are smaller than expected. We may have an issue with normality here. It’s hard to know how to treat the third and fourth largest positive effects.

13. 24 Designs Example 4 - EMR at A=Hi, C=Hi

14. 24 Designs Examples 2 and 4 Discussion
Examples 2 (from Lecture 6.2) and 4 are Related
Original Data Was In Tenths
The Numbers were Rounded Off for Ease of Calculation
Example 2
Half Fraction (24-1, 8 Runs) of the Data in Example 4.
The Runs in Example 4 when ABCD=1 were the runs used in Example 2.
Skip ahead to next slide to quickly show data table.

15. 24 Designs Examples 2 and 4 Runs

16. 24 Designs Example 2 and 4 - Effects Normal Probability Plots
Factor A Still Stands Out
The (Hidden) Replication in the Additional Runs Teased Out A Significant Effect Due to Factor C.