1. Factorial designs at two levels Ch. 5

2. Factorial Design Two levels All possible combinations. Two factors and variables. Two level  simple interpretation, few runs per factor Quantitative or qualitative factors Factors can interact (nonzero correlations!)

3. Example Three factors on clarity of film (wax formula): A: emulsifier, B: emulsifier, C: catalyst concentration. Each factor at two levels: 2 3 factorial design.

4. Example 1

5. Example 2

6. Example 3

8. Interactions: TK=(33-13)/2 =10 TK=(11.5+8.5)/2 =10 TCK=[(35-31)/2- (14-12)/2]/2 =0.5 CKT=[(-3+4)/2- (-7+6)/2]/2 =0.5

9. Example 3 TCK=(-60+72+54-68+52-83-45+80)/4=0.5

10. Example 3

11. if each factor was replicated a different number of times: Each estimated effect is a difference between two averages: v(effect)=(1/8+1/8)s 2 =8/4=2 Standard error=sqrt(2)=1.4

12. Ejemplo 3