Factorial designs at two levels
Ch. 5
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!)
Example
• Three factors on clarity of film (wax formula): A: emulsifier, B: emulsifier, C: catalyst concentration.
• Each factor at two levels: 23 factorial design.
Example 1
Example 2
Example 3
Example 3
Example 3• Interactions:TK=(33-13)/2=10TK=(11.5+8.5)/2=10TCK=[(35-31)/2- (14-12)/2]/2=0.5CKT=[(-3+4)/2- (-7+6)/2]/2=0.5
Example 3
TCK=(-60+72+54-68+52-83-45+80)/4=0.5
Example 3
Example 3•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)s2=8/4=2
Standard error=sqrt(2)=1.4
Ejemplo 3
Ejemplo 3