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Factorial designs at two levels Ch. 5

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Page 1: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Factorial designs at two levels

Ch. 5

Page 2: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

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!)

Page 3: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example

• Three factors on clarity of film (wax formula): A: emulsifier, B: emulsifier, C: catalyst concentration.

• Each factor at two levels: 23 factorial design.

Page 4: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 1

Page 5: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 2

Page 6: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 3

Page 7: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 3

Page 8: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

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

Page 9: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 3

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

Page 10: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Example 3

Page 11: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

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

Page 12: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Ejemplo 3

Page 13: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,

Ejemplo 3


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