factorial designs at two levels ch. 5. factorial design two levels all possible combinations. two...
TRANSCRIPT
![Page 1: Factorial designs at two levels Ch. 5. Factorial Design Two levels All possible combinations. Two factors and variables. Two level simple interpretation,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/1.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/2.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/3.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/4.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/5.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/6.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/7.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/8.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/9.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/10.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/11.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/12.jpg)
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,](https://reader035.vdocuments.net/reader035/viewer/2022062718/56649ebb5503460f94bc3cfd/html5/thumbnails/13.jpg)
Ejemplo 3