Two Level Factorial Design: Difference between revisions

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{{Reference Example|{{Banner DOE Reference Examples}}}}
{{Reference Example|{{Banner DOE Reference Examples}}}}
This example validates the calculation of the two level factorial design.
This example validates the calculation of the two level factorial design in Weibull++.


{{Reference_Example_Heading1}}
{{Reference_Example_Heading1}}
Data is from an example on page 223 in book “Design and Analysis of Experiments” by Douglas C. Montgomery, John Wiley & Sons, 2001.   
The data are from an example on page 223 in the book ''Design and Analysis of Experiments'' by Douglas C. Montgomery, John Wiley & Sons, 2001.   


{{Reference_Example_Heading2}}
{{Reference_Example_Heading2}}
{| {{Table}}
{| {{Table}}
!colspan="2" | Factor
!colspan="2" | Factor
!Treatment Combination
!rowspan="2" style="vertical-align:top"|Treatment Combination
!colspan="3" | Replicate
!colspan="3" | Replicate
|-
|-
| '''A'''||'''B'''||||'''1'''||'''2'''||'''3'''
!style="background:#f0f0f0;"|A
!style="background:#f0f0f0;"|B
!style="background:#f0f0f0;"|1
!style="background:#f0f0f0;"|2
!style="background:#f0f0f0;"|3
|-
|-
| -||-||A low, B low||28||25||27
| -||-||A low, B low||28||25||27
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|}
|}
{{Reference_Example_Heading3}}
{{Reference_Example_Heading3}}
Your text here.
 
Table 6-1 from the book shows the ANOVA table for this experiment.
 
{| {{Table}}
!Source of Variation
!Sum of Squares
!Degrees of Freedom
!Mean Square
!F value
!P-Value
|-
| A||208.33||1||208.33||53.15||0.0001
|-
| B||75.00||1||75.00||19.13||0.0024
|-
| AB||8.33||1||8.33||2.13||0.1826
|-
| Error||31.34||8||3.92||||
|-
| Total||323.00||11||||||
|-
|}


{{Reference_Example_Heading4|DOE++}}
{{Reference_Example_Heading4|DOE++}}
Your text here.
The results from the software are the same as the results from the book. Both show that A and B are significant factors.
 
[[Image:two_level_responses.png|center]]
 
 
[[Image:two_level_anova.png|center]]

Latest revision as of 21:08, 18 September 2023

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Two Level Factorial Design

This example validates the calculation of the two level factorial design in Weibull++.

Reference Case

The data are from an example on page 223 in the book Design and Analysis of Experiments by Douglas C. Montgomery, John Wiley & Sons, 2001.

Data

Factor Treatment Combination Replicate
A B 1 2 3
- - A low, B low 28 25 27
+ - A high, B low 36 32 32
- + A low, B high 18 19 23
+ + A high, B high 31 30 29

Result

Table 6-1 from the book shows the ANOVA table for this experiment.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F value P-Value
A 208.33 1 208.33 53.15 0.0001
B 75.00 1 75.00 19.13 0.0024
AB 8.33 1 8.33 2.13 0.1826
Error 31.34 8 3.92
Total 323.00 11

Results in DOE++

The results from the software are the same as the results from the book. Both show that A and B are significant factors.

Two level responses.png


Two level anova.png
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