One Factor Comparison 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 one factor comparison design in Weibull++. | |||
{{Reference_Example_Heading1}} | {{Reference_Example_Heading1}} | ||
The data are from Example 11-1 on page 71 in the book ''Design and Analysis of Experiments'' by Douglas C. Montgomery, John Wiley & Sons, 2001. | |||
{{Reference_Example_Heading2}} | {{Reference_Example_Heading2}} | ||
To test hypothesis: | |||
To test the hypothesis: | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
H_0:\mu_1=\mu_2=...=\mu_5 \\ | H_0:\mu_1=\mu_2=...=\mu_5 \\ | ||
H_1:\mu_1 | H_1:\mu_1\ne\mu_2\ne...\ne\mu_5 | ||
\end{align}</math> | \end{align}</math> | ||
{| {{Table}} | {| {{Table}} | ||
!rowspan="2" | | !rowspan="2" | Weight percentage of cotton | ||
!colspan="5" | Observed tensile strength ( lb/in<math>^2</math>) | !colspan="5" | Observed tensile strength (lb/in<math>^2</math>) | ||
|- | |- | ||
!style="background:#f0f0f0;"|1 | !style="background:#f0f0f0;"|1 | ||
| Line 38: | Line 39: | ||
{{Reference_Example_Heading3}} | {{Reference_Example_Heading3}} | ||
From the book the ANOVA table is: | From the book the ANOVA table is: | ||
| Line 59: | Line 61: | ||
|} | |} | ||
Suppose that the experimenter selects <math>\alpha=0.05\,\!</math>. Since <math>F_ | Suppose that the experimenter selects <math>\alpha=0.05\,\!</math>. Since <math>F_{0.05,4,20}=2.87\,\!</math>, and <math>14.76 >2.87 \,\!</math>, the engineer rejects <math>H_0\,\!</math> and concludes that treatment means differ. | ||
{{Reference_Example_Heading4|DOE++}} | {{Reference_Example_Heading4|DOE++}} | ||
The software results match the book results. The ANOVA table is: | The software results match the book results and the conclusions are matched. The ANOVA table is: | ||
[[Image: | [[Image:one_factor_anova.png|center]] | ||
Since P Value =9.13E-6 < 0.01, we reject <math>H_0\,\!</math>. | Since the P Value = 9.13E-6 < 0.01, we reject <math>H_0\,\!</math>. | ||
Latest revision as of 21:09, 18 September 2023
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