172 Chapter 7: Experimental Design General Linear Model: Hardness versus Temp, P
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172 Chapter 7: Experimental Design General Linear Model: Hardness versus Temp, Press, RH Factor Type Levels Values Temp fixed Press fixed RH 2 160, 200 2 120, 150 2 30, 50 fixed Analysis of Variance for Hardness, using Adjusted ss for Tests DF Seq Ss Adj ss Adj MS Source Temp Press RH 1 324.00 264.14 264.14 16.62 0.003 1 0.02 28.12 28.12 1.77 0.216 1 408.00 302.29 302.29 19.02 0.002 1 0.16 2.00 2.00 0.13 0.731 1 2.45 0.14 0.14 0.01 0.927 Temp RH Press RH 1 10.12 10.12 10.12 0.64 0.445 Error Total 9 143.00 143.00 15.89 15 887.75 S 3.98609 R-Sq 83.89% R-Sq ( adj ) :73.15% - : 5. You have obtained the following main effects plot for the experin Problem 4. Explain what you can deduce from the plot. Main Effects Plot (Data Means) for HardnessExplanation / Answer
Design of 2^3 Full Factorial
We have three fixed factors with 2 levels each.
Question: Evaluating the effects on the hardness of two levels of temperature, pressure and relative humidity.
ANOVA on 2^3 Full Factorial is performed and result from MINITAB as given in the figure.
Interpret the results:
To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. Significance level (alpha) of 0.05 is used for testing the association. If p-value < =0.05, the association is statistically significant else it is not statistically significant.
Temp is a fixed factor and this main effect is significant (F(1,15) = 0.003). This result indicates that the mean hardness is not equal for both the temperature levels.
Relative Humidity (RH) is a fixed factor and this main effect is significant (F(1,15) = 0.002). This result indicates that the mean hardness is not equal for both the relative humidity levels.
Pressure is a fixed factor and this main effect is not significant (F(1,15) = 0.216). This result indicates that the mean hardness is equal for both the pressure levels.
All the interactions are not significant indicates that the relationship between each factor and the response does not depend on the level of the other factor.
The coefficient of determination r-sq is equal to 83.89% indicating 83.89% of the variance in hardness is explained by temp, pressure and relative humidity. For these data, the R^2 value indicates the model provides a good fit to the data.
In order to comment on which factor will champion in getting maximum hardness, you would need to read Means Table which tells you about the associated hardness with each temp, pressure and relative humidity levels. From the ANOVA we can conclude that changing temp levels and Relative humidity levels will get us different mean hardness, and their interaction is not significant so each factor (Temp or Relative humidity) and the response does not depend on the level of the other factor (Temp or Relative humidity).
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