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Minitab DOE Tutorial interpretation

# Both plot of residuals versus fitted values and plot

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Both plot of residuals versus fitted values and plot of residuals versus run order do not show any pattern. Thus, both constant variance and independence assumptions are satisfied. Step 5. Interpreting ANOVA Results and Multiple Comparisons The ANOVA table shows that the power level has statistically significant effect on the etch rate. The Effect of the factor (power level) can be displayed using a boxplot as shown below. The boxplot shows that the etch rate increases as the power level increases. Constant Variance -- The variance of the observations in each treatment should be equal. The constant variance assumption can be checked with Residuals versus Fits plot. This plot should show a random pattern of residuals on both sides of 0, and should not show any recognizable patterns. A common pattern is that the residuals increase as the fitted values increase. Independence – ANOVA requires that t he observations should be randomly selected from the treatment population. The independence, especially of time- related effects, can be checked with the Residuals versus Order (time order of data collection) plot. A positive correlation or a negative correlation means the assumption is violated. If the plot does not reveal any pattern, the independence assumption is satisfied. Boxplot Boxplot here is a graphical summary of the distribution of Etch Rate at each Power Level.

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Dr. Jianbiao (John) Pan Minitab Tutorials for Design and Analysis of Experiments Page 7 of 32 After we conclude that there is significant different in etch rate between different power levels, the next question to ask is that which ones are different from the rest. In this case, a common method is to use Tukey’s multiple comparisons to construct confidence intervals for the differences between each pair of means. The Tukey’s multiple comparison results are displayed in the session window. Step 6. Save the analysis results You can save all the analysis work you have done by choosing File Æ Save Project as .
Dr. Jianbiao (John) Pan Minitab Tutorials for Design and Analysis of Experiments Page 8 of 32 Determining Sample Size in One-way ANOVA It is important to choose a proper sample size in planning an experiment. To determine one-way ANOVA sample size in Minitab, Click Stat Æ Power and Sample Size Æ One-Way ANOVA. Assume we want to determine sample size in Example #1 before the experiment was conducted. In the dialogue box, input “4” in “ Number of levels ” since the number of factor levels in Example #1 is 4. Input the estimated value, “75”, in “ Value of the maximum difference between means provided that we will conclude the factor has statistically significance effect on the response variable if the mean difference in the response variable resulted from two different treatment levels exceeds a specified value, “75” in this example.

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Both plot of residuals versus fitted values and plot of...

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