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Two-way ANOVA

Two-way ANOVA. Prepared by Res.Asst. Şura TOPTANCI. Two-way ANOVA compares means in groups of two different factors. Two-way ANOVA also considers interactions between the two different factors.

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Two-way ANOVA

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  1. Two-way ANOVA Prepared by Res.Asst. Şura TOPTANCI

  2. Two-way ANOVA compares means in groups of two different factors. • Two-way ANOVA also considers interactions between the two different factors. • In a Two-Way Analysis of Variance design, two factors are used to explain the variability in the response variable. We deal with the two factors by fixing them at different levels. We refer to the two factors as factor A and factor B. If factor A has n levels and factor B has m levels, we refer to the design as anfactorial design (Pearson, 2013).

  3. Example • Aircraft primer paints are applied to aluminium surfaces by two methods: dipping and spraying. The purpose of the primer is to improve paint adhesion. We would like to examine the effect of paint primer type and application method on paint adhesion. Data for adhesion forces were collected for this purpose. Identify the main effects. Determine which factor has an effect on paint adhesion (α = 0.05).

  4. The two factors are A: primertype and B: application method.

  5. Data entry into Minitab

  6. Hypothesis 1. 2. 3.

  7. Minitab Output Stat > ANOVA > Two Way Analyze the data from this experiment (use α = 0.05)

  8. Model Adequecy Checking Errors must be normally distributed (Normality assumption) The errorsare independent (Independence assumption) Errorshave the constant variance (Constant variance assumption). All assumptions must be satisfied.

  9. Model Adequecy Checking Analyze the residuals from this experiment. 1 vs 2 there is a significant difference. 2 vs 3 there is a significant difference. 1 vs 3 there is no significant difference.

  10. Plot of residuals versus primer type Store residuals and fitted values on the worksheet. You can also construct plot of residuals vs. application method.

  11. Main Effects Plot (Stat > Anova >Main effects plot)

  12. Interaction Plots

  13. Tukey Test (Stat > Anova >General Linear Model) When spreying method is applied, is there any difference between primer types?

  14. Tukey Test (Stat > Anova >General Linear Model) Construct a 95 percent confidence interval estimate on the mean difference among primer types? 1 vs 2 there is a significant difference. 2 vs 3 there is a significant difference. 1 vs 3 there is no significant difference.

  15. Construct a 95 percent confidence interval estimate on the mean difference among primer types? Dipping vs. Spraying there is a significant difference.

  16. When spraying method is applied, is there any difference between primer types? 1 vs 2 there is no significant difference. 1 vs 3 there is no significant difference. 2 vs 3 there is a significant difference.

  17. When spraying method is applied, is there any difference between primer types? 1 vs 2 there is no significant difference. 1 vs 3 there is no significant difference. 2 vs 3 there is a significant difference.

  18. When spraying method is applied, is there any difference between primer types? 1 vs 2 there is no significant difference. 1 vs 3 there is no significant difference. 2 vs 3 there is a significant difference.

  19. Example 2

  20. Analyze the data from this experiment. Use α = 0.05. Is there any evidence that feed rate, depth of cut and their interaction impacts surface finish? • Draw main effects and interaction effect plots. c) Use Tukey test to make comparisons among factors to determine specifically which feed rate and depth of cut differ in mean surface finish. d) Analyze the residuals from this experiment. Interpret all results and plots.

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