# Two factor ANOVA

You are the engineer for a paint process. You'd like to improve the quality of the process.

You have selected your response variable, which is ppm of dust. You have sixteen measurements that you take, you have 3 variables [resist thickness, develop time, and exposure].

You have two levels of each of the variables [say, level one and level 2].

You are interested in which variable or combinations of variables 'mater'.

Your data:

1. level 2 for resist thickness, develop time, and exposure, Measurement is 74 ppm

2. level 2 for resist thickness, develop time, and exposure, Measurement is 72 ppm

3. level 1 for resist thickness, develop time, and exposure, Measurement is 80 ppm

4. level 1 for resist thickness, develop time, and exposure, Measurement is 78 ppm

5. level 2 for resist thickness, develop time, and level 1 for exposure, Measurement is 84 ppm

6. level 2 for resist thickness, develop time, and level 1 for exposure, Measurement is 87 ppm

7. level 1 for resist thickness, develop time, and level 2 for exposure, Measurement is 68 ppm

8. level 1 for resist thickness, develop time, and level 2 for exposure, Measurement is 65 ppm

9. level 2 for resist thickness, level 1 for develop time and for exposure, Measurement is 84 ppm

10. level 2 for resist thickness, level 1 for develop time and for exposure, Measurement is 83 ppm

11. level 1 for resist thickness, level 2 for develop time and for exposure, Measurement is 70 ppm

12. level 1 for resist thickness, level 2 for develop time and for exposure, Measurement is 68 ppm

13. level 1 for resist thickness and for exposure and level 2 for develop time, Measurement is 72 ppm

14. level 1 for resist thickness and for exposure and level 2 for develop time, Measurement is 71 ppm

15. level 2 for resist thickness and for exposure and level 1 for develop time, Measurement is 75 ppm

16. level 2 for resist thickness and for exposure and level 1 for develop time, Measurement is 76 ppm

First, eyeball your process.

Print up a few plots and descriptive statistics

Then try a t-test, using the overall mean as the target [spec], to determine what is going on [if anything].

Do one factor ANOVAs, one for each of the variables.

Do two factor ANOVAs and possible one with all three variables.

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Explain and analyze during each step of the way, so that one can see that you are aiming at the paint process improvement.

Do enough calculations that one can see that you know what you are doing, list your statistical model, and explain yourself well.

#### Solution Preview

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Analysis of the problem using t-test and ANOVA

You are the engineer for a paint process. You'd like to improve the quality of the process. You have selected your response variable, which is ppm of dust. You have sixteen measurements that you take, you have 3 variables [resist thickness, develop time, and exposure].

You have two levels of each of the variables [say, level one and level 2].

You are interested in which variable or combinations of variables 'mater'.

Your data:

1. level 2 for resist thickness, develop time, and exposure, Measurement is 74 ppm

2. level 2 for resist thickness, develop time, and exposure, Measurement is 72 ppm

3. level 1 for resist thickness, develop time, and exposure, Measurement is 80 ppm

4. level 1 for resist thickness, develop time, and exposure, Measurement is 78 ppm

5. level 2 for resist thickness, develop time, and level 1 for exposure, Measurement is 84 ppm

6. level 2 for resist thickness, develop time, and level 1 for exposure, Measurement is 87 ppm

7. level 1 for resist thickness, develop time, and level 2 for exposure, Measurement is 68 ppm

8. level 1 for resist thickness, develop time, and level 2 for exposure, Measurement is 65 ppm

9. level 2 for resist thickness, level 1 for develop time and for exposure, Measurement is 84 ppm

10. level 2 for resist thickness, level 1 for develop time and for exposure, Measurement is 83 ppm

11. level 1 for resist thickness, level 2 for develop time and for exposure, Measurement is 70 ppm

12. level 1 for resist thickness, level 2 for develop time and for exposure, Measurement is 68 ppm

13. level 1 for resist thickness and for exposure and level 2 for develop time, Measurement is 72 ppm

14. level 1 for ...

#### Solution Summary

ANOVA for resist thickness, develop time, exposure data are discussed in the solution.