1. INT 506/706: Total Quality Management Lec #9, Analysis Of Data

2. Outline Confidence Intervals t-tests –1 sample –2 sample ANOVA 2

3. Hypothesis Testing Often used to determine if two means are equal

4. Hypothesis Testing Null Hypothesis (H o )

5. Hypothesis Testing Alternative Hypothesis (H a )

6. Hypothesis Testing Uses for hypothesis testing

7. Hypothesis Testing Assumptions

8. Confidence Intervals Estimate +/- margin of error

9. Confidence Intervals CONCLUSION DRAWN Do Not Reject H o Reject H o THE TRUE STATE Ho is TRUECORRECT TYPE I Error (α risk) Ho is FALSE TYPE II Error (β risk)CORRECT You conclude there is a difference when there really isn’t You conclude there is NO difference when there really is

10. Confidence Intervals Balancing Alpha and Beta Risks Confidence level = 1 - α Power = 1 - β

11. Confidence Intervals Sample size Large samples means more confidence Less confidence with smaller samples

12. Confidence Intervals

13. t-tests A statistical test that allows us to make judgments about the average process or population

14. t-tests Used in 2 situations: 1)Sample to point of interest (1-sample t-test) 2)Sample to another sample (2-sample t-test)

15. t-tests t-distribution is wider and flatter than the normal distribution

16. 1-sample t-tests Compare a statistical value (average, standard deviation, etc) to a value of interest

17. 1-sample t-tests

18. Example An automobile mfg has a target length for camshafts of 599.5 mm +/- 2.5 mm. Data from Supplier 2 are as follows: Mean=600.23, std. dev. = 1.87

19. 1-sample t-tests Null Hypothesis – The camshafts from Supplier 2 are the same as the target value Alternative Hypothesis – The camshafts from Supplier 2 are NOT the same as the target value

20. 1-sample t-tests

22. 2-sample t-tests Used to test whether or not the means of two samples are the same

23. 2-sample t-tests “mean of population 1 is the same as the mean of population 2”

24. 2-sample t-test Example The same mfg has data for another supplier and wants to compare the two: Supplier 1: mean = 599.55, std. dev. =.62, C.I. (599.43 – 599.67) – 95% Supplier 2: mean = 600.23, std. dev. = 1.87, C.I. (599.86 – 600.60) – 95%

25. 2-sample t-tests

27. ANOVA Used to analyze the relationships between several categorical inputs and one continuous output

28. ANOVA Factors: inputs Levels: Different sources or circumstances

29. ANOVA Example Compare on-time delivery performance at three different facilities (A, B, & C). Factor of interest: Facilities Levels: A, B, & C Response variable: on-time delivery

30. ANOVA To tell whether the 3 or more options are statistically different, ANOVA looks at three sources of variability Total Total: variability among all observations Between Between: variation between subgroups means (factors) Within Within: random (chance) variation within each subgroup (noise, statistical error)

31. ANOVA

32. Factor SS = 4*(Factor mean-Grand mean)^2 SS = (Each value – Grand mean) 2 Total SS = ∑ (Each value – Grand mean) 2

33. ANOVA (Each mean – Factor mean) 2 ∑

34. ANOVA Total Total: variability among all observations 184.92 Between Between: variation between subgroups means (factors) 118.17 Within Within: random (chance) variation within each subgroup (noise, statistical error) 66.75

35. ANOVA Between group variation (factor) 118.17 + Within group variation (error/noise) 66.75 Total Variability 184.92

36. ANOVA

38. Two-way ANOVA More complex – more factors – more calculations Example: Photoresist to copper clad, p. 360

39. ANOVA