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INT 506/706: Total Quality Management

INT 506/706: Total Quality Management. Lec #9, Analysis Of Data. Outline. Confidence Intervals t-tests 1 sample 2 sample ANOVA. Hypothesis Testing. Often used to determine if two means are equal. Hypothesis Testing. Null Hypothesis (H o ). Hypothesis Testing.

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INT 506/706: Total Quality Management

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

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

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

  4. Hypothesis Testing Null Hypothesis (Ho)

  5. Hypothesis Testing Alternative Hypothesis (Ha)

  6. Hypothesis Testing Uses for hypothesis testing

  7. Hypothesis Testing Assumptions

  8. Confidence Intervals Estimate +/- margin of error

  9. Confidence Intervals 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: • Sample to point of interest (1-sample t-test) • 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. 1-sample t-tests 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

  21. 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

  26. 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: variability among all observations Between: variation between subgroups means (factors) Within: random (chance) variation within each subgroup (noise, statistical error)

  31. ANOVA

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

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

  34. ANOVA Total: variability among all observations 184.92 Between: variation between subgroups means (factors) 118.17 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

  37. ANOVA

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

  39. ANOVA

  40. ANOVA

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