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

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

Hypothesis Testing Often used to determine if two means are equal

Hypothesis Testing Null Hypothesis (H o )

Hypothesis Testing Alternative Hypothesis (H a )

Hypothesis Testing Uses for hypothesis testing

Hypothesis Testing Assumptions

Confidence Intervals Estimate +/- margin of error

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

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

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

Confidence Intervals

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

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)

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

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

1-sample t-tests

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

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

1-sample t-tests

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

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

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

2-sample t-tests

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

ANOVA Factors: inputs Levels: Different sources or circumstances

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

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)

ANOVA

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

ANOVA (Each mean – Factor mean) 2 ∑

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

ANOVA Between group variation (factor) Within group variation (error/noise) Total Variability

ANOVA

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

ANOVA