1. Statistical Science 9544A
Case Study II

2. Steel Testing
thirty-six samples were taken from one end of a coil of steel that is approximately 700 meters long.

3. Description of the Experiment
Twelve strips of five meters in length and thirty centimeters wide were taken from the coil. Then samples were taken from across the width of each strip (two edges E1 and E2 and the center CTR). Each of the sample types E1, E2 and CTR were mixed amongst themselves and divided into three lots of four samples. All the samples were subjected to the same heat treatment which could add sample to sample variation. A lot of each of E1, E2, and CTR was sent to each of three different labs for destructive testing. The measurement taken are the bend angles at which the samples were destroyed.

4. Data

5. Research Questions Primary Do the labs give the same results?
Secondary
Are there differences in where the sample is taken (E1, E2 and CTR)?

6. First Step: Plot the Data
> boxplot(Angle~Part+Lab)

7. ANOVA
> boxplot(Angle~Part+Lab) > steellm<-lm(Angle~Part*Lab) > anova(steellm) Analysis of Variance Table Response: Angle Df Sum Sq Mean Sq F value Pr(>F) Part Lab e-05 *** Part:Lab Residuals Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

8. Residual Analysis > resids<-residuals(steellm)
> qqnorm(resids)
> qqline(resids)

9. Where are the Two Residuals From?
> resids
E1 B
E2 C

10. Post Hoc Tests – First Step
First extract the mean square error
> anova(steellm)
Analysis of Variance Table
Response: Angle
Df Sum Sq Mean Sq F value Pr(>F)
Part
Lab e-05 ***
Part:Lab
Residuals
---
Signif. codes: 0 ‘***’ ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> mse<-anova(steellm)[["Mean Sq"]][4]
> mse
[1]

11. Post Hoc Test – Do Pairwise Comparisons
> labdata<-split(Angle,Lab) > labmeans<-sapply(labdata,mean) > labmeans A B C > (labmeans[1]-labmeans[2])/sqrt(2*mse/12) > (labmeans[1]-labmeans[3])/sqrt(2*mse/12) > (labmeans[2]-labmeans[3])/sqrt(2*mse/12)

12. Why is Lab C different from the other two?
Back to the Client
Why is Lab C different from the other two?