1. Statistics 400 - Lecture 17

2. zLast Day: ANOVA zToday: ANOVA Example, Transformations, Paired Comparisons zAssignment: 10.17, 14.34(a), 14.29 (show and interpret the ANOVA Table), 10.46 (a) and (b)

3. Example zPatients with advanced cancers of the stomach, bronchus, colon, ovary or breast were treated with ascorbate zThe purpose of the study was to determine if the survival times differ with respect to the organ affected by the cancer zThe “factor” of interest is the cancer type zThe response variable, y, is the survival time in days

4. Data

5. Box-Plots

6. QQ-Plots

7. Transformations zFrequently, normal scores plots reveal data that is not normally distributed zCan ANOVA be used when data is not normal? zIf there is a large sample from EACH population then ANOVA can be used because the distribution of the sample mean for each population is

8. zWhen the sample size in each population is not normal, can also transform the data so it appears normal zCommon transformations are: ySquare root: x.5 yNatural logarithm: ln(x) yReciprocal transformation: 1/x zApply the transformation to all of the data and re-check normality assumptions zIf normal, then do analysis on transformed data

10. Normal Scores Plot After Square-Root Transformation

11. ANOVA Table

12. Example (Boys Shoes) zCompany ran an experiment to determine if a new synthetic material is better than the existing one used for making the soles of boys' shoes zExperiment was run to see if the new, cheaper sole wears at the same rate at which the soles wear out

13. Example (Boys Shoes) z10 boys were selected at random zEach boy was given a pair of shoes zEach pair had 1 shoe with the old sole (Sole A) and 1 shoe with the new sole (sole B) zFor each pair of shoes, the sole type was randomly assigned to the right or left foot

14. Data

16. zCan we use a 2-sample t-test or ANOVA here? zWould the 2-sample t-test or ANOVA detect a significant difference?

17. Paired or Matched Pairs T-test zSituation: yTwo measurements made on same experimental unit yCompute difference (say B-A) in observation on the same experimental unit yAnalyze differences using a 1-sample t-test zBecause we analyze the differences using a 1-sample t-test, what must we assume about the difference?

18. Data

19. Analyzing the Data