1. Chapter 15 – Analysis of Variance Math 22 Introductory Statistics

2. Analysis of Variance (ANOVA) Purpose: To compare a group of means simultaneously. Assumptions: Each sample has been randomly and independently selected from the population it represents The parent distributions are all normal The variances of the k samples are equal (similar to each other)

3. ANOVA It is important to keep in mind that we looking for gross violations of the assumptions of normality. Minor departures are not a concern.

4. ANOVA Null Hypothesis: Alternative Hypothesis: At least one mean is not equal.

5. Multiple Comparisons Calculating One-Way ANOVA Multiple Comparisons - Process of identifying groups that differ from one another.

6. Fisher’s Least Significance Difference (LSD) Use in detecting true differences between group means if applied after an ANOVA which indicates a difference exists. The form of the confidence interval is:

7. Components of Fisher’s LSD

8. Kruskal-Wallis Test Nonparametric alternative to the One- Way ANOVA. Used when there is a gross violation to the normality or similar variance assumption. Does computations with the ranks of the data rather than original data values. We would compare medians as oppose to means.

9. Kruskal-Wallis Test Null Hypothesis: Alternative Hypothesis: At least one median is not equal.