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Chapter 15 – Analysis of Variance Math 22 Introductory Statistics.

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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.


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