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Chapter 15 – Analysis of Variance

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

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Chapter 15 – Analysis of Variance

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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 grossviolations 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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