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# chap19_2010 - Chapter 19 Analysis of Variance(ANOVA ANOVA...

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Chapter 19 Analysis of Variance (ANOVA)

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ANOVA How to test a null hypothesis that the means of more than two populations are equal. H 0 : μ 1 = μ 2 = μ 3 H 1 : Not all three populations are equal Test hypothesis with ANOVA procedure (Analysis of variance) ANOVA tests use the F distribution
F Distribution F distribution has 2 numbers of degree of freedom (DF) -- numerator and denominator. EXAMPLE: df = (8,14) Change in numerator df has a greater effect on the shape of the distribution. Properties: Continuous and skewed to the right Has 2 df numbers Nonnegative unites.

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Finding the F value Example 19.1 SITUATION: Find the F value for 8 degrees of freedom for the numerator, 14 degrees of freedom for the denominator and .05 area in the right tail of the F curve. Consult Table V of Appendix A corresponding to .05 area. Locate the numerator on the top row, and the denominator along the left. Find where they intersect. This will give the critical value of F. Excel: FDIST (x, df1, df2), FINV(prob., df1, df2)
Assumptions in ANOVA To test H 0 : μ 1 = μ 2 = μ 3 H 1 : Not all three populations are equal The following must be true: Population from which samples are drawn are normally distributed Population from which the samples are drawn have the same variance (or standard deviation) The samples are drawn from different populations that are random and independent.

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How does ANOVA work? The purpose of ANOVA is to test differences in means (for groups or variables) for statistical significance. By partitioning the total variance into the component that is due to true random error (i.e., within-group SSE ) and the components that are due to differences between groups (SSG). SSG is then tested for statistical significance, and, if significant, the null hypothesis of no differences between means is rejected. Always right-tailed with the rejection region in the right tail
Types of ANOVA One-way ANOVA: Only one factor is considered Two-way ANOVA Answer the question if the tow categorical variables act together to impact the averages for the various groups?

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chap19_2010 - Chapter 19 Analysis of Variance(ANOVA ANOVA...

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