# Analysis of Variance (ANOVA)

1. Why are you no longer directly comparing sample means?

2. How does using the F test - the analysis of variance (ANOVA) reduce your Type I error rate?

3. What is the difference between a within-groups and a between-groups variance?

4. If F is significant, why should you follow up with a post hoc test?

5. Why don't you use post hoc tests when F is not significant?

6. What are the assumptions of the F test?

7. How is the F test an extension of the t test?

8. Why are there two df measures with this test?

9. How do you interpret the findings of an ANOVA in terms of a variance measured

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#### Solution Preview

1. Why are you no longer directly comparing sample means?

-Due to the possibility that the data from which the means were calculated do not come from the same populations. When this is true, we cannot compare even two sample means - this would be tantamount to comparing the mean price of apples to the meant price on crackers.

-Due to the errors that may go into collecting the data that produced the means. Some examples are sampling error, random error, and measurement errors. These errors make direct comparison of just the means faulty.

- Due to the observations from which the means were calculated and not independent. If there is a correlation between the observations of the separate groups, direct means comparison is not accurate.

-Another not-so-important reason is that the variance of the response or dependent variable is not the same for all the populations of the different.

When the last two points are true, comparing three or more means is not a good scientific approach.

2. How does using the F test - the analysis of variance (ANOVA) - reduce your Type I error rate?

Assume we are to compare five means. We may do one ANOVA test or 10 pairwise comparison T-tests. The number of hypotheses tested with ANOVA is less than that with ...

#### Solution Summary

Comparing sample means and doing anova with a follow up post hoc multtiple comparison test