Wiki Page, Math 13 - Perez Sandbox : Unit 10 - ANOVA Review

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2026-01-17T21:16:11-08:00

This concludes the lesson for Unit 10 (Module 26).

Let's summarize

We use the ANOVA F-test when we compare more than two population means. We can also think of the ANOVA F-test as a way to examine the relationship between a categorical explanatory variable that has more than two values and a quantitative response variable.

The hypotheses that are being tested in the ANOVA F-test are:
:
: are not all equal %%%%% This equation is not portable --Erich %%%%%

Alternatively, we can state the null hypothesis as there is no relationship between the explanatory and response variables, and the alternative hypothesis as there is a relationship between the explanatory and response variables.

Conditions for the ANOVA F-test are as follows:

Samples are randomly selected and independent.

Distribution of the response variable in each population is normal in shape. If we cannot verify this, we examine the distribution of the response variable in each sample. If the sample distributions are not heavily skewed, then we assume that the response variable is normally distributed in each population.

The standard deviation of the response variable in each population is the same. If we cannot verify this, we compare the sample standard deviations. If the ratio of the largest to the smallest sample standard deviation is less than 2, we assume that the standard deviations in the population are the same.

The idea behind the ANOVA F-test is to check whether the variation among the sample means is due to true differences among the μ's or merely due to sampling variability. We use the F-statistic, which is a ratio of the difference in sample means to the variation within each sample.
%%%%% This equation is not portable %%%%%

Once we verify that we can safely proceed with the ANOVA F-test, we use StatCrunch or other software to carry it out.

If the ANOVA F-test has rejected the null hypothesis we can look at the confidence intervals for the population means to get a visual insight into why was rejected (i.e., which of the means differ).