Oneway Analysis of Variance

Example: Modeling the Height of Men and Women

We assume:

Mean Height for Everyone is 5'6" (men and women combined).

Mean Height for Men is 5'8" (you have to go up 2" to get the male group from the population mean).

Mean Height for Women is 5'4" (you have to go down 2" to get to the female group).

Then I have to go to your score.

Look at how the graphic takes you through
and introduces a formula for the model:

(X = m+a+e).

The Idea of the F-ratio

In the graphic we see that the groups differ. Men are taller than women. This because while there are short men and tall women (and vice versa), the group effect (a) exists.

If it did not, then the means of men and women would be the same and equal to the population mean. So if a has nonzero values, the groups are different.

The F-ratio will tell us how to proceed.

Significant F's mean there are some differences.

Insignificant F's mean that we did not find any differences.

More than 2 Groups and F and a

What is the situation where we have more than two groups? There are two possible scenarios (the Null Hypothesis is True vs. the Null Hypothesis is False).

Reminder:

Null Hypothesis = True = No differences

Null Hypothesis = False = You have Some differences

Let's say the groups are the 1^st Year, Sophomores, Juniors and Seniors.

We are interested in their drinking behavior as mentioned before.

We get a sample of each year. We calculate the group means. Lo and behold, you get some differences. They look like this