Oneway Analysis of Variance

Why is this Important?

How do you find out if ANY groups in a set larger than two differ significantly from each other? *
The F -ratio will tell us this!

Can you estimate whether the differences are relatively big or small?
Measures of Explain Variance will test us this!

Here's the issue in a nutshell:

*Nuance - you could really do a two group situation with the t-test but Anova works also.

Which groups differ from each other? There are a lot of possible pairs if you have more than two groups.

So let's get started

Data Types

For our discussion of Anova, we will be using measurement data (numerical scores).

We Will Need:

Measures of central tendency: The Mean

Measures of variability Standard Deviation

Our First Intuitive Example

An example: College Drinking

You are concerned with college drinking behavior.
You think it is related to your year in school.
You collected data from 1^st year, sophomores, juniors and seniors about how many drinks they have per week.
You calculate the means.
They look different - But are they?

There could be many different patterns of means!

Look at the pattern of means:

All groups could be equal. 1

1^st years and sophomores could drink less than Juniors and Seniors. 2

1^st years could drink a great deal. Sophomores and Juniors less and then it goes up for Seniors 3