Oneway Analysis of Variance

There are two possibilities:

1^st Pass at These Two:

All college kids drink the same = Year Doesn't Matter = Null Hypothesis is True

Some Years Drink Different Amounts = Year Does Matter = Null Hypothesis is True

2^nd Pass at These Two:

All college kids drink the same = Year Doesn't Matter = Null Hypothesis is False

(X = m+a+e)

This means:

a Does Not Exist.
No Group Effect.
Group Differences are by Chance:
You have an Insignificant F- Ratio

That's Why a is Grayed Out in the Linear Model

Pictorially, the illustration above shows that all four groups of students are mixed together into one big population of students.

By sheer luck, you sampled low end 1^st years, a little higher Sophomores, even higher Juniors, and hard drinking Seniors.

You missed the low drinking Seniors and hard drinking 1^st years.

Your differences are just luck.

There are no Alphas (a) between Groups

%Ï Some Years Drink Different Amounts = Year Does Matter = Null Hypothesis is False

(X = m+a+e).

This means:

a Does Exist.
There is a Group Effect.
Group Differences are Real
You Will Have a Significant F-Ratio

There are Alphas (a) between Groups.

Some of the Group Means are Different From the Total Mean

We Reject the Null Hypothesis

Our Sample Means (or at least some of them) Come from Different Populations.