Oneway Analysis of Variance

So What Does This Have to do with the Group Differences?

The First Big Set of Ideas!!

A A A

We will Calculate
the F-ratio.
& not t

%

We Will Not Calculate Individual t-tests between all Possible Pairs.

There are 6 of them:

1^st vs soph

1^st Vs Junior

1^st Vs Senior

2^nd Vs Junior

2^nd Vs Senior

Junior Vs Senior

Warning, Warning, Danger, Young Statistician!

If we calculate all t-tests, we will DRAMATICALLY INCREASE THE TYPE 1 ERROR RATE!

TYPE 1 ERROR IS SAYING THERE IS A DIFFERENCE WHEN THERE ISN'T ONE!

THERE WILL BE A 26.5% CHANCE THAT WE MAKE AT LEAST 1 TYPE ERROR!

IT'S LIKE RUSSIAN ROULETTE.

THERE IS A ONE IN 6 CHANCE OF DISASTER EACH TIME YOU PLAY. BUT IF YOU PLAY 6 TIMES, THE ODDS YOU SHOOT YOUR SELF AT LEAST ONCE IS 26.5%

the F-ratio Avoids this problem

%

How Do We Calculate F?

The F - ratio is calculated by using rather complex looking formulas - you will find them in your books.

However, the idea is simple.

It is based the general linear model of a score.

The Idea of a Linear Model

[x = m+a+e]

Your score can be consider as a map to you.

1. Start at the mean of everybody, independent of groups.

2. Go to your group

3. Go to you.

This map can be considered as a sum:

Your score =
Population Mean + [Distance to your Group] + Distance to You