anova demo part 1: explanation

ANOVA DemoPart 1: Explanation

Psy 320Cal State Northridge

Andrew Ainsworth PhD

ANOVA works by:

• Breaking down participants score into parts– If everyone is from the same population to start

with (before any treatment is given to them) then they should all start at the same mean – the grand mean

i GMY Y

Grand Mean

Grand Mean Alone

ANOVA works by:

• Then states that any distance the subject’s score is away from the grand mean is “caused” of the group they belong to (i.e. which treatment they received, etc.)…

i GM IVY Y Effect

Grand Mean

1X 2X 3X

ANOVA works by:

• Then states that any difference the subject’s score is away from the grand mean is because of the group they belong to (i.e. which treatment they received)

• Plus some random subject variation

i GM IVY Y Effect Random

Grand Mean

1X 2X 3X

ANOVA works by:

• If this is done for every person then the Effect (Between Group) Variation and the Random (Within Group) Variation together make up the Total Variability of the participants’ scores around the Grand mean

Grand Mean

1X 2X 3X

The job of an ANOVA is to

• Separate the Real Variation “caused” by the different levels of the IV from the random (“fake”) Variation that is also present

• This is sometimes referred to as trying to see the Signal (the real effect) through the Noise (the random variation)

• The F-test in an ANOVA is often referred to as a signal-to-noise ratio

• So let’s illustrate the pieces of ANOVA…

Grand Mean

Grand Mean

Total Variability

Grand Mean1X

2X

3X

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability

Grand Mean1X

2X

3X

Between Group Variability + Within Group Variability

Grand Mean1X

2X

3X

Total = Between Group Variability + Within Group Variability

Within Group Variability

Within Group Variability

Within Group Variability

Within Group Variability

Grand Mean

Between Group (with WG shown): Random Differences Alone

Grand Mean

Between Group (with WG shown): Real + Random Differences

Summary: ANOVA tries to…• Identify the size of the Random (Average Within

Groups) variance so that we have an idea of how large the randomness is in our data

• Identify if the Between Groups variance (“caused” by our IV) is large enough for us to believe that it isn’t really just random

• Indicate whether our BG variance is significantly large (an not just random) when compared to the Random (WG) variance we identified

• Assess the size of the BG ratio by calculating the BG and WG variances and forming the F-ratio (see Part 2)