Crash Course in

ANOVAs and MANOVAs

(Design Theory) First, Let's Review We use Analysis of Variance designs when we want to answer the question:

Are the means of all the different groups equal? Null Hypothesis (H0) All means are equal to the grand mean Alternative Hypothesis (H1) At least one mean is not equal to the grand mean this line = the mean of the distribution of group 2 So we test the following hypotheses... VS. What are these "groups"

and

how do I get them? Independent Variables We figure out what the groups are, based on the independent (predictor) variables aka "factors" we're interested in. remember these are the things we think are causing effects. One Independent Variable We want to know whether being tired or not influences grumpiness. So we have our independent variable (let's call it tiredness) IV1 = Tiredness We want to look at whether or not people are tired or not, so we split them into two levels (not tired vs. tired) IV1 = Tiredness IV1a = Not Tired

IV1b = Tired So going back to the picture... we now have This is a one-way design This is a two-way design

aka.

a 2x2 Factorial design Variations Two Independent Variables Now, we want to know whether the tiredness and coffee influences grumpiness. So we have TWO independent variables (let's call them tiredness and coffee) We want to look at whether or not people are tired or not, so again we split them into two levels (not tired vs. tired) IV1 = Tiredness IV1a = Not Tired

IV1b = Tired IV1 = Tiredness

IV2 = Coffee IV1 = Coffee? IV2a = no coffee

IV1b = yes coffee We want to have a group where we give people coffee, and other one where we don't so we split people into two levels (no coffee vs. coffee) How many "ways" is the design? So we have

2 (tired vs. not tired)

x

2 (coffee vs. no coffee)

= 4 conditions You can have as many IVs ("ways") as you see fit You can have as many levels of each IV as you see fit IV1: Tiredness (one-way)

+ IV2: Coffee (two-way)

+ IV3: Gender (three-way)

+ IV4: Personality type (four-way)

etc. IV1: Tiredness (tired vs. not tired)

+ IV2: Coffee (coffee vs. no coffee) - 2 x 2

+ IV3: Gender (male vs. female ) - 2 x 2 x 2

+ IV4: MBTI Personality type (all 16 types) - 2 x 2 x 2 x 16

etc. So I now know how many ways

my design is...

Do I use ANOVA or MANOVA? Dependent Variable We figure out what analyses

(ANOVA or MANOVA) to use,

based on the dependent (criterion) variable we're interested in. Specifically, we look at how we measure the dependent variable Recall, our dependent variable

(or what we're interested in what the factors effect)

is grumpiness. So how are we measuring grumpiness? Let's say, I'm measuring grumpiness by asking people how grumpy they feel (self-report) If that's my only indicator of grumpiness, then this is univariate (one thing represents the DV) So we would use ANOVA Recall, our dependent variable

(or what we're interested in what the factors effect)

is grumpiness. So how are we measuring grumpiness? Let's say, now I'm measuring grumpiness by

1. asking people how grumpy they feel (self-report)

2. asking how angry they feel (self-report)

3. I'm going to video tape them while I do something that might piss them off

(behavioral) If I now have more than one indicator of grumpiness, then this is multivariate variate (multiple aspects represent one DV) So we would use MANOVA 1 2+ Variations and Notes You can have as many measures of your dependent variable as you see fit *IMPORTANT NOTES*:

IF you have more than one dependent variable, that does not mean you use MANOVA. MANOVA is only used when you have multiple aspects/measures of ONE dependent variable.

When dealing with multiple dependent variables. You run separate ANOVAs and MANOVAs depending on how each dependent variable is measured. Grumpiness how grumpy do you feel? Grumpiness Grumpiness how grumpy do you feel? how angry do you feel? video tape of reaction

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# Factorial ANOVA/MANOVA Crash Course

For Wilson