## Effect Size

I agree this is going to be the lesson

on performing effect size analyses we're

gonna specifically focus on the Cohen's

D effect size and the partial ADA

squared effect size so we have a data

set here with just three columns we have

participant ID some condition called

discussed condition and saying called

conservative attitudes imagine that in

the study individuals are brought into

the lab and they are asked to smell

something some individuals smell

something that has absolutely no sense

some individuals smell something that is

kind of floral smells nice while other

individuals smell something that smells

very very bad like rotten food if we go

to variable view we can see that a

disgust condition is saying called

manipulated disgust that's our

independent variable if we click on

values we can see that a negative one is

the pleasant to kind of floral smell the

zero is the control no disgust and the

one is the heinousness that's something

really nasty and then our dependent

variable is conservative attitudes do

people have more conservative attitudes

after smelling after being disgusted the

perhaps hypothesis is that they do so

we'll start off with a Cohen's D

analysis Cohen's D effect size is used

when you are comparing two groups so

let's say we want to perform an

independent sample t-test comparing the

the control group 0 and the disgust

group 1 so this is ignoring the negative

one the floral condition if we hit OK

and then we move a conservative at its

over here we'll run our independent

sample t-test we'll hit OK and we'll

find that in fact the groups do do

differ this is a significant difference

it's a T value of negative three point

seven eight two with ten degrees of

freedom and that's significant well

below the point zero five now if we look

at our means we can we'll use this for

determining our Cohen's D what we'll

need to do is we will go to an internet

browser and we will go to the following

address www

CCS edu backslash tilde faculty slash

Becker slash and it'll bring us to this

website which is an effect size

calculator this is a really good

calculator it allows you to calculate

Cohen's D in a number of ways we're

gonna see here we have group one mean

and Sand deviation and group two mean

and standard deviation so what we're

gonna do is we're gonna start inputting

these numbers the first mean it doesn't

matter which group is which we have a

mean of four with this information of

one point four one so we'll put in four

and one point four one and then for

group two it's a six point eight three

and one point one seven so six point

three and and if we hit compute we will

get our Cohen's D down here this

negative two point one according to

Cohen 0.2 0.2 0.3 is a small effect 0.5

is a moderate effect point eight is a

large effect so an effective two point

one or negative two point one would be

huge ignore the positive and negative we

take the absolute value so this would be

a very large effect and that's perhaps

not surprising given how big the means

are and the different thing that means

in this the relative small standard

deviation now let's say we wanted to

calculate partial a two squared which is

the effect size over a number of

variables are a number of different

levels not just two if we go back to our

data we can go to analyze general linear

model and univariate now you might be

thinking to yourself well we only have

one variable one independent variable

discuss why are we running a univariate

analysis why don't we just run a one-way

ANOVA well one way ANOVA doesn't give us

any options to calculate effect size so

we have to do a univariate analysis and

univariate analysis can be used for

one-way ANOVA is you can even use it for

T tests all univariate means is that you

have one dependent variable so the fact

that we tend to use you know independent

sample t-tests option when we do T tests

and the one way between solution over

option when we do one way between so

there's no but doesn't mean we couldn't

do

of area so we're gonna move manipulated

to discuss into fixed factors and

conservative attitudes into the

dependent variable and all we're gonna

do now is going to click on options and

we're gonna click on estimates of effect

size we can also click on descriptive

statistics if we want so you can find

that means and certain variations for

those groups we can hit ok and then ok

again we can see these are between

survey's factors there's six people in

each group here are the descriptive

statistics so it looks like there's a

difference between the three groups we

can go over to our between-subjects

effect test and see that the F is 5.9

where the significance of point 0 1 3

meaning that this is there is a

significant difference among all of the

groups we would write this as F 2 comma

15 equals five point nine zero three

comma P equals point zero one three the

partial eighth is squared however is

0.44 this would be a very large effect

and and this is how we get our partial a

2 squared which can be read and written

as as the ADA symbol squared equals

point four four zero and that is how you

calculate Cohen's D and partial 8a

squared in SPSS