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• 00:01

DANIEL LITTLE: In this video, I will describe the effect sizeand how to compute the effect size for twoparticular statistical tests.One for a t-test and the other one for ANOVA.So there's a problem with statistical testing.If you compute a statistical testand you find out you have a significant effect,it doesn't tell you how large the effect is.

• 00:22

DANIEL LITTLE [continued]: That's the job of the effect size measure.Effect size is a quantitative measure of the sizeor the strength of your particular effect.You may have a small effect, or you may have a large effect,and both of those might lead you to a significant statisticaltest.The significance of the test in and of itself

• 00:42

DANIEL LITTLE [continued]: doesn't tell you about the size of your actual effect.So let's consider two particular measures of effect size-- onecalled Cohen's D. This one is particularly useful wheneveryou've conducted a t-test.And the other one's called partial eta-squared.And this one is useful for when you've conducted an ANOVA.

• 01:03

DANIEL LITTLE [continued]: For a t-test, our statistical measure, the t-statistic,tells us about whether or not we have a significant differencebetween the means of two groups, or whether one group issignificantly different from zero.Our effect size measure, Cohen's D,is also based on the distance between the means.Here's how you compute Cohen's D. To compute it

• 01:25

DANIEL LITTLE [continued]: we use the following formula.In this particular formula, we have a number of variables.So to compute Cohen's D, we take the differencebetween the means of both of our groups, so the mean of group 1and the mean of group 2, and divide them by s.Now, in this example, s is the pooled standard deviation,

• 01:50

DANIEL LITTLE [continued]: which I will show you how to compute on the following slide.M1 is the mean of group 1, and M2 is the mean of group 2.Our pooled standard deviation is computed using this equation.The equation looks a somewhat complicated,but it's actually quite simple.We need a few things here.

• 02:11

DANIEL LITTLE [continued]: The first thing we need is the size of our group 1.So how many samples are in group 1.And that's denoted here by N1.And we also need our observed standard deviation of group 1,and that's denoted here by S1.Our first quantity, this particular quantity here,

• 02:31

DANIEL LITTLE [continued]: refers to information that we getfrom our first group, the sample size and the standard deviationof our first group.And it's simply the sample size of that groupminus 1 times the standard deviation squaredof that particular group.We add this to the same quantity from our second group.

• 02:53

DANIEL LITTLE [continued]: So the sample size of our second groupminus 1 times the standard deviation of our second groupsquared.And then finally, we take the square rootof that entire quantity and divide itby the sample size of our first group plus the sample sizeof our second group minus 2.And that gives us an estimate of our pooled standard deviation,

• 03:16

DANIEL LITTLE [continued]: from which we can compute Cohen's D.Once we've computed Cohen's D, Cohenprovides some rules of thumb for interpreting the effect size.Cohen's D of 0.2 is considered a small effect.0.5 is considered a medium effect.and 0.8 is considered a large effect.Be aware that these are only guidelines.

• 03:38

DANIEL LITTLE [continued]: Cohen himself was a bit circumspectabout suggesting these guidelines,warning that the operation of suggesting these rules of thumbwas fraught with many dangers.So take them with a grain of salt.But they nonetheless give us some guidelinesfor how we can interpret the effect size measure.For an ANOVA, an ANOVA assesses the variability

• 03:60

DANIEL LITTLE [continued]: of our particular groups that we'reinterested in as expected based on chance aloneor based on chance plus some experimental effect.It makes sense in this case to use an effect sizemeasure which is based on the amount of variance explained.The particular effect size measurethat we're going to consider first

• 04:20

DANIEL LITTLE [continued]: is one called eta-squared.So this symbol here that looks like an nis actually the Greek letter eta.And this entire quantity is pronounced eta-squared.To compute eta-squared, we would simplytake the sum of squares between groupsand divide it by the sum of squares total.

• 04:41

DANIEL LITTLE [continued]: Recall that whenever you're computing a one-way ANOVA,the sum of squares total is the sum of squares between groupsplus the sum of squares within groups.Another popular measure of effect sizewhich is used by the statistics software program SPSSis called partial eta-squared.And it's very, very similar to eta-squared,

• 05:02

DANIEL LITTLE [continued]: but it's slightly different.So it's important for us to understandwhat the actual difference is.So to indicate that we're dealingwith partial eta-squared now, we've subscripted this etavalue with the letter p.So partial eta-squared is computed slightlydifferent from eta-squared.

• 05:23

DANIEL LITTLE [continued]: To compute partial eta-squared, we take the sum of squaresbetween and divide it by the sum of the sum of squaresbetween plus the sum of squares of the errors.Now, for a one-way ANOVA, there'sno difference between eta-squared and partialeta-squared, but this is generally nottrue for more complicated ANOVAs, where you've gotinteractions between variables.

• 05:43

DANIEL LITTLE [continued]: And those interactions require different error termsthen your main effects.Consequently, when you run, say, a two-way ANOVA, or a higherlevel ANOVA, partial eta-squared will give youa different answer than eta-squared.But in general, either one of those measurescan be used as a measure of an ANOVA's effect size.Here's an example of some output from SPSS, a table of values

• 06:09

DANIEL LITTLE [continued]: that you get whenever you run a one-way ANOVA in SPSS.Note that SPSS gives you the sum of squaresvalues for between groups, within groups, and in total.So you have all of the informationyou need from the SPSS table to compute eta-squared or partial

• 06:33

DANIEL LITTLE [continued]: eta-squared.Cohen, again, recommends the following guidelinesfor interpreting eta-squared.0.02 is a small effect size.0.13 is a medium effect size.And 0.26 is a large effect size.Again, the same guidelines can beused for interpreting partial eta-squared as well,

• 06:55

DANIEL LITTLE [continued]: with the appropriate caveat that these are simply rules of thumband should be taken with a grain of salt.So here we've examined three measures of effect size.One for t-test, Cohen's D, and two for ANOVA,eta-squared and partial eta-squared.To compensate for the fact that our statistical tests do nottell us the size of our effect, we report effect size measures

• 07:17

DANIEL LITTLE [continued]: as well.There are, in fact, many other effect size measuresapart from the three that we've actually talked about.In general, each of the effect size measureshas different properties that youmight want to consider whenever you're computing your effectsize.But for t-test and ANOVA, usually what you'll see

• 07:39

DANIEL LITTLE [continued]: is either Cohen's D or some measureof eta-squared or partial eta-squared.

### Video Info

Series Name: Statistics for Psychology

Episode: 4

Publisher: University of Melbourne

Publication Year: 2014

Video Type:Tutorial

Methods: Effect size, T-test, Analysis of variance

Keywords: mathematical concepts

### Segment Info

Segment Num.: 1

Persons Discussed:

Events Discussed:

Keywords:

## Abstract

In the fourth chapter of the series "Statistics for Psychology," Professor Daniel Little discusses calculating effect size in statistics. He demonstrates effect size calculations for both t-tests and ANOVA using Cohen's D and eta-squared.