Statistics Effect Size & Power

Hi, welcome to educator.com.0000

We are going to talk about effect size and power.0002

So effect size and power, 2 things you need to think about whenever you do hypothesis testing.0005

So first effect size.0011

We are going to talk about what effect sizes is by contrasting it to the T statistic.0013

They actually have a lot in common but there is just one subtle difference that makes a huge difference.0019

Then we are going to talk about the rules of effect size and why we need effect size.0026

Then we are going to talk about power.0032

What is it, why do we need it, and how do all these different things affect power for instance sample size,0035

effect size, variability in alpha, the significance level.0042

So first things first, just a review of what the sample T really means.0048

So a lot of times people just memorize the T formula, it is you know the X bar minus mu over standard error but think about what this actually means.0056

So T equals X bar minus mu over the standard error.0070

And all right that is S sub X bar.0076

What this will end up giving you is this distance so the distance between your sample and your hypothesized mu.0079

And when you divided by standard error you get how many standard errors you need in order to get from bar to your mu.0087

So you get distance in terms of standard error.0097

So distance in terms of standard error.0102

And you want to think of in terms sort of like instead of using like feet or inches or number of friends, we get distance in the unit of standard error.0111

So whatever your standard error is for instance here that looks about right, because this is the normal0123

distribution that should be about 68% so that is the standard error.0132

Your T is how many of these you need in order to get to T.0139

So this might be like a T of 3 1/2, 3 1/2 standard errors away gets you from mu to your sample difference and so this is the case of the two sample t-test.0146

So independent samples are paired samples where we know the mu is zero.0164

So this is sort of the concept behind the T statistic.0169

Now here is the problem with this T statistic.0175

It is actually pretty sensitive to N.0181

So let us say you have a difference that is very, that is going to stay the same so a difference between, you know let us say 10 and 0.0185

So we have not that difference.0199

If you have a very very large N then your S becomes a lot skinnier.0202

And because of that your standard error is also going to shrink so the standard error shrinks as N shrinks.0212

And because of that, even though we have not changed anything about this mean, about the X bar or mu,0226

by shrinking our standard error we made our T quite large.0237

So we made our T like all of a sudden were 6 standard or errors away but I really have not changed the picture.0244

So that is actually a problem that T is so highly affected by N.0252

The problem with that is that you could artificially make a difference between means, look statistically significant by having a very large N.0258

So we need something that tells us this distance that is less affected by N and that is after effects size comes in.0268

So in effect size what we are doing is we want to know the distance in terms of something that is not so affected by N.0278

And in fact we are going to use the population standard deviation because let us think about T.0288

So that is X bar minus mu over standard error.0295

So this contrast that to looking at the distance in terms of the standard deviation of the population, what would that look like.0303

Well, we could actually derive the formula ourselves.0307

We want that distance in terms of you know number of inches or number problem correct or whatever the0321

raw score is over instead the standard error we would just use S or if you had it you would use Sigma.0328

So you could think of this as the estimated Sigma and this is like the real deal Sigma.0341

And that is what effect size is and effect size is often symbolized by the letters D and G.0349

D is reserved for when you have when you have Sigma, G is used for when you use S.0360

Now let us talk about the roles of effect size.0367

The nice thing about effect size is that the N does not matter as much whether you have a small sample or large sample the effect size stays similar.0373

In test statistics suggest T or Z, the N matters quite a bit and let us think again about why.0384

So the T statistic I have been writing at so far as over standard error but let us think about what standard error is.0396

Standard error is S divided by the square root of N, now as N gets bigger and bigger so let us think about N getting bigger.0406

This whole thing in the denominator, this whole idea this whole thing becomes smaller and smaller.0417

And when you divide a positive or negative or positive, if you divide some distance by a small number then0430

you end up getting a more extreme value, more extreme.0441

So by more extreme I mean way more positive, more positive ,more on the positive side or way more negative.0448

So the T statistic is very very sensitive to N so is the Z because Z the only difference is instead of S we use Sigma.0463

And so the same logic applies but for effect size T and G we do not divide by square root of N so in that way N does not really have as much.0474

Okay so one thing to remember is if you know Sigma use covens D, if you need to estimate the standard deviation from the sample S, you want to use hedges G.0488

Okay so now you know what effect size is and it is nice that it is not as affected by N but why do we need it?0500

Well effect size is what we use, the statistically used to interpret practical significant so for instance we 0839.8 might have some sort of very small difference between group 1 and group 2 so with the males and females0510

on some game or task, there is a very tiny difference like you know let us just say males are ahead by .0001 points.0527

And practically, it sort if does not matter but if you have a large enough effect size if you have a large0540

enough N you could get a small enough standard error that you can make that tiny difference seem like a0549

big deal and you can imagine that would be sort of odd situation.0556