Statistics Chi-Square Goodness-of-Fit Test

Hi, welcome to educator.com.0000

We are going to talk about the chi-square goodness of fit test.0002

So first, we are going to start with the bigger review of where the chi-square test actually fits in.0005

Amongst all the different inferential statistics we have been learning so far and then we are going to talk0012

about a new kind of hypothesis testing, the goodness of fit hypothesis test.0018

So it is going to be similar to hypothesis testing as we been doing so far but there is a slightly different logic behind it.0023

So because it is a slightly different logic there is a new all hypothesis as well as the alternative hypothesis.0029

Then we are going to introduce the chi-square distribution and the chi-square statistic.0037

And then we are going to talk about the conditions for chi-square test when do we actually do it.0044

So where does the chi-square test belong?0049

And it is been a while since we have looked at this if you are going in order with the videos but I think it is0054

pretty good to stop right now and sort of think where we come from?0059

Where are we now?0063

So the first thing we want to think about are the different independent variables that we been able to look at.0065

We been able to look at independent variables the predictor variables that are either categorical or continuous.0072

When the idea is categorical you have groups right?0084

Or different samples, right?0095

When the idea is continuous you do not have different groups you have a different levels that predict something.0098

So just to give you a idea of a categorical IV that would be something like experimental group versus the0107

control group or something like this categorical IV may be someone who gets a drug versus someone who0116

gets the placebo , a group that gets the drivers of the group that gets the placebo and example of the0127

continuous IV might be looking at how much you study predicting your score on a test , so how much you0132

study would be a continuous IV.0140

So that is one of the dimensions that we need to know, is your IV categorical or continuous.0143

You also need to know whether the DV is categorical or continuous so the DV is the thing that were0150

interested in measuring at the end of the day the things that we want to know that this thing change this is0160

the thing we want to predict right, and so far here is how would come.0167

At the very beginning we looked at continuous types of tests and those types of measures and those were0177

the regression, linear regression, as well as correlation.0187

Remember R and regression was that stuff about like Y equals the not + b sub 1 times X, so that was0193

regression and correlation way back in the day.0210

We have been covering a lot of this quadrant actually looking at t-tests and ANOVA right?0215

One important thing to know that t-tests and ANOVAs are both hypothesis tests, only so far have not0224

learned hypothesis testing with regression and correlation.0238

A lot of inferential statistics in college does not cover hypothesis testing of regression until you get to more advance levels of statistics.0241

So what do ANOVAs and t-tests sort of have in common?0255

Well they have in common that they are both categorical IV and continuous DV.0261

The IV is categorical and you only have one, one IV.0269

And your DV is continuous.0277

So that sort of what they have in common, what is different about them?0282

Well the difference is that the IV in t-tests has two levels in only two levels so there is only two groups or two samples.0287

In ANOVAs we could test for more than two samples, we can do that for 3 4 5 samples.0297

So that IV has greater than two levels and so that is where we been spending a lot of our time.0302

So for the most part continuous DV are really important because they tell us a lot, they tell us the find ways0312

that we could actually be different, that the data could actually be different.0320

So you are going to, it is more rare that you will use the categorical dependent variable, that is not going to0327

be as informative to us but it is still possible and that is where the chi-square is going to come in.0334

The chi-square is been coming right in this quadrant where we have categorical IV also a categorical DV so0340

for instance we might want to see something like if you are given a particular job or the placebo, do you0347

feel like you are getting better, yes or no right?0357

So that is a categorical DV, it is not like the score that we can find a mean and so this is where the chi-square tests come in.0360

And there is going to be 2 chi-square tests that we are going to look at.0375

The first one, we are going to cover today and it is called goodness of fit.0379

The next one is in the next lesson and it is called a test of homogeneity.0382

They are both chi-square test.0386

The other way you will see that what is written is chi-squared, so sometimes, do not think of, oh what is this doing here?0387

When it has this little curvy part here we need chi-square, the Greek letter chi, finally this is a test that0398

rarely is covered in inferential statistics but at more advanced levels of statistics he did cover it and it is called0407

the logistic test and logistic test takes you from continuous IV to categorical DV.0415

But that is rare design used in conducting science, it is not as informative as continuous to continuous or categorical to continues.0424

Alright so we are going to spend your time right in here.0436

So there is a new twist on hypothesis testing, it is not totally different, it is still very similar but there is there is a subtle difference.0441

Today we are going to start off with the chi-square goodness of fit test.0454

Basically let us think about hypothesis testing in general.0457

In general you want to determine whether a sample is very different from expected results that is the big idea of hypothesis testing0462

and expected results come from your hypothesized population.0470

If your sample is very different than we usually determine that with some sort of test statistic and looking0474

at how far it is on the on the tested statistics distribution right and we look at whether it is past that Alpha0481

cut off or the critical test statistic right and then we say, oh this sample is so different than would be0489

expected given that the null hypothesis is true that we are going to reject the null hypothesis.0496

That is usually hypothesis testing. It still takes that idea whether to look at whether a sample is very0504

different from expected results, but the question is how are we going to compare these two things?0511

We are not going to compare means anymore, we are not going to look at the distance between means,0517

nor are we going to look at the proportion of variances that is not what we are going to look at either.0521

Instead we are going to determine whether the sample proportions for some category are very different0527

from the hypothesized population proportion.0539

And the question will be how do we determine very different and here is what I mean by determine0542

whether the sample proportions are different from the hypothesized population proportion.0549

So here I am just going to draw for you sort of schematically what the hypothesized population proportions might look like.0554

So this is just sort about the idea, so you might think of the population as being like this and in the0569

population you might see a proportion of one third being blue, one third being red, and one third being yellow.0577

Now already it is hard to think about like you could already sort of see, well we cannot get the average of0588