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Chi-Square Test for Association and Independence

Chi-Square Test for Association and Independence

Author: Katherine Williams
Description:

Calculate the degrees of freedom for a data set.

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Tutorial

Source: Table created by Katherine Williams

Video Transcription

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This tutorial talks about the chi-square test for association. It's also known as the Chi-square test for independence. When we're doing, this the null hypothesis is that there is no association between categorical variables in a single population. So the key part here is that we're in one single population or treatment. And then the alternative hypothesis is going to be that there is an association between categorical variables in a single population.

Now with this, the key here is talking about association. We could also replaces the word independence. We could say that the null hypothesis is that there is no association, so the null hypothesis is that the variables are independent. The alternative hypothesis is that the variables are dependent, that there is an association. And then, again, there are conditions that we have to check just like always. We need to make sure that the data comes from a random sample. We need to make sure that all the expected counts are at least five and that the individual observations are independent.

So here in this example, we're looking at whether or not gender, eating, and meat are independent. So we're looking at one population. And we are looking at whether or not they're independent. And then our alternative hypothesis is that they are not independent.

So here we have our results from our survey. And when we compute the Chi-squared statistic for these results, we find out that we get 16.2. And when we combine that information with our distribution for Chi-square in our degrees of freedom, we get a p-value of 0.0003.

As a result, we can reject the null hypothesis because it is smaller than 0.05, the standard level of significance. Then we can reject the null hypothesis. So we can reject this. So we are rejecting that gender and eating meat are independent. So we are thinking that they are not independent then. This is on your tutorial on the Chi-square Statistic test for association, also known as the Chi-square test for independence.

Terms to Know
Chi-Square Test of Independence/Association

A hypothesis test that tests whether two qualitative variables have an association or not.

Formulas to Know
Chi-square Degrees of Freedom
d e g r e e s space o f space f r e e d o m equals left parenthesis r o w space t o t a l minus 1 right parenthesis left parenthesis c o l u m n space t o t a l minus 1 right parenthesis