Two Variable Two Variable StatisticsStatistics

Introduction ToIntroduction To

Chi-Square Test for Chi-Square Test for IndependenceIndependence

CorrelationCorrelation

Finding the relationship between two quantitative variables without being able to infer causal relationships

Correlation is a statistical technique used to determine the degree to which two variables are related

What is the Chi-square test for?What is the Chi-square test for?

The chi-squared or The chi-squared or ΧΧ22 test is used to test is used to determine whether two variables from determine whether two variables from the same sample are the same sample are independentindependent or or not independentnot independent..

A chi-squared test is designed to A chi-squared test is designed to analyze analyze categorical datacategorical data. That . That means that the data has been means that the data has been counted and divided into categories. counted and divided into categories.

For example, if you want to test whether For example, if you want to test whether attending class influences how students perform attending class influences how students perform on an exam, using test scores (from 0-100) as on an exam, using test scores (from 0-100) as data would data would NOTNOT be appropriate for a Chi-square be appropriate for a Chi-square test.test.

However, arranging students into the categories However, arranging students into the categories "Pass" and "Fail" "Pass" and "Fail" would be appropriatewould be appropriate..

Appropriate Categorical DataAppropriate Categorical Data

The chi-squared test is only meant to test the The chi-squared test is only meant to test the probability of independence probability of independence of a distribution of of a distribution of data. It will data. It will NOTNOT tell you any details about the tell you any details about the relationshiprelationship between them. between them.

The variables you consider must be The variables you consider must be mutually mutually exclusiveexclusive; participation in one category should ; participation in one category should not entail or allow participation in another. In not entail or allow participation in another. In other words, the data from all of your cells should other words, the data from all of your cells should add up to the total count, and no item should be add up to the total count, and no item should be counted twice. counted twice.

More Important facts about Chi-Squared More Important facts about Chi-Squared TestTest

How do you calculate the chi-How do you calculate the chi-squared test by hand?squared test by hand?