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The chi-square test of independence is used to test whether two categorical variables are related to each other. Chi-square is often written as Χ 2 and is pronounced “kai-square” (rhymes with “eye-square”). It is also called chi-squared.
You test whether a given χ2 is statistically significant by testing it against a table of chi-square distributions, according to the number of degrees of freedom for your sample, which is the number of categories minus 1. The chi-square assumes that you have at least 5 observations per category.
To perform a chi-square test, you compare a sample’s chi-square to a critical value. To find the right critical value, you need to use the chi-square distribution with the appropriate degrees of freedom.
This degrees of freedom calculator will help you determine this crucial variable for one-sample and two-sample t-tests, chi-square tests, and ANOVA. Read the text to find out: What degree of freedom is (degrees of freedom definition); How to find degrees of freedom; and; The degrees of freedom formula.
Critical values of a chi-square distribution with degrees of freedom df are found in Figure 7.1.6. A chi-square test can be used to evaluate the hypothesis that two random variables or factors are independent.
How to Find Degrees of Freedom for Tables in Chi-Square Tests. The chi-square test of independence determines whether there is a statistically significant relationship between categorical variables in a table. Just like other hypothesis tests, this test incorporates DF.
The subscript “c” is the degrees of freedom. “O” is your observed value and E is your expected value. It’s very rare that you’ll want to actually use this formula to find a critical chi-square value by hand. The summation symbol means that you’ll have to perform a calculation for every single data item in your data set.
You can use a chi-square test of independence, also known as a chi-square test of association, to determine whether two categorical variables are related. If two variables are related, the probability of one variable having a certain value is dependent on the value of the other variable.
An important parameter in a chi-square distribution is the degrees of freedom \(df\) in a given problem. The random variable in the chi-square distribution is the sum of squares of df standard normal variables, which must be independent.
by Marco Taboga, PhD. A random variable has a Chi-square distribution if it can be written as a sum of squares of independent standard normal variables. Sums of this kind are encountered very often in statistics, especially in the estimation of variance and in hypothesis testing.