Chi-Square Test
Pearson Chi-Square Test
There are several kinds of chi-square tests but the most common is the Pearson chi-square test which allows us to test the independence of two categorical variables. All chi-square tests are based upon a chi-square distribution, similar to the way a t-test is based upon a t distribution or an F-test is based upon an F distribution.
Chi-Square Example
Suppose we have a hypothesis that the pass/fail rate in a particular mathematics class is different for male and female students. Say we take a random sample of 100 students and measure both gender (male/female) and class status (pass/fail) as categorical variables.
The data for these 100 students can be displayed in a contingency table, also known as a cross-classification table. A chi-square test can be used to test the null hypothesis (i.e., that the pass/fail rate is not different for male and female students).
Chi-Square Statistic
Just as in a t-test, or F-test, there is a particular formula for calculating the chi-square test statistic. This statistic is then compared to a chi-square distribution with known degrees of freedom in order to arrive at the p-value.
We use the p-value to decide whether or not we can reject the null hypothesis. If the p-value is less than "alpha" which is typically set at .05, then we can reject the null hypothesis, and in this case, we say that our data indicates that the likelihood of passing the class is related to the student's gender. See Statistical Data Analysis for more about statistical inference.
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