Chi-Square Test

Use chi-square tests to compare the observed distribution of your data to an expected distribution of data.

To add output from a chi-square test, go to Add and complete a form.

In This Topic

Chi-square goodness-of-fit
Chi-square test of independence

Chi-square goodness-of-fit

Use a chi-square goodness of fit test to determine whether the proportion of items in each category is significantly different from the proportions that you specify.

You can test whether the proportions are equal across the categories (uniform), specify a different proportion for each category, or specify historical counts for each category.

For example, a buyer performs a chi-square goodness-of-fit test to determine whether the proportions of t-shirt sizes sold are consistent with the proportion of t-shirt sizes ordered. To see an example, go to Minitab Help: Example of Chi-Square Goodness-of-Fit Test.

Data considerations

Each sample should be large enough so that there is a reasonable chance of observing outcomes in every category. If the expected counts are too low, the p-value for the test may not be accurate. For details, go to Minitab Help: Data considerations for Chi-Square Goodness-of-Fit Test.

Chi-square test of independence

Use a chi-square test of independence when you have data that are categorized by one or more categorical variables.

With a chi-square test of independence, you can determine the counts or percentages for combinations of categories across two or more categorical variables and investigate the relationship between variables. The chi-square test of independence, also known as the chi-square test of association, is found within the Cross Tabulation and Chi-Square tool in Minitab.

For example, an engineer wants to determine how many defective parts were created on different production lines during each shift. To see an example, go to Minitab Help: Example of Cross Tabulation and Chi-Square.

Data considerations

Your data must be a table containing the counts of each combination of the categorical X and Y values. Independence of the observations is a critical assumption for this test. For details, go to Minitab Help: Data considerations for Cross Tabulation and Chi-Square.