# Chi-Square Test

The Chi-Square Test procedure tabulates a variable into categories and computes a chi-square statistic. This goodness-of-fit test compares the observed and expected frequencies in each category to test that all categories contain the same proportion of values or test that each category contains a user-specified proportion of values.

**Examples.** The chi-square test could be used to determine
whether a bag of jelly beans contains equal proportions of blue, brown,
green, orange, red, and yellow candies. You could also test to see
whether a bag of jelly beans contains 5% blue, 30% brown, 10% green,
20% orange, 15% red, and 15% yellow candies.

**Statistics.** Mean, standard deviation, minimum, maximum,
and quartiles. The number and the percentage of nonmissing and missing
cases; the number of cases observed and expected for each category;
residuals; and the chi-square statistic.

Chi-Square Test Data Considerations

**Data.** Use ordered or unordered numeric categorical variables
(ordinal or nominal levels of measurement). To convert string variables
to numeric variables, use the Automatic Recode procedure, which is
available on the Transform menu.

**Assumptions.** Nonparametric tests do not require assumptions
about the shape of the underlying distribution. The data are assumed
to be a random sample. The expected frequencies for each category
should be at least 1. No more than 20% of the categories should have
expected frequencies of less than 5.

To Obtain a Chi-Square Test

This feature requires the Statistics Base option.

- From the menus choose:
- Select one or more test variables. Each variable produces a separate test.
- Optionally, click Options for descriptive statistics, quartiles, and control of the treatment of missing data.

This procedure pastes NPAR TESTS command syntax.