*51*

AÂ **Chi-Square Goodness of Fit TestÂ **is used to determineÂ whether or not a categorical variable follows a hypothesized distribution.

This tutorial explains how to perform a Chi-Square Goodness of Fit TestÂ in Stata.

**Example: Chi-Square Goodness of Fit Test in Stata**

To illustrate how to perform this test, we will use a dataset calledÂ *nlsw88*, which contains information about labor statistics for women in the U.S. in 1988.

Use the following steps to perform a Chi-Square Goodness of Fit test to determine if the true distribution of race in this dataset is as follows: 70% White, 20% Black, 10% Other.

**Step 1: Load and view the raw data.**

First, we will load the data by typing in the following command:

sysuse nlsw88

We can view the raw data by typing in the following command:

br

Each line displays information for an individual including their age, race, marital status, education level, and a variety of other factors.

**Step 2: Load the goodness of fit package.**

To perform a Goodness of Fit Test, we will need to install theÂ *csgofÂ *package. We can do so by typing in the following command:

findit csgof

A new window will pop up. Click the link that saysÂ *csgof from https://stats.idre.ucla.edu/stat/stata/ado/analysis*.

Another window will pop up. Click the link that saysÂ *click here to install*.Â

The package should only take a few seconds to install.

**Step 3: Perform the Goodness-of-Fit Test.**

Once the package is installed, we can perform the Goodness of Fit Test on the data to determine if the true distribution of race is as follows: 70% White, 20% Black, 10% Other.

We will use the following syntax to perform the test:

**csgof variable_of_interest, expperc(list_of_expected_percentages)**

Here is the exact syntax weâ€™ll use in our case:

csgof race, expperc(70, 20, 10)

Here is how to interpret the output:

**Summary box:Â **This box shows us the expected percent, expected frequency, and observed frequency for each race. For example:

- The expected percent of white individuals was 70%. This is the percentage that we specified.Â
- The expected frequency of white individuals was 1,572.2. This is calculated using the fact that there were 2,246 individuals in the dataset, so 70% of that number is 1,572.2.
- The observed frequency of white individuals was 1,637. This is the actual number of white individuals in the dataset.

**Chisq(2):Â **This is the Chi-Square test statistic for the Goodness of Fit Test. It turns out to be 218.13.

**p:Â **This is the p-value associated with the Chi-Square test statistic. It turns out to be 0. Since this is less than 0.05, we fail to reject the null hypothesis that the true distribution of race isÂ 70% White, 20% Black, 10% Other. We have sufficient evidence to conclude that the true distribution of race is different from this hypothesized distribution.