The chi-square goodness-of-fit test procedure tabulates a single variable into categories and computes a chi-square statistic based on the differences between observed and expected frequencies. (To obtain chi-square tests of relationship between two or more variables, use the Crosstabs Procedure.)

Example

Minorities make up 30% of the population in a community. There are 20 minority faculty members among the 100 teachers in a school district. Does the observed proportion (20%) differ significantly from the expected proportion (30%)?

SPSS for Windows

This study involves comparing the sample frequency distribution of a categorical variable with a predetermined frequency distribution of that variable.

A. Assign 1 to the minority group and assign 0 to the non-minority group. Define the following variables (freq and mino) and enter their values. Note that 100 - 20 = 80 

B. Weighting Cases 

From the menus choose: Data \ Weight Cases. Next, click the Weight cases by radio button and select the variable freq as the frequency variable. Click on OK.  

C. To obtain the chi-square test, from the menus choose: Analyze / Nonparametric Tests / Chi-Square.  

Click on the variable “mino” to highlight it. Click on the > push-button. The variable “mino” will appear on the Test Variable List.

Next, in the Expected Values area, click Values. The first expected value on the list corresponds to the lowest group value of the test variable. Thus, click on the text box. Enter the first expected proportion “.70” for the group coded as “0”. (1 - .30 = .70). Click on Add. Next, click inside of  the values text box. Enter the expected proportion “.30” for the group coded as “1”. Click Add. Click on OK.