Chi-Square Goodness of Fit Test in SPSS: Step-by-Step English Guide with Example (2025)

The Chi-Square Goodness of Fit Test is a statistical method used to determine whether the observed frequency distribution of a categorical variable matches a specified expected frequency distribution. This test is applied to a single categorical variable and is straightforward to perform in SPSS.

In this 2025 English guide, we provide a step-by-step process for conducting the Chi-Square Goodness of Fit Test in SPSS, complete with a practical example. This guide is designed for students, researchers, and professionals interested in categorical data analysis.

What is the Chi-Square Goodness of Fit Test?

This test evaluates whether observed data follows a theoretical or expected pattern. It is used when you have a single categorical variable and want to determine if its frequency distribution significantly differs from an expected distribution.

Formula:

Where:

• \(O_i\): Observed frequency.
• \(E_i\): Expected frequency.
• \(\sum\): Sum across all categories.

SPSS automates these calculations and provides the p-value for interpretation.

How to Perform the Chi-Square Goodness of Fit Test in SPSS: Step-by-Step Guide

Below is the process with an example dataset to check if a 6-sided die is fair.

Example Dataset

Problem: A researcher wants to determine if a 6-sided die is fair. For a fair die, each number (1 to 6) should have a 1/6 probability. The researcher rolled the die 120 times and collected the following data.

Data: Observed frequencies:

Hypothesis:

• Null Hypothesis (H₀): The die is fair (each number has an equal frequency).
• Alternative Hypothesis (H₁): The die is not fair (frequencies are not equal).

Expected Frequencies: Expected frequency for each number = \( \frac{120}{6} = 20 \).

Step 1: Prepare the Dataset in SPSS

1. Open SPSS and create a new dataset.
2. In Variable View:
   • Create a variable named Number (Type: Numeric, Measure: Nominal).
   • Create a variable named Frequency (Type: Numeric, Measure: Scale).
3. In Data View, enter the data:

   Number	Frequency
   1	15
   2	25
   3	22
   4	18
   5	20
   6	20

4. Save the dataset (File > Save As).

Step 2: Set Weight Cases

1. Go to the top menu and select:
   • Data > Weight Cases.
2. In the Weight Cases dialog box:
   • Move the Frequency variable to the Weight cases by box.
3. Click OK. This tells SPSS to count the frequency of each category.

Step 3: Select the Chi-Square Test Command

1. Go to the top menu and select:
   • Analyze > Nonparametric Tests > Legacy Dialogs > Chi-Square.
2. A Chi-Square Test dialog box will open.

Step 4: Set Variables and Expected Frequencies

1. In the Chi-Square Test dialog box:
   • Move the Number variable to the Test Variable List box.
2. In the Expected Values section:
   • The default option is All categories equal. For this example, we want a uniform distribution (equal frequency = 20 for each category), so keep this option selected.
   • If you have custom expected frequencies, select Values and enter the frequencies one by one (e.g., 20, 20, 20, 20, 20, 20).
3. Click OK.

Step 5: Interpret SPSS Output

The SPSS output will display two main tables:

1. Frequencies Table

This table shows the observed and expected frequencies.

Interpretation: The observed frequencies (15, 25, 22, 18, 20, 20) differ from the expected frequencies (20 for all), which the Chi-Square test will analyze.

2. Test Statistics Table

This table shows the Chi-Square statistic and p-value.

Interpretation:

• Chi-Square Statistic: 2.900
• Degrees of Freedom (df): 5 (since categories = 6, df = 6-1).
• p-value: 0.713 (greater than 0.05, so we do not reject H₀).
• Conclusion: The die is fair, as the observed frequencies do not significantly differ from the expected frequencies.

Step 6: Check Assumptions

Assumptions for the Chi-Square Goodness of Fit Test:

• Categorical Variable: Number (1-6) is categorical.
• Independent Observations: Die rolls are independent.
• Expected Frequencies: All expected counts are ≥ 5 (here, 20).
• Random Sampling: Assumed that rolls are random.

All assumptions are satisfied.

Step 7: Report Results (APA Style)

For formal reporting, use APA style:

A Chi-Square Goodness of Fit Test was conducted to assess the fairness of a die. The results indicated that the observed frequencies did not significantly differ from the expected uniform distribution, \(\chi^2(5, N=120) = 2.900, p = 0.713\).

Common Errors and Troubleshooting

• Error: Expected Count < 5:
  • Solution: Combine categories or use an exact test.
• No Output:
  • Solution: Ensure the variable is in the Test Variable List and Weight Cases is set.
• Incorrect Frequencies:
  • Solution: Verify that the Frequency variable is correctly weighted.
• Non-Categorical Variable:
  • Solution: Convert the variable to categorical (Transform > Recode).

Tips for Accurate Chi-Square Goodness of Fit Test in SPSS

• Data Preparation: Ensure frequencies are correctly entered in the dataset.
• Weight Cases: Always set Weight Cases for frequency-based data.
• Custom Expected Frequencies: Use the Values option if expected frequencies are not uniform.
• Save Output: Save the SPSS output (File > Export) for future reference.
• Visualization: Create a bar chart (Graphs > Chart Builder) for better presentation.

Summary

• Chi-Square Goodness of Fit Test: Compares observed and expected distributions of a categorical variable.
• SPSS Process: Data > Weight Cases > Analyze > Nonparametric Tests > Chi-Square > Select variable > Set expected values > OK.
• Example: Die roll data yielded \(\chi^2 = 2.900\), df = 5, p = 0.713, indicating the die is fair.
• Assumptions: Categorical variable, independent observations, expected counts ≥ 5.

This 2025 guide will help you perform the Chi-Square Goodness of Fit Test in SPSS effectively. For further questions, please leave a comment!