How to Calculate Cramer’s V in SPSS

Cramer’s V is a measure of the strength of association between two nominal variables.

It ranges from 0 to 1 where:

• 0 indicates no association between the two variables.
• 1 indicates a strong association between the two variables.

It is calculated as:

Cramer’s V = √(X2/n) / min(c-1, r-1)

where:

• X2: The Chi-square statistic
• n: Total sample size
• r: Number of rows
• c: Number of columns

The easiest way to calculate Cramer’s V in SPSS is to use Analyze > Descriptive Statistics > Crosstabs.

The following example shows how to do so in practice.

Example: How to Calculate Cramer’s V in SPSS

Suppose we would like to understand if there is an association between two exam prep methods and the passing rate of students.

The following dataset in SPSS shows the pass / fail result of students along with the exam prep method they used:

Note: There are 36 total observations but only the first 23 are shown in this screenshot.

We can calculate Cramer’s V to determine the strength of association between exam prep method and the passing rate of students.

To do so, click the Analyze tab, then click Descriptive Statistics, then click Crosstabs:

In the new window that appears, drag the Method variable to the Rows panel, then drag the Result variable to the Columns panel:

Then click the Statistics button.

Then check the box next to Phi and Cramer’s V:

Then click Continue. Then click OK.

The following output will appear:

The first table shows the number of total observations. There are N = 36 total observations.

The second table displays a crosstab that summarizes the count of students based on pass / fail result and the exam prep method used.

The third table displays Cramer’s V.

From this third table we can see that Cramer’s V turns out to be 0.162.

We can use the following table to determine whether a Cramer’s V should be considered a small, medium, or large effect size based on the degrees of freedom used:

In this example, the degrees of freedom is equal to 1. Thus, a Cramer’s V of 0.162 would be considered a small effect size.

In other words, there is a weak association between the exam prep method used and the passing rate of students.