Graziano and Raulin (8th ed)Graziano & Raulin
Research Methods (8th edition)

Phi Coefficient

The phi coefficient is the equivalent of the correlation between nominal variables. You compute it in SPSS for Windows in the crosstabs procedure. We will illustrate it with the data from Table 5.2

Select the Analyze menu item, the Descriptive Statistics submenu item, and the crosstabs procedure, which will give you this screen. We want to look at the relationship between sex and political affiliation, so we move one of those variables into the rows section and the other into the columns section, as shown in this screen

To compute Phi, we click on the statistics button and select Phi from the list of available statistics, as shown in this screen. Clicking continue returns you to the crosstabs box and clicking OK performs the computations. The results are shown on this screen, with the Phi coefficient and the associated probability value given in the box at the bottom. 

In this case, the Phi coefficient is .45, with a p-value of .088. Since the p-value is greater than the traditional value of alpha (.05), we would fail to reject the null hypothesis and therefore would conclude that we do not have evidence from this sample that the distribution of political affiliations are different in male and female populations.


We have prepared an animation that will walk you through this procedure. To run the animation, simply click on the title of the animation in the table below. 

Note that we do not recommend that you try to run the animations if you have a slow connection, such as a dial-up connection. You will find that the animations take forever to load with a slow connection.

Computing a Phi Coefficient