Title: Phi
Course: UGQuants (SSPS) > Section: Association for Nominal and Ordinal Variables

Phi

Phi is a correlation coefficient for 2 x 2 tables such as the following report of gender and voter turnout. The Chi square result for this table is 32.48.

Table 1: Gender and Turnout

Voted | Gender
Male | Female
Yes | 38 | 15
No | 7 | 40
Total | 45 | 55 |

Phi - which we can calculate once we know the Chi square value-  tells us about the strength of the relationship we observe in the table. Values of Phi vary from 0 to 1, and we would generally interpret its results as follows:

0-.29 = weak association

.30-.59 = moderate association

.60-1 = strong association

The formula for Phi is as follows:

Where

χ2 is the value of chi square

N is the total number of cases

In our particular example, this would be:

In light of this we would say that there is a moderate correlation between gender and voting.