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What is the Phi Coefficient?

The Phi Coefficient is offered to understand the stamin of the relationship between two variables. To usage it, your variables that interest need to be binary. See an ext below.


The Phi Coefficient is also called the typical square contingency coefficient.

Assumptions because that the Phi Coefficient

Every statistical method has assumptions. Assumptions mean that your data have to satisfy specific properties in order for statistical an approach results to be accurate.

The assumptions for the Phi Coefficient include:

Binary variables

Let’s dive into what that means.


For this test, your 2 variables need to be binary. Binary method that her variable is a group with just two possible values. Some an excellent examples that binary variables include gender (male/female) or any True/False or Yes/No variable.

When to usage the Phi Coefficient?

You have to use the Phi Coefficient in the adhering to scenario:

You desire to understand the relationship between two variablesYour variables that interest room binaryYou have only two variables

Let’s clarify these to help you understand when to usage the Phi Coefficient.


You are searching for a statistical test come look at how two variables are related. Other types of analyses include testing for a difference between two variables or predicting one variable using an additional variable (prediction).


For this test, your 2 variables must be binary. Binary way that your variable is a category with just two possible values. Some great examples the binary variables encompass gender (male/female) or any kind of True/False or Yes/No variable.

If your data are continuous, you might want to use Pearson Correlation. If one of your variables is consistent and the other is binary, you have to use allude Biserial Correlation. And if her variables have an ext than two categories, you must use Cramer’s V.

Two Variables

The Phi Coefficient deserve to only be offered to compare 2 variables.

Phi Coefficient Example

Variable 1: GenderVariable 2: Heart condition Diagnosis

In this example, we are interested in investigating the relationship between gender and heart disease. To begin, we collect these data from a team of people.

Because both of these variables space binary with just two feasible values every variable (male/female, yes/no), we recognize that the Phi Coefficient is a perfect test.

The evaluation will result in a Phi Coefficient and also a p-value. Phi values range from -1 come 1. A negative value the Phi suggests that the variables space inversely related, or when one variable increases, the various other decreases. ~ above the various other hand, confident values indicate that once one variable increases, for this reason does the other.

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The p-value represents the chance of seeing our outcomes if there to be no yes, really relationship between our variables. A p-value less than or equal to 0.05 way that our result is statistically far-ranging and we have the right to trust that the distinction is not as result of chance alone.

Frequently inquiry Questions

Q: how do I gain the Phi Coefficient in SPSS or R?A: is concentrated on helping you choose the right statistical technique every time. Over there are countless resources easily accessible to aid you number out exactly how to run this technique with your data:SPSS article: video: article: