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Phi-coefficient

Correlation between two dichotomous categorical variables

The phi-coefficient is used to assess the relationship between two dichotomous categorical variables. Odds ratios or relative risk statistics can be calculated to establish a stronger inference versus phi-coefficient. The width of the 95% confidence intervals associated with the odds ratio or relative risk will narrow with more observations of two variables being correlated with the phi-coefficient. Smaller sample sizes will significantly decrease the statistical power of phi-coefficient analysis.

The Venn diagram below depicts the correlation of two categorical variables. Phi-coefficient is the correlation test used for two categorical variables.
Phi-coefficient is a correlation test that establishes the association between two categorical variables.

The steps for conducting a phi-coefficient in SPSS

1. The data is entered in a within-subjects fashion.

2. Click Analyze.

3. Drag the cursor over the Descriptive Statistics drop-down menu.

4. Click on Crosstabs.

5. Click on the first dichotomous categorical outcome variable to highlight it.

6. Click on the arrow to move the variable into the Row(s): box.

7. Click on the second dichotomous categorical outcome variable to highlight it.

8. Click on the arrow to move the variable into the Column(s): box.

9. Click on the Statistics button.

10. Click on the Phi and Cramer's V box to select it.

11. Click Continue.

12. Click OK.

The steps for interpreting the SPSS output for a phi-coefficient

1. In the Symmetric Measures table, look under the Approx. Sig. column for the Phi row. This is the p-value that is interpreted. The number in the Value column is the actual Phi-coefficient. 

Click on the Download Database and Download Data Dictionary buttons for a pre-configured database and data dictionary for phi-coefficient. Click on the Adjusing for Multiple Comparisons ​button to learn more about Bonferroni, Tukey's HSD, and Scheffe's test. Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.
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Adjusting for Multiple Comparisons
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