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.
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.
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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