How to Use Phi Coefficient in SPSS: English Guide with Example
Table of Contents
What is Phi Coefficient?
The Phi Coefficient (φ) is a statistical measure that quantifies the association between two binary variables (like Yes/No, Male/Female). It ranges between -1 and +1:
- +1: Perfect positive association (both variables increase together)
- 0: No association
- -1: Perfect negative association (one increases while other decreases)
The formula for Phi Coefficient is:
\[ \phi = \frac{n_{11}n_{00} – n_{10}n_{01}}{\sqrt{n_{1\bullet}n_{0\bullet}n_{\bullet 0}n_{\bullet 1}}} \]
Where:
- \(n_{11}\): Count where both variables are positive (e.g., Yes-Yes)
- \(n_{00}\): Count where both variables are negative (e.g., No-No)
- \(n_{10}\): First variable positive, second negative (e.g., Yes-No)
- \(n_{01}\): First variable negative, second positive (e.g., No-Yes)
- Marginal totals: Row and column totals in the contingency table
When to Use Phi Coefficient?
| Situation | Description | Example |
|---|---|---|
| Binary Variables | When both variables are binary (dichotomous) | Gender (M/F) and Smoking (Yes/No) |
| 2×2 Contingency Table | When data can be represented in a 2×2 table | Treatment (Drug/Placebo) vs Outcome (Success/Failure) |
| Association Measurement | To measure strength of association | Vaccination status vs Disease occurrence |
When Not to Use Phi Coefficient?
| Situation | Problem | Alternative |
|---|---|---|
| Non-Binary Variables | Requires both variables to be binary | Pearson or Spearman correlation |
| Small Sample Size | Low statistical power with small samples | Fisher’s Exact Test |
| Low Expected Counts | Expected counts < 5 in any cell | Fisher’s Exact Test |
Step-by-Step Calculation in SPSS
Example: Gender and Smoking Status Association
Problem: A survey collected data from 100 people recording their gender (Male/Female) and smoking status (Smoker/Non-Smoker). We want to check if there’s an association between these variables.
Data in SPSS:
| ID | Gender (1=Male, 0=Female) | Smoking (1=Smoker, 0=Non-Smoker) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 0 | 0 |
| 3 | 1 | 0 |
| … | … | … |
Contingency Table:
| Smoker | Non-Smoker | Total | |
|---|---|---|---|
| Male | 20 | 30 | 50 |
| Female | 10 | 40 | 50 |
| Total | 30 | 70 | 100 |
Step 1: Enter Data in SPSS
Create two variables in SPSS Data View:
- Gender: 1=Male, 0=Female
- Smoking: 1=Smoker, 0=Non-Smoker
Step 2: Run Crosstabs Analysis
- Go to Analyze > Descriptive Statistics > Crosstabs
- Add Gender to Row(s)
- Add Smoking to Column(s)
Step 3: Select Statistics
- Click Statistics button
- Check Phi and Cramer’s V
- Click Continue
Step 4: Run Analysis
Click OK to run the analysis and view results.
Interpreting Results
SPSS Output Tables
1. Case Processing Summary
| Valid Cases | Missing Cases | Total |
|---|---|---|
| 100 | 0 | 100 |
2. Gender * Smoking Crosstabulation
| Smoker | Non-Smoker | Total | |
|---|---|---|---|
| Male | 20 | 30 | 50 |
| Female | 10 | 40 | 50 |
| Total | 30 | 70 | 100 |
3. Symmetric Measures
| Measure | Value | Approx. Sig. |
|---|---|---|
| Phi | 0.316 | 0.001 |
| Cramer’s V | 0.316 | 0.001 |
Interpretation
Phi = 0.316 indicates a moderate positive association between gender and smoking status.
p-value = 0.001 (less than 0.05) means this association is statistically significant.
Strength Guidelines:
- |φ| < 0.3: Weak association
- |φ| 0.3–0.5: Moderate association
- |φ| > 0.5: Strong association
Tips for Accurate Analysis
- Check Data Coding: Ensure binary variables are properly coded (0/1)
- Verify Expected Counts: All expected counts should be ≥5 for valid results
- Consider Fisher’s Exact Test: Use when expected counts are <5
- Examine Effect Size: Phi coefficient itself is an effect size measure
- Don’t Confuse with Causation: Association doesn’t imply causation
Summary
- Phi Coefficient measures association between two binary variables (-1 to +1)
- In SPSS, use Crosstabs procedure with Phi and Cramer’s V option
- Our example showed φ = 0.316 (moderate association) with p = 0.001 (significant)
- Check assumptions (binary variables, expected counts ≥5) before interpreting
- For non-binary variables, use other correlation measures
Very Nice Information………