Enter the values for a 2x2 contingency table below, then click "Calculate" to see the Phi coefficient and interpret the association between variables.
| Positive Outcome | Negative Outcome | |
|---|---|---|
| Group 1 | ||
| Group 2 |
Understanding the Phi Coefficient
The Phi Coefficient, represented by \( \phi \), is a measure of association for 2x2 contingency tables. It calculates the strength of association between two binary variables.
Formula
The formula for the Phi Coefficient is:
\( \phi = \frac{ad - bc}{\sqrt{(a + b)(c + d)(a + c)(b + d)}} \)
- \( a, b, c, \) and \( d \): The cell counts in the 2x2 table.
Interpretation
The Phi Coefficient ranges from -1 to +1:
- A positive \( \phi \) indicates a positive association.
- A negative \( \phi \) indicates a negative association.
- A value of 0 indicates no association.
Example Calculation
Suppose we are studying the effectiveness of a new health program in improving a specific health outcome. We have two groups:
- Group 1: Individuals who participated in the health program
- Group 2: Individuals who did not participate in the program (control group)
The following table summarizes the results:
| Positive Outcome (Improved Health) | Negative Outcome (No Improvement) | |
|---|---|---|
| Program Participants (Group 1) | 30 | 10 |
| Non-Participants (Group 2) | 5 | 55 |
Using the Phi coefficient formula, we calculate:
\( \phi = \frac{(30)(55) - (10)(5)}{\sqrt{(30 + 10)(5 + 55)(30 + 5)(10 + 55)}} = 0.7384 \)
Interpretation of Result
This Phi coefficient of \( \phi = 0.7384 \) suggests a strong positive association between participation in the health program and experiencing a positive health outcome. This indicates that individuals who participated in the program had a greater likelihood of health improvement compared to those who did not, though the relationship is not perfectly predictive.
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.