basic

φ (Phi) Coefficient from a 2×2 Contingency Table Calculator

φ = (ad − bc) / √((a+b)(c+d)(a+c)(b+d)).

Compute the φ (phi) coefficient — the Pearson correlation between two binary variables — from a 2 × 2 contingency table with cell counts a, b (top row) and c, d (bottom row). φ ranges from −1 (perfect negative association) to +1 (perfect positive association); 0 = independence. φ² · n = chi-square statistic.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

φ = (ad − bc) / √((a+b)(c+d)(a+c)(b+d)).

In depth

Compute the φ (phi) coefficient — the Pearson correlation between two binary variables — from a 2 × 2 contingency table with cell counts a, b (top row) and c, d (bottom row). φ ranges from −1 (perfect negative association) to +1 (perfect positive association); 0 = independence. φ² · n = chi-square statistic.