Chi-Square Independence

183. Chi-Square Independence

183.0.1. Test of independence

Compares two observed categorical distributions.

Χ^{2} = \sum_{𝑖 = 1}^{𝑘} \frac{{(𝑜_{𝑖 𝑗} - 𝑒_{𝑖 𝑗})}^{2}}{𝑒_{𝑖 𝑗}}

$𝑜_{𝑖 𝑗}$ : observed frequency in cell $(𝑖, 𝑗)$
$𝑒_{𝑖 𝑗}$ : expected frequency in category $(𝑖, 𝑗)$ calculated as:

𝐸_{𝑖 𝑗} = \frac{𝑅_{𝑖} \times 𝐶_{𝑗}}{𝑁}

$𝑅_{𝑖}$ : Row total for row $𝑖$
$𝐶_{𝑗}$ : Column total for column $𝑗$
$𝑁$ : Total number of observations