x^2 statistics §

$k=$ number of values $O_i=$ variable 1 (e.g. expected values) $E_i=$ variable 2 (e.g. observed values)

$X^2={\sum }_{i=1}^k\frac{(O_i-E_i{)}^2}{E_i}$

Degrees of freedom §

$=k$ - number of constraints

Problem: §

• df = 1 → 📉 Binomial distribution doesn’t look like a 🔔 Normal distribution
• Fix: Yates correction hack: $X^2={\sum }_{i=1}^k\frac{(O_i-E_i|-0.5{)}^2}{E_i}$

Use cases: §

• Chi-squared goodness-of-fit test
• 💥 Effect Size

Distribution §