X^2 Goodness-of-fit test §

= a hypothesis test that works with independent categorical (nominal) data of sufficient size (>5)

How? §

1. Formulate 💭 Statistical Hypothesis pair
   • → H0: P = (.25,.25,.25,.25); H1: P ≠ (.25,.25,.25,.25);
2. Construct a test statistic that measures the closeness to H0

values \ k variables	a	b	c	d
expected frequency Ei	50	50	50	50
observed frequency Oi	35	51	64	50
difference Oi - Ei	-15	1	14	0

3. Calculate chi-saquared statistics, look up critical value
   • → X^2: 8.44; df: 4-1 = 3; Crit value: 7.81
4. Check if the result is above the critical value
5. (Calculate Cramèr’s V)