AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.15 Carrying Out a Chi-Square Test for Homogeneity or Independence
Notes
$$\chi^2=\sum\frac{(O-E)^2}{E},\quad df=(r-1)(c-1)$$
- Larger $\chi^2$ means the data differ more from what $H_0$ predicts.
Practice
A 3 × 4 table has degrees of freedom:
$2\times3$.
Observed 30, expected 25. That cell's contribution:
$\displaystyle \frac{25}{25}$.
A very small p-value in a test of independence means:
Reject $H_0$ of independence.
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