A null hypothesis (H0) is a statistical claim tested against an alternative hypothesis (Ha). In a conditional-independence test, H0 states that two variables are independent given specified controls; Ha states that they are not. The test calculates a statistic and p-value, then compares the p-value with a significance level such as .05 or .01. section 4.3.2
A frequentist test applies the null hypothesis through a compact decision workflow:
- Specify variables X and Y, conditioning variables Z, and the null claim X ⊥ Y | Z. section 4.3.2
- Compute a test statistic and p-value from observed data. section 4.3.2
- Favor H0 when the p-value exceeds the significance threshold; favor Ha when it falls below it. section 4.3.2
- Interpret a small p-value as evidence against the null claim, not as proof that the alternative is true. section 4.4.2
The null hypothesis becomes subtle when testing a causal DAG. A traditional test treats conditional independence as H0, so rejecting it indicates a dependence that conflicts with the graph. Yet a causal model predicts absences of patterns; rigorously, the model-right alternative would assert independence, while the null would assert dependence. Standard libraries generally support the traditional direction, making it a heuristic refutation method rather than a complete test of causal-model correctness. section 4.4.2
Transportation DAG
For a transportation survey, a graph implies E ⊥ T | O, R: education and travel should be independent after controlling for occupation and residence. A chi-squared test in pgmpy uses E, T, and [O, R] with a .05 significance level. Repeating the test across the graph’s d-separation statements identifies which predicted independences pass or fail. section 4.3.2
In DoWhy refutation, the null hypothesis instead states that the causal assumptions are not refuted. A p-value below .05 supports concluding that the assumptions are refuted, aligning the test direction with sensitivity analysis of an estimate. section 11.5
