causalis.scenarios.classic_rct.inference.welch_permutation_t_test API Reference | Causalis

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causalis.scenarios.classic_rct.inference.welch_permutation_t_test.welch_permutation_t_test

welch_permutation_t_test

Run a Welch permutation t-test comparing treated and control outcomes.

This test uses the Welch t-statistic as the test statistic but calculates the p-value using a permutation distribution rather than the t-distribution. This is useful when the normality assumption of the t-test is suspect, while still being robust to unequal variances between groups.

Notes

The permutation p-value is calculated as:

p = \frac{\sum_{b=1}^B I(|t^*_b| \ge |t_{obs}|) + 1}{B + 1}

where $t_{obs}$ is the observed Welch t-statistic and $t^*_b$ are the t-statistics calculated from $B$ random permutations of the treatment labels. The addition of 1 in the numerator and denominator is a standard correction to ensure the test is valid (never returning a p-value of exactly 0).

Confidence intervals for the absolute and relative differences are still calculated using the Welch-Satterthwaite and Delta method approximations respectively, to remain consistent with other inference methods.

Examples

Parameters

dataCausalData: The CausalData object containing treatment and outcome variables.
alphafloat, default 0.05: Significance level for the theoretical Welch confidence interval.
Bint, default 10000: Number of Monte Carlo label permutations.
alternative{“two-sided”, “greater”, “less”}, default “two-sided”: Alternative hypothesis for the permutation p-value.
seedint, optional: Random seed for reproducible permutations.

Returns

Dict[str, Any]

A dictionary containing the permutation p-value, observed Welch statistic, absolute and relative differences, confidence intervals, number of permutations, and alternative.

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causalis.scenarios.classic_rct.inference.welch_permutation_t_test.welch_permutation_t_test

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