# vimp_hypothesis_test: Perform a hypothesis test against the null hypothesis of... In bdwilliamson/nova: Perform Inference on Algorithm-Agnostic Variable Importance

 vimp_hypothesis_test R Documentation

## Perform a hypothesis test against the null hypothesis of δ importance

### Description

Perform a hypothesis test against the null hypothesis of zero importance by: (i) for a user-specified level α, compute a (1 - α)\times 100% confidence interval around the predictiveness for both the full and reduced regression functions (these must be estimated on independent splits of the data); (ii) if the intervals do not overlap, reject the null hypothesis.

### Usage

vimp_hypothesis_test(
predictiveness_full,
predictiveness_reduced,
se,
delta = 0,
alpha = 0.05
)


### Arguments

 predictiveness_full the estimated predictiveness of the regression including the covariate(s) of interest. predictiveness_reduced the estimated predictiveness of the regression excluding the covariate(s) of interest. se the estimated standard error of the variable importance estimator delta the value of the δ-null (i.e., testing if importance < δ); defaults to 0. alpha the desired type I error rate (defaults to 0.05).

### Details

See the paper by Williamson, Gilbert, Simon, and Carone for more details on the mathematics behind this function and the definition of the parameter of interest.

### Value

a list, with: the hypothesis testing decision (TRUE if the null hypothesis is rejected, FALSE otherwise); the p-value from the hypothesis test; and the test statistic from the hypothesis test.

bdwilliamson/nova documentation built on Feb. 13, 2023, 9:52 a.m.