We propose
ϕ-test, a global feature-selection and significance procedure for black-box predictors that combines Shapley attributions with selective inference. Given a trained model and an evaluation dataset,
ϕ-test performs SHAP-guided screening and fits a linear surrogate on the screened features via a selection rule with a tractable selective-inference form. For each retained feature, it outputs a Shapley-based global score, a surrogate coefficient, and post-selection
p-values and confidence intervals in a global feature-importance table. Experiments on real tabular regression tasks with tree-based and neural backbones suggest that
ϕ-test can retain much of the predictive ability of the original model while using only a few features and producing feature sets that remain fairly stable across resamples and backbone classes. In these settings,
ϕ-test acts as a practical global explanation layer linking Shapley-based importance summaries with classical statistical inference.