  Deep artificial neural networks show high predictive performance in many
fields, but they do not afford statistical inferences and their black-box
operations are too complicated for humans to comprehend. Because positing that
a relationship exists is often more important than prediction in scientific
experiments and research models, machine learning is far less frequently used
than inferential statistics. Additionally, statistics calls for improving the
test of theory by showing the magnitude of the phenomena being studied. This
article extends current XAI methods and develops a model agnostic hypothesis
testing framework for machine learning. First, Fisher's variable permutation
algorithm is tweaked to compute an effect size measure equivalent to Cohen's f2
for OLS regression models. Second, the Mann-Kendall test of monotonicity and
the Theil-Sen estimator is applied to Apley's accumulated local effect plots to
specify a variable's direction of influence and statistical significance. The
usefulness of this approach is demonstrated on an artificial data set and a
social survey with a Python sandbox implementation.
