Corrected resampled t-test for repeated splits

Correct the variance for overlapping training sets

Repeated random splits (or repeated cross-validation) reuse training data, so the per-split differences are correlated. Nadeau and Bengio (2003) fix the variance by inflating it with the ratio of test to training size. For k repeats with differences d_i, the corrected statistic is

t = mean(d) / sqrt((1/k + n_test / n_train) * var(d)), with var using k - 1.

Implement corrected_resampled_t(diffs, n_train, n_test) and return t as a float.

Constraints

• diffs is a 1-D array with k >= 2 entries.
• n_train > 0 and n_test > 0. Otherwise raise ValueError.
• Zero variance in diffs raises ValueError, since the statistic is undefined.
• Do not modify the input.

Hints