Session-level statistics
One difference per session; the session is the inferential unit throughout.
Why an exhaustive sign-flip permutation, and not the "exact" Wilcoxon
Under the null that Ds is symmetric about zero, all 2k sign assignments are equally likely, so enumerating them is complete rather than sampled — there is no seed and no resample count to reproduce. Sign-flipping an exact zero changes nothing, so the enumeration runs over the non-zero sessions only.
All three Ds vectors contain ties in |Ds|. SciPy's own documentation states its exact Wilcoxon null holds only when there are no ties, so the exact Wilcoxon value is invalid here and is reported in the tables as a secondary diagnostic under a name that says so. Using it as a headline test was an error caught in review; the numbers moved (Test 1 0.9375 → 0.875, Test 2 7.63e-5 → 8.39e-5) and no conclusion changed.
n = 7 eligible sessions, all non-zero, median -60 ms, 128 assignments enumerated. Directions are mixed across sessions. not replicated This one is naturally read as a replicated null: the smallest attainable exact p at n = 7 is 0.0156, so the test could have detected a consistent difference and did not.
n = 21 sessions (18 non-zero), median +7.27 pp, 262,144 assignments enumerated, Holm p = 1.7e-04. replicated — the primary positive result of Analysis 6A
n = 11 sessions (10 non-zero), median +20 ms, 1,024 assignments enumerated. not significant / insufficient session-level evidence Deliberately not called a null: unlike C1 this is a shift in a consistent direction that the available number of sessions cannot establish.
All three, with secondary diagnostics
| test | n_sessions | n_nonzero_sessions | median_D | signflip_exact_p | n_permutations_enumerated | holm_p | wilcoxon_p_secondary | sign_test_p_secondary |
|---|---|---|---|---|---|---|---|---|
| SPK increase-vs-decrease timing (session sign x timing) | 7 | 7 | -60 | 0.875 | 128 | 0.875 | 0.798788 | 1 |
| LFP high- minus low-frequency fraction temporally resolved | 21 | 18 | 7.27 | 8.39233e-05 | 262144 | 0.000167847 | 0.000453102 | 0.00131226 |
| SPK omission-minus-stimulus latency shift | 11 | 10 | 20 | 0.0527344 | 1024 | — | 0.0738971 | 0.34375 |
Wilcoxon and sign-test columns are secondary diagnostics recorded for transparency. They are not competing headline tests and must not be quoted as such.