Pulse Documentation

name: op-test-wilcoxon-sr
description: Wilcoxon signed-rank test on per-row difference d = Field − Field2; buffered tie-corrected sign-rank.
kind: operator
category: TEST
operator: TEST_WILCOXON_SR
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, tier-1-test, nonparametric, paired, before-after, buffered-pipeline]

Tests emit statistic / p-value / effect size; no Response.Components.

Use when

Rank-based check of whether paired before/after values tend to shift in one direction, without assuming a bell curve.

Questions it answers:

• Did each customer’s rating tend to go up after the redesign?
• Do patients’ skewed symptom scores tend to fall between visits?

Use something else:

• TEST_MANN_WHITNEY_U when the two sets of values come from different, unrelated subjects.

Params

• alpha — float, default 0.05, in (0, 1).
• weight — slot weight (null opts out), kind frequency only (a probability weight is PULSE_WEIGHT_UNSUPPORTED naming the kind): a pair of weight w ranks as w identical pairs — equals the test on the expanded pairs. Details add sum_weights beside n; n and zero_diffs stay raw row counts.

Slot params: Field (required, numeric), Field2 (required, numeric — the pre value).

• multiplicity — optional {method, family}; adds p_adjusted beside the raw p (multiplicity-correction).

Inputs

Field — numeric: u4/u8/u16/u32/u64, f32/f64, date. Field2 — numeric (same set; paired per-row with Field).

Output

Statistic = min(W⁺, W⁻); PValue two-sided normal approx, tie-corrected. Details: n (non-zero pairs), w_plus, w_minus, mu_w, var_w, z, zero_diffs; effect_size.rank_biserial = (W⁺ − W⁻)/(W⁺ + W⁻) — > 0 ⇒ Field tends to exceed Field2 (sign of z).

Reading the output

• statistic: The smaller of the two signed-rank sums: rank the non-zero differences (Field - Field2) by size, add the ranks of the positive ones and of the negative ones, and keep the smaller. The smaller it is, the more one direction dominates.
• p_value: a p-value. Below alpha (0.05 unless the request sets another) the result is called significant; that is not the same as important, so read the effect size for how big it is.
• details.z: The normal score the p-value is read from, with a continuity correction of one half.

Gotchas

• Buffered — |d| ranked across the whole set.
• Zero-diff pairs are dropped (Wilcoxon convention); reported in Details.zero_diffs.
• Nonparametric alternative to a paired t-test when d is non-normal.
• Asymptotic only; < 6 non-zero pairs is PULSE_TEST_INSUFFICIENT_N.
• Tier-2 variant asymptotic_post runs over two result-row columns.
• Pairing is per row: both values sit on one record.

See

• pulse_examples_search tags=[paired]
• Skills: statistical-testing, op-test-paired-t, op-test-mann-whitney-u