Pulse Documentation

name: op-test-kruskal-wallis
description: Nonparametric k-group location test; ANOVA-like rank sums under tie correction.
kind: operator
category: TEST
operator: TEST_KRUSKAL_WALLIS
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, tier-1-test, nonparametric, k-sample, comparison, buffered-pipeline]

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

Use when

Rank-based check of whether values tend to be larger in some groups than in others, across two or more groups.

Questions it answers:

• Do satisfaction ratings tend to differ across the four regions?
• Do skewed repair times differ across product lines?

Use something else:

• TEST_ANOVA_WELCH when the data are roughly normal and you want to compare averages.
• TEST_MANN_WHITNEY_U when there are only two groups.

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 row of weight w ranks as w identical rows — equals the test on the expanded rows. Details add sum_weights shaped like n; n / n_total stay raw row counts.
• multiplicity — optional {method, family}; adds p_adjusted beside the raw p (multiplicity-correction).

Inputs

Field (required) — numeric: u4/u8/u16/u32/u64, f32/f64, date. SplitBy (required, ≥ 2 groups) — categorical: categorical_u8/u16/u32, packed_bool.

Output

Statistic = tie-corrected H; DF = k − 1; PValue via χ² survival. Details: groups, n, rank_sums, n_total, tie_factor; effect_size.epsilon_squared = H·(n+1)/(n²−1), omitted when every value ties.

Reading the output

• statistic: H measures how far each group’s average rank sits from the overall average rank, corrected for ties; larger values are stronger evidence that some groups tend to have higher values than others; the p-value says whether this H is large enough to be surprising.
• 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.

Gotchas

• Buffered — combined values ranked across all groups under tie correction.
• Nonparametric alternative to one-way ANOVA for skewed or heavy-tailed data.
• Global only — no Dunn / Conover post-hoc; use pairwise TEST_MANN_WHITNEY_U with a multiplicity block (Holm/Bonferroni).
• Groups under ~5 rows: shaky p; only N < 2k is refused (PULSE_TEST_INSUFFICIENT_N). ε² unbanded.
• Tests stochastic equality, not equal medians — differing shapes can reject on shape alone.

See

• pulse_examples_search tags=[k-sample]
• Skills: statistical-testing, op-test-anova-f, op-test-mann-whitney-u, op-test-anova-welch