Pulse Documentation

name: op-test-brown-forsythe
description: Homogeneity-of-variance test; one-way ANOVA on absolute deviations from per-group medians.
kind: operator
category: TEST
operator: TEST_BROWN_FORSYTHE
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, tier-1-test, homogeneity-test, parametric, k-sample, buffered-pipeline]

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

Use when

Checks whether the spread of a numeric field differs across groups: a robust test of equal variances.

Questions it answers:

• Is delivery time more variable at some warehouses than at others?
• How different is the spread of the measure across groups?

Use something else:

• TEST_ANOVA_WELCH when you want to compare the group averages themselves.
• TEST_SHAPIRO_WILK when you want to check whether a measure is bell-shaped.

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): weighted group medians, ANOVA on Σw — equals the expanded rows. Details add sum_weights beside n (raw rows).

Slot params: Field (required, numeric), SplitBy (required, categorical, ≥ 2 groups).

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

Inputs

Field — numeric: u4/u8/u16/u32/u64, f32/f64, date. SplitBy — categorical: categorical_u8/u16/u32, packed_bool.

Output

Statistic = F (ANOVA on absolute deviations from per-group medians); DF = k-1 (df_within = N-k in Details); PValue via F-distribution survival. Flat Details: groups, n, group_medians, abs_dev_means, ss_between, ss_within.

Reading the output

• statistic: F on each row’s distance from its group median: larger values are stronger evidence that the groups differ in spread; the p-value says whether this F is large enough to be surprising.
  • Caveat: It tests spread only, not averages.
• 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 — per-group medians require a sort.
• Not a pre-ANOVA gate: a large p is not evidence of equal spread.
• More robust than Levene (mean-based) under non-normality — that’s the whole point.
• Tier-2 variant TEST_BROWN_FORSYTHE/median_post runs over result columns.
• Tiny groups destabilize the median; n_i < 2 or N ≤ k → PULSE_TEST_INSUFFICIENT_N.

See

• pulse_examples_search tags=[homogeneity-test]
• Skills: statistical-testing, op-test-anova-f, op-test-anova-welch