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name: op-test-mardia
description: Mardia's multivariate normality test on a vector — skewness χ² and kurtosis z; buffered.
kind: operator
category: TEST
operator: TEST_MARDIA
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, tier-1-test, normality-test, multivariate, buffered-pipeline]

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

Use when

Checks whether a set of numeric fields looks jointly normal, through their combined skew and tail weight.

Questions it answers:

  • Before comparing segment profiles, are the metrics close enough to jointly normal?
  • Are the distance-based outlier flags safe to read as chi-square p-values?

Use something else:

  • TEST_SHAPIRO_WILK when there is only one numeric field and you want a sharper normality test.

Params

  • statistic — skewness (default) or kurtosis: the headline. alpha — default 0.05. missing — listwise only.

Slot: one of vector (a vectors entry) / fields, ≥ 1 member; no split_by.

  • weight — frequency only (= expanded rows); sum_weights beside raw n.

Inputs

Members: u4…u64, f32/f64.

Output

Skewness: χ² = N·b1p/6 on p(p + 1)(p + 2)/6 df. Kurtosis: z, DF 0. Variant names the headline. Details: skewness (b1p), skewness_chisq / _df / _p_value, kurtosis (b2p), kurtosis_z / _p_value, small_sample, members, n, n_dropped.

Reading the output

  • statistic: The skewness chi-square (default) or the kurtosis z named by variant; a small p-value says the fields are not jointly normal.
    • Caveat: A large p only means no departure was detected, which is likely with few rows.
  • 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.skewness: Mardia’s multivariate skewness, 0 for jointly normal data; it grows as the joint shape leans to one side.

Gotchas

  • Buffered: keeps n × p values.
  • N < 20: skewness gets the small-sample factor.
  • Singular covariance: PULSE_MATRIX_SINGULAR, null figures.

See