Pulse Documentation

name: op-overlay-pairwise-weighted-two-means-z
kind: operator
category: OVERLAY
operator: OVERLAY_PAIRWISE_WEIGHTED_TWO_MEANS_Z
description: Intra-matrix axis-pairwise two-means z-test on weighted-mean cells under a required n_basis (weights | kish).
type: reference
applies_to: process, compose
examples_tags: [overlay, cross-tabulation, hypothesis-test, pairwise]

Weighted pairwise two-means z: pairs rows (row scope) or columns (column) on weighted means. Reads Response.Components.

Use when

Large-sample z-tests between every pair of rows (or columns) of one crosstab of weighted averages, with a sample-size basis you choose.

Questions it answers:

• Which weighted segments differ from each other in average satisfaction?
• Which regions differ in weighted average spend once survey weights are applied?

Use something else:

• OVERLAY_PAIRWISE_WELCH_T when the cells are unweighted averages.

Params

Scope (required) — row or column. Ref empty. params.n_basis (REQUIRED, no default) — weights or kish. params.pair_along_dim (int) — same-bucket pairs. n_source / p_source / bad n_basis → PULSE_OVERLAY_PARAM_MISSING; weights on a probability-weighted cell (incl. weight_field) → PROCESSING_CONFIG.

• multiplicity — optional {method, family, alpha}; adds p_adjusted figures, raw p untouched (multiplicity-correction).

Host shape

MATRIX crosstab, weighted-moment cell: AGG_WEIGHTED_MEAN or a weighted AGG_AVERAGE. Reads weighted_mean, m2_weighted, sum_weights, sum_weights_sq — never floor n. Else PULSE_OVERLAY_REF_INCOMPATIBLE_WITH_SHAPE; components off → PULSE_OVERLAY_COMPONENTS_REQUIRED.

Output

Pair × opposite-axis two-sided p-values. weights: var = m2/(Σw−1), n = Σw. kish: var = m2/(Σw−Σw²/Σw), n = n_eff. z = (m_i−m_j)/sqrt(var_i/n_i + var_j/n_j), p = 2Φ(−|z|).

Reading the output

• cells.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.
  • Caveat: Each cell holds the two-sided z-test p-value for one pair of weighted means; params.n_basis sets the sample size (sum of weights, or Kish’s effective sample size).
  • Caveat: It accounts for weighting only, not clustering or other design effects, so with such designs the p-values come out too small.

Gotchas

• Skips (PULSE_OVERLAY_REF_ZERO): weights leg Σw ≤ 1; kish leg with one weighted row; zero SE.
• Mergeable cell: stays fused. n_basis sets n: weights needs frequency weights (Σw is no sample size under probability); probability → kish.

See

• Skills: op-overlay-pairwise-two-means-z, op-agg-weighted-mean, overlay-system.