Pulse Documentation

name: op-overlay-t-cell
kind: operator
category: OVERLAY
operator: OVERLAY_T_CELL
description: Compose-host per-cell Welch t-test against the reference slot's matching cell; parity overlay reading from CellComponents.
type: reference
applies_to: compose
examples_tags: [overlay, compose, hypothesis-test, welch, byte-equal-test]

Compose-only parity overlay. Overlays decorate the host; no Response.Components.

Use when

Welch t-test for every crosstab cell in a Compose request: does the target’s mean in that cell differ from the reference’s?

Questions it answers:

• Which segment-by-product cells changed in average rating since last wave?
• Where does the new site’s average handling time differ from the old site’s?

Use something else:

• OVERLAY_Z_CELL when every cell is large and you want the normal-curve version.

Params

Scope required, must be cell. Reference / Targets required slot labels. Optional overrides params.variance_target/_ref (float, 1.0), params.sample_size_target/_ref (int, 2). Without AGG_WELFORD these ONE values per side apply to EVERY cell, so the p-values describe the supplied values (and the measure’s units), not each cell’s spread.

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

Host shape

COMPOSE — MATRIX crosstab on both slots. Parity overlay — reads {n, mean, variance} from Response.Components.Crosstab.CellComponents[r][c] (populated by AGG_WELFORD via MetaAggregator), else the params triple.

Output

MATRIX — Cells[r][c].Value = two-sided p-value. One layer per target; Baseline unset.

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 Welch t-test p-value comparing the target’s mean in that cell with the reference’s.
  • Caveat: Without AGG_WELFORD values (or explicit variance and sample-size params) Pulse computes the p-value from placeholder inputs (variance 1, n 2), and it then describes those placeholders, not your data.

Gotchas

• Weighted (both kinds, any weight source): a cell carrying sum_weights reads N* = sum_weights (frequency) or n_eff (probability) — never the raw n — and its variance from m2 on w*. Summary.Parameters adds sum_weights (+ n_eff) over the legs read.
• Byte-equal to Welch’s t-test on the same inputs — both read {n, mean, variance} via Welford and share studentTTwoSidedP and the df recurrence.
• Legacy processing.WelfordTriple smuggle REMOVED v0.20.0 — MatrixCell.Value carries the scalar mean.
• Canonical pairing: AGG_WELFORD + OVERLAY_T_CELL. Buffered (inferential).

See

• Skills: overlay-system, response-components, op-overlay-z-cell, op-overlay-t-vs-ref, op-agg-welford.