Pulse Documentation

name: op-test-t
description: One-sample or two-sample Welch t-test on a numeric field; SplitBy switches to the two-sample variant.
kind: operator
category: TEST
operator: TEST_T
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, t-test, tier-1-test, parametric, two-sample, one-sample, streaming-friendly]

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

Use when

Checks whether a numeric field’s average differs from a target value, or between two groups (Welch’s version).

Questions it answers:

• Is the average order value different from our target of 50?
• Do new and returning customers spend different amounts on average?

Use something else:

• TEST_PAIRED_T when the same subjects are measured twice, such as before and after.
• TEST_ANOVA_WELCH when there are three or more groups.

Params

• alpha — float, default 0.05, in (0, 1).
• mu — float, default 0.0. Hypothesized mean, one-sample only; ignored when SplitBy is set.
• weight — slot weight (null opts out), both kinds: moments on w*, N* = Σw (frequency) or Kish n_eff (probability); df = N*−1 (two-sample: Welch df on N*_g), may be fractional. Details add sum_weights (+ n_eff, probability) shaped like n (raw rows); n_eff < 2 warns PULSE_WEIGHT_LOW_NEFF.
• 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 (optional → two-sample Welch) — categorical_u8/u16/u32, packed_bool.

Output

Statistic = t; DF; PValue two-sided. One-sample Details: mu, n, mean, variance, ci_low/ci_high, effect_size.cohens_d = (mean − mu)/sd. Two-sample: per-group n/mean/variance, diff, CI, pooled-SD cohens_d.

Reading the output

• statistic: t is the gap between averages measured in standard errors: the sample mean minus the target value (one-sample), or the first group’s mean minus the second’s (two-sample, Welch). Values far from 0 in either direction are unlikely if the true gap is zero.
• 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.diff: Two-sample only: the first group’s mean minus the second’s, in the field’s own units.

Gotchas

• Two-sample needs exactly 2 SplitBy groups, else PULSE_TEST_INVALID_SPLITBY.
• Streamable — running Welford state per SplitBy group.
• Constant Field within a group → PULSE_TEST_VARIANCE_ZERO.
• n < 2 (per group) → PULSE_TEST_INSUFFICIENT_N.

See

• pulse_examples_search tags=[t-test]
• Skills: statistical-testing, op-test-welch, op-test-z-two-sample, op-test-paired-t