{
  "slug": "pearson-correlation",
  "name": "Pearson correlation",
  "aliases": [
    "Pearson r",
    "Linear correlation"
  ],
  "definition": "How closely two metrics move together in a straight-line sense, over aligned time buckets.",
  "category": "Statistics",
  "type": "statistical verdict",
  "unit": "coefficient between −1 and 1",
  "direction": "neutral",
  "verification": "verified",
  "calculation": "Each metric is fetched as a bucketed series through a governed read, the two series are aligned on the shared time bucket in the compute engine, and the product-moment coefficient is computed on the aligned pairs. A t-statistic is formed from the coefficient with two fewer degrees of freedom than pairs, but its probability is NOT read from a t-distribution: the statistic is rescaled by a Cornish to Fisher term and fed to the standard normal curve. A perfect coefficient short-circuits to a probability of zero.",
  "numerator": "The covariance of the two aligned series",
  "denominator": "The product of their standard deviations",
  "aggregation": "One coefficient per pair of series. Coefficients are never averaged or chained.",
  "grain": "One value per metric pair, date range and bucket size.",
  "dimensions": [
    "bucket"
  ],
  "requiredFilters": [
    "date_range"
  ],
  "sources": [
    "search-console",
    "web-analytics",
    "google-ads",
    "rank-tracking",
    "lighthouse"
  ],
  "reports": [],
  "skills": [
    "cross-domain-correlator",
    "anomaly-investigator"
  ],
  "verbs": [
    "correlate_domains"
  ],
  "rungs": [
    "R5",
    "R2"
  ],
  "levers": [],
  "questions": [
    "Does page speed move with our clicks?",
    "Does search market share track traffic?"
  ],
  "interpretation": "A relationship, described in bounded language: correlates, moves with, consistent with. Never drives, causes or explains. Where the answer would drive spend or work, the correct next step is a designed test rather than a stronger adjective.",
  "caveats": [
    "The significance attached to the coefficient is approximate: a normal approximation with a Cornish to Fisher correction, which is anti-conservative at small degrees of freedom, at five, the probability can be understated by roughly a quarter. A cross-domain correlation often runs on a handful of aligned buckets, so treat a borderline significance on a short series as unproven.",
    "Correlation is not causation, and the payload carries that caveat with the sample size attached.",
    "Shared trends and confounds inflate it, two metrics that both rise seasonally will correlate without being related.",
    "It measures straight-line association only and is sensitive to outliers; the rank-based coefficient is the robust alternative and both are returned by default.",
    "At least three buckets are needed on each side and at least three aligned buckets after the join, or the tool returns an explanatory note instead of a coefficient.",
    "The two series are aligned by bucket, so the freshness of the slowest contributing source governs the whole read, page experience is the least predictable and is named when it is one of the pair.",
    "An insignificant coefficient is reported as no detectable relationship at this power, not as no relationship."
  ],
  "freshness": "varies by site, priority URLs can run nightly; most pages far less often. The collection date rides on the card rather than being assumed.",
  "failureModes": [
    "Describing the significance as a t-test result, no t-distribution is evaluated.",
    "Reading a strong coefficient as a causal mechanism.",
    "Correlating two metrics that share an obvious driver and reporting the result as a finding.",
    "Computing a coefficient by hand when the tool declined to and presenting it as a product number."
  ],
  "notSameAs": [
    {
      "slug": "spearman-correlation",
      "why": "Pearson measures straight-line association on the values; Spearman measures monotonic association on their ranks. They disagree exactly where the relationship is real but not linear, or where an outlier dominates."
    },
    {
      "slug": "practical-effect-magnitude",
      "why": "A coefficient describes the tightness of a relationship, not its business size, and no interval is computed around it."
    }
  ],
  "related": [
    "spearman-correlation",
    "significance-p-value"
  ],
  "workflows": [],
  "lastVerified": "2026-08-04"
}