Correlation Matrix (multi-variable scan)

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Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

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Pairwise correlations across ≥ 3 numeric variables, all computed simultaneously.

Reports Pearson r, Spearman ρ, and Kendall τ-b per cell with Fisher-z 95% CIs and multiple-comparison corrected p-values (Bonferroni, Holm, or Benjamini-Hochberg FDR). Surfaces the top-N strongest pairs and flags cells where Pearson and Spearman diverge (non-linearity signal). The k(k-1)/2 off-diagonal pairs are the testing family for correction.

Worked example

How are several variables inter-related at a glance?

A correlation matrix reports every pairwise correlation among a set of variables, flagging strong or non-linear pairs.

Result

Most pairs correlated moderately (.30–.55); two showed Pearson/Spearman divergence, hinting at non-linearity.

How you'd report it (APA)

A correlation matrix summarised the inter-variable relationships (most r .30–.55), flagging two possibly non-linear pairs.

When to use it

Exploratory screen of multiple continuous measurements
A psychometrician has 8 subscale scores from a new personality inventory administered to 300 respondents.
Pre-factor-analysis / pre-PCA assessment
A market researcher prepares 12 customer-experience Likert items for an EFA.

When NOT to — use instead

Single pair of variables
A 1-pair matrix is just a single correlation — use the focused single-pair test for cleaner reporting. → Pearson Correlation (linear association)
Categorical variables
Pairwise correlations on categorical data don't have a meaningful interpretation; build a contingency analysis. → Chi-Square Test of Independence
Hypothesis-confirmatory analysis with one specific predictor and one outcome
When you have a single a priori hypothesis, use a focused regression — the matrix is for exploration. → Linear Regression \u2014 OLS (continuous y + predictors)
Need to control for confounding across the matrix
Marginal correlations in a matrix can be misleading when confounders are present. → Partial Correlation (linear, controlling for covariates)

Hypotheses

For each cell (i, j): H₀: ρ_{ij} = 0 — no linear (or monotone, depending on method) association between variable i and variable j.

Hₐ: ρ_{ij} ≠ 0 — two-sided, per cell.

Parameter tested: vector of population ρ's — one per pair

Assumptions (and what to do if they fail)

Each pairwise correlation has adequate n of complete cases (≥ 10 recommended, ≥ 30 for Fisher-z CI precision).high

Check: Report n_min across all matrix cells.

If violated: Thin cells yield unstable r, wide CIs, and unreliable p-values.

Pearson r assumes LINEAR association per pair. Spearman ρ only requires monotonicity. Kendall τ-b is concordance-based.medium

Check: Inspect the divergence table — cells with large |r − ρ|.

If violated: Pearson under-represents non-linear monotone relationships.

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🔎 Worked example

✓ When to use it

✗ When NOT to — use instead

Hypotheses

Assumptions (and what to do if they fail)

Worked example

When to use it

When NOT to — use instead