# Measure correlation Shape / inspect correlation or association matrix, contingency table Page: ## Status Runs as a SQL step. arcform carries it as a `sql:` step today. ## The DuckDB step correlation of two columns It reads the `orders` table the proofs share. Create it first: ```sql CREATE TABLE orders AS SELECT * FROM (VALUES (1, 'Alice Ng', 'north', DATE '2026-01-03', 120.00, 'widget', 'a|b', '{"channel":"web","items":[1,2]}'), (2, 'alice ng', 'north', DATE '2026-01-05', 80.50, 'gadget', 'b', '{"channel":"shop","items":[3]}'), (3, 'Bob Okafor', 'south', DATE '2026-01-05', 300.00, 'widget', 'a|c', '{"channel":"web","items":[4,5,6]}'), (4, 'Carla Díaz', 'east', DATE '2026-01-09', NULL, 'gizmo', NULL, '{"channel":"web","items":[]}'), (5, 'Bob Okafor', 'south', DATE '2026-01-12', 45.25, 'gadget', 'c', '{"channel":"phone","items":[7]}'), (6, 'Dev Patel', 'west', DATE '2026-01-12', 510.00, 'widget', 'a', '{"channel":"web","items":[8,9]}'), (7, 'Carla Diaz', 'east', DATE '2026-01-20', 99.99, 'gizmo', 'b|c', '{"channel":"shop","items":[10]}'), (8, 'Dev Patel', 'west', DATE '2026-02-02', 510.00, 'widget', 'a', '{"channel":"web","items":[8,9]}'), (9, 'Eve Larsen', NULL, DATE '2026-02-03', 15.00, 'gadget', NULL, '{"channel":"web","items":[11]}'), (10, 'Alice Ng', 'north', DATE '2026-02-10', 220.00, 'gizmo', 'a|b|c', '{"channel":"phone","items":[12,13]}') ) t(order_id, customer, region, order_date, amount, product, tags, meta); ``` Then run the statement: ```sql CREATE TEMP TABLE result AS SELECT round(corr(amount, order_id), 4) AS r, round(covar_samp(amount, order_id), 2) AS cov, round(corr(amount, amount * 2 + 1), 4) AS with_itself_scaled FROM orders; SELECT * FROM result; SELECT CASE WHEN ((SELECT r BETWEEN -1 AND 1 AND with_itself_scaled = 1 AND r = 0.1683 FROM result)) THEN 'as expected' ELSE error('the correlation is out of range, or a column does not correlate 1 with a linear copy of itself') END AS verdict; ``` It needs nothing installed beyond DuckDB itself. ## Variants - Measure covariance: Compute the population or sample covariance of two numeric columns. - [Cross-tabulate two columns](https://meridian.online/operations/measure-correlation/cross-tabulate-two-columns): Count the rows for each combination of values in two or more categorical columns, with association tests such as chi-square. - [Build a correlation matrix](https://meridian.online/operations/measure-correlation/build-a-correlation-matrix): Correlate every pair of chosen columns at once, giving a matrix of coefficients, covariances or mutual information. - Other association measures: Measure internal consistency across columns, or count how often each value follows another. - Correlate two columns: Compute one correlation coefficient, Pearson or rank-based, between two numeric columns. ## What other tools call it Meridian's classification; an independent blind rating agreed on 86.2% of 312 rows (exact class, version 2). - Alteryx Designer: [`Association Analysis`](https://help.alteryx.com/current/en/designer/tools/data-investigation/association-analysis-tool.html) (read 2026-09-27) - Alteryx Designer: [`Contingency Table`](https://help.alteryx.com/current/en/designer/tools/data-investigation/contingency-table-tool.html) (read 2026-09-27) - Alteryx Designer: [`Pearson Correlation`](https://help.alteryx.com/current/en/designer/tools/data-investigation/pearson-correlation-tool.html) (read 2026-09-27) - Alteryx Designer: [`Spearman Correlation`](https://help.alteryx.com/current/en/designer/tools/data-investigation/spearman-correlation-tool.html) (read 2026-09-27) - Apache DataFusion: [`corr`](https://datafusion.apache.org/user-guide/sql/aggregate_functions.html) (read 2026-09-27) - Apache DataFusion: [`covar_pop`](https://datafusion.apache.org/user-guide/sql/aggregate_functions.html) (read 2026-09-27) - Apache DataFusion: [`covar_samp`](https://datafusion.apache.org/user-guide/sql/aggregate_functions.html) (read 2026-09-27) - DuckDB: [`corr`](https://duckdb.org/docs/current/sql/functions/aggregates) (read 2026-09-27) - DuckDB: [`covar_pop`](https://duckdb.org/docs/current/sql/functions/aggregates) (read 2026-09-27) - DuckDB: [`covar_samp`](https://duckdb.org/docs/current/sql/functions/aggregates) (read 2026-09-27) - AWS Glue: [`ColumnCorrelation`](https://docs.aws.amazon.com/glue/latest/dg/dqdl-rule-types.html) (read 2026-09-27) - KNIME Analytics Platform: [`Cronbach Alpha`](https://api.hub.knime.com/nodes/*iFALu0VL45kWr1b1?details=full) (read 2026-09-27) - KNIME Analytics Platform: [`Crosstab`](https://api.hub.knime.com/nodes/*pNm03fXRSkMzHV8O?details=full) (read 2026-09-27) - KNIME Analytics Platform: [`Linear Correlation`](https://api.hub.knime.com/nodes/*0gFnKniNdXkr6DtW?details=full) (read 2026-09-27) - KNIME Analytics Platform: [`Rank Correlation`](https://api.hub.knime.com/nodes/*sC8qjjAYkSsMFjOc?details=full) (read 2026-09-27) - KNIME Analytics Platform: [`Standardized Cronbach Alpha`](https://api.hub.knime.com/nodes/*oE1zFiY4KVBa9S2x?details=full) (read 2026-09-27) - Polars: [`DataFrame.corr`](https://docs.pola.rs/api/python/stable/reference/dataframe/miscellaneous.html) (read 2026-09-27) - RapidMiner Studio: [`Correlation Matrix`](https://docs.rapidminer.com/latest/studio/operators/modeling/correlations/correlation_matrix.html) (read 2026-09-27) - RapidMiner Studio: [`Covariance Matrix`](https://docs.rapidminer.com/latest/studio/operators/modeling/correlations/covariance_matrix.html) (read 2026-09-27) - RapidMiner Studio: [`Mutual Information Matrix`](https://docs.rapidminer.com/latest/studio/operators/modeling/correlations/mututal_information_matrix.html) (read 2026-09-27) - RapidMiner Studio: [`Transition Matrix`](https://docs.rapidminer.com/latest/studio/operators/modeling/correlations/transition_matrix.html) (read 2026-09-27)