{"id":"correlation-kendall-tau","version":"1.0.0","description":"Compute Kendall tau-b correlation with tie correction and return a precision-rounded decimal coefficient.","supported_operations":["kendall tau correlation between two columns","calculate Kendall tau-b with ties","count concordant and discordant pairs","compare ordinal association of paired values","tie corrected rank correlation","find Kendall coefficient from decimal columns"],"unsupported_operations":["Kendall tau-a or tau-c","correlation significance test or p-value","missing-value imputation"],"semantics":["The coefficient is rounded to precision decimal places, with exact halves away from zero; rounded zero has no minus sign.","Inputs are paired decimal strings or finite JSON numbers; decimal text is interpreted exactly.","Tau-b is (concordant minus discordant) divided by the square root of both non-tied pair counts.","A column with every pair tied produces not_computable. No significance test, confidence interval, or p-value is computed.","standard_version is R92-NIST-Dataplot-Kendall1945-v1."],"limits":{"max_input_bytes":16384,"max_items":128,"max_decimal_chars":128,"max_iterations":8128,"max_output_bytes":93},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["x","y","precision"],"properties":{"x":{"type":"array","minItems":2,"maxItems":128,"items":{"type":["string","number"]}},"y":{"type":"array","minItems":2,"maxItems":128,"items":{"type":["string","number"]}},"precision":{"type":"integer","minimum":0,"maximum":18}}},"output_schema":{"type":"object","additionalProperties":false,"required":["correlation","standard_version"],"properties":{"correlation":{"type":"string","maxLength":21,"pattern":"^-?(?:0|1)(?:\\.\\d{1,18})?$"},"standard_version":{"type":"string","const":"R92-NIST-Dataplot-Kendall1945-v1"}}},"examples":[{"input":{"x":[1,2,3],"y":[3,2,1],"precision":4},"output":{"correlation":"-1.0000","standard_version":"R92-NIST-Dataplot-Kendall1945-v1"}},{"input":{"x":[1,1,2],"y":[1,2,3],"precision":6},"output":{"correlation":"0.816497","standard_version":"R92-NIST-Dataplot-Kendall1945-v1"}}],"execute_url":"/v1/tools/correlation-kendall-tau/versions/1.0.0/execute"}