ClickHouse/docs/en/sql-reference/aggregate-functions/reference/theilsu.md

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theilsU

The theilsU function calculates the Theil's U uncertainty coefficient, a value that measures the association between two columns in a table. Its values range from −1.0 (100% negative association, or perfect inversion) to +1.0 (100% positive association, or perfect agreement). A value of 0.0 indicates the absence of association.

Syntax

theilsU(column1, column2)

Arguments

• column1 and column2 are the columns to be compared

Returned value

• a value between -1 and 1

Return type is always Float64.

Example

The following two columns being compared below have a small association with each other, so the value of theilsU is negative:

SELECT
    theilsU(a ,b)
FROM
    (
        SELECT
            number % 10 AS a,
            number % 4 AS b
        FROM
            numbers(150)
    );

Result:

┌────────theilsU(a, b)─┐
│ -0.30195720557678846 │
└──────────────────────┘