cramersV

Cramer's V (sometimes referred to as Cramer's phi) is a measure of association between two columns in a table. The result of the cramersV function ranges from 0 (corresponding to no association between the variables) to 1 and can reach 1 only when each value is completely determined by the other. It may be viewed as the association between two variables as a percentage of their maximum possible variation.

Note

For a bias corrected version of Cramer's V see: cramersVBiasCorrected

Syntax

cramersV(column1, column2)

Parameters

column1: first column to be compared.
column2: second column to be compared.

Returned value

a value between 0 (corresponding to no association between the columns' values) to 1 (complete association).

Type: always Float64.

Example

The following two columns being compared below have no association with each other, so the result of cramersV is 0:

Query:

SELECT
    cramersV(a, b)
FROM
    (
        SELECT
            number % 3 AS a,
            number % 5 AS b
        FROM
            numbers(150)
    );

Result:

┌─cramersV(a, b)─┐
│              0 │
└────────────────┘

The following two columns below have a fairly close association, so the result of cramersV is a high value:

SELECT
    cramersV(a, b)
FROM
    (
        SELECT
            number % 10 AS a,
            if(number % 12 = 0, (number + 1) % 5, number % 5) AS b
        FROM
            numbers(150)
    );

Result:

┌─────cramersV(a, b)─┐
│ 0.9066801892162646 │
└────────────────────┘

cramersV

Introduced in: v22.1

Note

For a bias corrected version of Cramer's V see: cramersVBiasCorrected

Syntax

cramersV(column1, column2)

Arguments

column1 — First column to be compared. (U)Int* or Float* or Decimal
column2 — Second column to be compared. (U)Int* or Float* or Decimal

Returned value

Returns a value between 0 (corresponding to no association between the columns' values) to 1 (complete association). Float64

Examples

No association between columns

SELECT
    cramersV(a, b)
FROM
    (
        SELECT
            number % 3 AS a,
            number % 5 AS b
        FROM
            numbers(150)
    )

┌─cramersV(a, b)─┐
│              0 │
└────────────────┘

High association between columns

SELECT
    cramersV(a, b)
FROM
    (
        SELECT
            number % 10 AS a,
            number % 5 AS b
        FROM
            numbers(150)
    )

┌─────cramersV(a, b)─┐
│ 0.8944271909999159 │
└────────────────────┘

cramersV​

cramersV