Statistical aggregate functions

GoogleSQL for BigQuery supports statistical aggregate functions. To learn about the syntax for aggregate function calls, see Aggregate function calls.

Function list

Name	Summary
CORR	Returns the Pearson coefficient of correlation of a set of number pairs.
COVAR_POP	Returns the population covariance of a set of number pairs.
COVAR_SAMP	Returns the sample covariance of a set of number pairs.
STDDEV_POP	Returns the population (biased) standard deviation of the values.
STDDEV_SAMP	Returns the sample (unbiased) standard deviation of the values.
STDDEV	An alias of the STDDEV_SAMP function.
VAR_POP	Returns the population (biased) variance of the values.
VAR_SAMP	Returns the sample (unbiased) variance of the values.
VARIANCE	An alias of VAR_SAMP.

CORR

CORR(
  X1, X2
)
[ OVER over_clause ]

over_clause:
  { named_window | ( [ window_specification ] ) }

window_specification:
  [ named_window ]
  [ PARTITION BY partition_expression [, ...] ]
  [ ORDER BY expression [ { ASC | DESC }  ] [, ...] ]
  [ window_frame_clause ]

Description

Returns the Pearson coefficient of correlation of a set of number pairs. For each number pair, the first number is the dependent variable and the second number is the independent variable. The return result is between -1 and 1. A result of 0 indicates no correlation.

All numeric types are supported. If the input is NUMERIC or BIGNUMERIC then the internal aggregation is stable with the final output converted to a FLOAT64. Otherwise the input is converted to a FLOAT64 before aggregation, resulting in a potentially unstable result.

This function ignores any input pairs that contain one or more NULL values. If there are fewer than two input pairs without NULL values, this function returns NULL.

NaN is produced if:

• Any input value is NaN
• Any input value is positive infinity or negative infinity.
• The variance of X1 or X2 is 0.
• The covariance of X1 and X2 is 0.

To learn more about the optional aggregate clauses that you can pass into this function, see Aggregate function calls.

To learn more about the OVER clause and how to use it, see Window function calls.

Return Data Type

FLOAT64

Examples

SELECT CORR(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 5.0 AS x),
      (3.0, 9.0),
      (4.0, 7.0)]);

/*--------------------*
 | results            |
 +--------------------+
 | 0.6546536707079772 |
 *--------------------*/

SELECT CORR(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 5.0 AS x),
      (3.0, 9.0),
      (4.0, NULL)]);

/*---------*
 | results |
 +---------+
 | 1       |
 *---------*/

SELECT CORR(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, 3.0)])

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT CORR(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, NULL)])

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT CORR(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 5.0 AS x),
      (3.0, 9.0),
      (4.0, 7.0),
      (5.0, 1.0),
      (7.0, CAST('Infinity' as FLOAT64))])

/*---------*
 | results |
 +---------+
 | NaN     |
 *---------*/

SELECT CORR(x, y) AS results
FROM
  (
    SELECT 0 AS x, 0 AS y
    UNION ALL
    SELECT 0 AS x, 0 AS y
  )

/*---------*
 | results |
 +---------+
 | NaN     |
 *---------*/

COVAR_POP

COVAR_POP(
  X1, X2
)
[ OVER over_clause ]

over_clause:
  { named_window | ( [ window_specification ] ) }

window_specification:
  [ named_window ]
  [ PARTITION BY partition_expression [, ...] ]
  [ ORDER BY expression [ { ASC | DESC }  ] [, ...] ]
  [ window_frame_clause ]

Description

Returns the population covariance of a set of number pairs. The first number is the dependent variable; the second number is the independent variable. The return result is between -Inf and +Inf.

All numeric types are supported. If the input is NUMERIC or BIGNUMERIC then the internal aggregation is stable with the final output converted to a FLOAT64. Otherwise the input is converted to a FLOAT64 before aggregation, resulting in a potentially unstable result.

This function ignores any input pairs that contain one or more NULL values. If there is no input pair without NULL values, this function returns NULL. If there is exactly one input pair without NULL values, this function returns 0.

NaN is produced if:

• Any input value is NaN
• Any input value is positive infinity or negative infinity.

To learn more about the optional aggregate clauses that you can pass into this function, see Aggregate function calls.

To learn more about the OVER clause and how to use it, see Window function calls.

Return Data Type

FLOAT64

Examples

SELECT COVAR_POP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (9.0, 3.0)])

/*---------------------*
 | results             |
 +---------------------+
 | -1.6800000000000002 |
 *---------------------*/

SELECT COVAR_POP(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, 3.0)])

/*---------*
 | results |
 +---------+
 | 0       |
 *---------*/

SELECT COVAR_POP(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, NULL)])

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT COVAR_POP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (NULL, 3.0)])

/*---------*
 | results |
 +---------+
 | -1      |
 *---------*/

SELECT COVAR_POP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (CAST('Infinity' as FLOAT64), 3.0)])

/*---------*
 | results |
 +---------+
 | NaN     |
 *---------*/

COVAR_SAMP

COVAR_SAMP(
  X1, X2
)
[ OVER over_clause ]

over_clause:
  { named_window | ( [ window_specification ] ) }

window_specification:
  [ named_window ]
  [ PARTITION BY partition_expression [, ...] ]
  [ ORDER BY expression [ { ASC | DESC }  ] [, ...] ]
  [ window_frame_clause ]

Description

Returns the sample covariance of a set of number pairs. The first number is the dependent variable; the second number is the independent variable. The return result is between -Inf and +Inf.

All numeric types are supported. If the input is NUMERIC or BIGNUMERIC then the internal aggregation is stable with the final output converted to a FLOAT64. Otherwise the input is converted to a FLOAT64 before aggregation, resulting in a potentially unstable result.

This function ignores any input pairs that contain one or more NULL values. If there are fewer than two input pairs without NULL values, this function returns NULL.

NaN is produced if:

• Any input value is NaN
• Any input value is positive infinity or negative infinity.

To learn more about the optional aggregate clauses that you can pass into this function, see Aggregate function calls.

To learn more about the OVER clause and how to use it, see Window function calls.

Return Data Type

FLOAT64

Examples

SELECT COVAR_SAMP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (9.0, 3.0)])

/*---------*
 | results |
 +---------+
 | -2.1    |
 *---------*/

SELECT COVAR_SAMP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (NULL, 3.0)])

/*----------------------*
 | results              |
 +----------------------+
 | --1.3333333333333333 |
 *----------------------*/

SELECT COVAR_SAMP(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, 3.0)])

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT COVAR_SAMP(y, x) AS results
FROM UNNEST([STRUCT(1.0 AS y, NULL AS x),(9.0, NULL)])

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT COVAR_SAMP(y, x) AS results
FROM
  UNNEST(
    [
      STRUCT(1.0 AS y, 1.0 AS x),
      (2.0, 6.0),
      (9.0, 3.0),
      (2.0, 6.0),
      (CAST('Infinity' as FLOAT64), 3.0)])

/*---------*
 | results |
 +---------+
 | NaN     |
 *---------*/

STDDEV_POP

STDDEV_POP(
  [ DISTINCT ]
  expression
)
[ OVER over_clause ]

over_clause:
  { named_window | ( [ window_specification ] ) }

window_specification:
  [ named_window ]
  [ PARTITION BY partition_expression [, ...] ]
  [ ORDER BY expression [ { ASC | DESC }  ] [, ...] ]
  [ window_frame_clause ]

Description

Returns the population (biased) standard deviation of the values. The return result is between 0 and +Inf.

All numeric types are supported. If the input is NUMERIC or BIGNUMERIC then the internal aggregation is stable with the final output converted to a FLOAT64. Otherwise the input is converted to a FLOAT64 before aggregation, resulting in a potentially unstable result.

This function ignores any NULL inputs. If all inputs are ignored, this function returns NULL. If this function receives a single non-NULL input, it returns 0.

NaN is produced if:

• Any input value is NaN
• Any input value is positive infinity or negative infinity.

To learn more about the optional aggregate clauses that you can pass into this function, see Aggregate function calls.

If this function is used with the OVER clause, it's part of a window function call. In a window function call, aggregate function clauses can't be used. To learn more about the OVER clause and how to use it, see Window function calls.

Return Data Type

FLOAT64

Examples

SELECT STDDEV_POP(x) AS results FROM UNNEST([10, 14, 18]) AS x

/*-------------------*
 | results           |
 +-------------------+
 | 3.265986323710904 |
 *-------------------*/

SELECT STDDEV_POP(x) AS results FROM UNNEST([10, 14, NULL]) AS x

/*---------*
 | results |
 +---------+
 | 2       |
 *---------*/

SELECT STDDEV_POP(x) AS results FROM UNNEST([10, NULL]) AS x

/*---------*
 | results |
 +---------+
 | 0       |
 *---------*/

SELECT STDDEV_POP(x) AS results FROM UNNEST([NULL]) AS x

/*---------*
 | results |
 +---------+
 | NULL    |
 *---------*/

SELECT STDDEV_POP(x) AS results FROM UNNEST([10, 14, CAST('Infinity' as FLOAT64)]) AS x

/*---------*
 | results |
 +---------+
 | NaN     |
 *---------*/