# statistics

ADVANCED

This module contains functions to perform spatial statistics calculations.

P_VALUE(z_score)

**Description**

This function computes the p-value (two-tails test) of a given z-score assuming the population follows a normal distribution where the mean is 0 and the standard deviation is 1. The z-score is a measure of how many standard deviations below or above the population mean a value is. It gives you an idea of how far from the mean a data point is. The p-value is the probability that a randomly sampled point has a value at least as extreme as the point whose z-score is being tested.

`z_score`

:`FLOAT`

**Return type**

`FLOAT`

**Example**

SELECT CARTO.CARTO.P_VALUE(value) as p_value

FROM LATERAL FLATTEN(input => ARRAY_CONSTRUCT(-2,-1,0,1,2));

-- 0.04550012577451279,

-- 0.31731052766472745,

-- 0.999999999,

-- 0.31731052766472745,

-- 0.04550012577451279

GETIS_ORD_H3(input, output_table, index_col, value_col, size, kernel)

**Description**

This procedure computes the Getis-Ord Gi* statistic for each row in the input table.

`input`

:`STRING`

the query to the data used to compute the coefficient. A qualified table name can be given as well:`<project-id>.<dataset-id>.<table-name>`

.`output_table`

:`STRING`

qualified name of the output table:`<project-id>.<dataset-id>.<table-name>`

.`index_col`

:`STRING`

name of the column with the H3 indexes.`value_col`

:`STRING`

name of the column with the values for each H3 cell.`size`

:`INT`

size of the H3 kring (distance from the origin). This defines the area around each index cell that will be taken into account to compute its Gi* statistic.`kernel`

:`STRING`

kernel function to compute the spatial weights across the kring. Available functions are: uniform, triangular, quadratic, quartic and gaussian.

**Output**

The results are stored in the table named

`<output_table>`

, which contains the following columns:`index`

:`STRING`

`gi`

:`FLOAT`

computed Gi* value.`p_value`

:`FLOAT`

computed P value.

**Example**

CALL CARTO.CARTO.GETIS_ORD_H3(

'myproject.mydataset.h3table',

'myproject.mydataset.outputtable',

'h3',

'value'

3,

'gaussian'

);

GETIS_ORD_QUADBIN(input, output_table, index_col, value_col, size, kernel)

**Description**

This procedure computes the Getis-Ord Gi* statistic for each row in the input table.

`input`

:`STRING`

the query to the data used to compute the coefficient. A qualified table name can be given as well:`<project-id>.<dataset-id>.<table-name>`

.`output_table`

:`STRING`

qualified name of the output table:`<project-id>.<dataset-id>.<table-name>`

.`index_col`

:`STRING`

name of the column with the Quadbin indexes.`value_col`

:`STRING`

name of the column with the values for each Quadbin cell.`size`

:`INT`

size of the Quadbin kring (distance from the origin). This defines the area around each index cell that will be taken into account to compute its Gi* statistic.`kernel`

:`STRING`

kernel function to compute the spatial weights across the kring. Available functions are: uniform, triangular, quadratic, quartic and gaussian.

**Output**

The results are stored in the table named

`<output_table>`

, which contains the following columns:`index`

:`BIGINT`

`gi`

:`FLOAT`

computed Gi* value.`p_value`

:`FLOAT`

computed P value.

**Example**

CALL CARTO.CARTO.GETIS_ORD_QUADBIN(

'myproject.mydataset.quadbintable',

'myproject.mydataset.outputtable',

'quadbin',

'value'

3,

'gaussian'

);

MORANS_I_H3(input, output_table, index_col, value_col, size, decay)

**Description**

`input`

:`STRING`

the query to the data used to compute the coefficient. A qualified table name can be given as well:`<project-id>.<dataset-id>.<table-name>`

.`output_table`

:`STRING`

qualified name of the output table:`<project-id>.<dataset-id>.<table-name>`

.`index_col`

:`STRING`

name of the column with the H3 indexes.`value_col`

:`STRING`

name of the column with the values for each H3 cell.`size`

:`INT`

size of the H3 kring (distance from the origin). This defines the area around each index cell where the distance decay will be applied.`decay`

:`STRING`

decay function to compute the distance decay. Available functions are: uniform, inverse, inverse_square and exponential.

**Output**

The results are stored in the table named

`<output_table>`

, which contains the following column:`morans_i`

:`FLOAT`

Moran's I spatial autocorrelation.

**Example**

CALL CARTO.CARTO.MORANS_I_H3(

'myproject.mydataset.h3table',

'myproject.mydataset.outputtable',

'h3',

'value'

5,

'uniform'

);

MORANS_I_QUADBIN(input, output_table, index_col, value_col, size, decay)

**Description**

This procedure computes the Moran's I spatial autocorrelation from the input table with Quadbin indexes.

`input`

:`STRING`

the query to the data used to compute the coefficient. A qualified table name can be given as well:`<project-id>.<dataset-id>.<table-name>`

.`output_table`

:`STRING`

qualified name of the output table:`<project-id>.<dataset-id>.<table-name>`

.`index_col`

:`STRING`

name of the column with the Quadbin indexes.`value_col`

:`STRING`

name of the column with the values for each Quadbin cell.`size`

:`INT`

size of the Quadbin kring (distance from the origin). This defines the area around each index cell where the distance decay will be applied.`decay`

:`STRING`

decay function to compute the distance decay. Available functions are: uniform, inverse, inverse_square and exponential.

**Output**

The results are stored in the table named

`<output_table>`

, which contains the following column:`morans_i`

:`FLOAT`

Moran's I spatial autocorrelation.

**Example**

CALL CARTO.CARTO.MORANS_I_QUADBIN(

'myproject.mydataset.quadbintable',

'myproject.mydataset.outputtable',

'quadbin',

'value'

5,

'uniform'

);

Last modified 19d ago