mannWhitneyUTest

Applies the Mann-Whitney rank test to samples from two populations.

Syntax

mannWhitneyUTest[(alternative[, continuity_correction])](sample_data, sample_index)

Values of both samples are in the sample_data column. If sample_index equals to 0 then the value in that row belongs to the sample from the first population. Otherwise it belongs to the sample from the second population. The null hypothesis is that two populations are stochastically equal. Also one-sided hypothesises can be tested. This test does not assume that data have normal distribution.

Arguments

• sample_data — sample data. Integer, Float or Decimal.
• sample_index — sample index. Integer.

Parameters

• alternative — alternative hypothesis. (Optional, default: 'two-sided'.) String.
  • 'two-sided';
  • 'greater';
  • 'less'.
• continuity_correction — if not 0 then continuity correction in the normal approximation for the p-value is applied. (Optional, default: 1.) UInt64.

Returned values

Tuple with two elements:

• calculated U-statistic. Float64.
• calculated p-value. Float64.

Example

Input table:

┌─sample_data─┬─sample_index─┐
│          10 │            0 │
│          11 │            0 │
│          12 │            0 │
│           1 │            1 │
│           2 │            1 │
│           3 │            1 │
└─────────────┴──────────────┘

Query:

SELECT mannWhitneyUTest('greater')(sample_data, sample_index) FROM mww_ttest;

Result:

┌─mannWhitneyUTest('greater')(sample_data, sample_index)─┐
│ (9,0.04042779918503192)                                │
└────────────────────────────────────────────────────────┘

See Also

• Mann–Whitney U test
• Stochastic ordering

mannWhitneyUTest

Introduced in: v21.1

Applies the Mann-Whitney rank test to samples from two populations.

Values of both samples are in the sample_data column. If sample_index equals to 0 then the value in that row belongs to the sample from the first population. Otherwise it belongs to the sample from the second population. The null hypothesis is that two populations are stochastically equal. Also one-sided hypotheses can be tested. This test does not assume that data have normal distribution.

Syntax

mannWhitneyUTest[(alternative[, continuity_correction])](sample_data, sample_index)

Parameters

• alternative — Optional. Alternative hypothesis. 'two-sided' (default): two populations are not stochastically equal. 'greater': values in the first sample are stochastically greater than those in the second sample. 'less': values in the first sample are stochastically less than those in the second sample. String
• continuity_correction — Optional. If not 0 then continuity correction in the normal approximation for the p-value is applied. The default value is 1. UInt64

Arguments

• sample_data — Sample data. (U)Int* or Float* or Decimal*
• sample_index — Sample index. (U)Int*

Returned value

Returns a tuple with two elements: calculated U-statistic and calculated p-value. Tuple(Float64, Float64)

Examples

Mann-Whitney U test example

CREATE TABLE mww_ttest (sample_data Float64, sample_index UInt8) ENGINE = Memory;
INSERT INTO mww_ttest VALUES (10, 0), (11, 0), (12, 0), (1, 1), (2, 1), (3, 1);

SELECT mannWhitneyUTest('greater')(sample_data, sample_index) FROM mww_ttest;

┌─mannWhitneyUTest('greater')(sample_data, sample_index)─┐
│ (9,0.04042779918503192)                                │
└────────────────────────────────────────────────────────┘