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

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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

Original article