welchTTest

Applies Welch's t-test to samples from two populations.

Syntax

welchTTest([confidence_level])(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 means of populations are equal. Normal distribution is assumed. Populations may have unequal variance.

Arguments

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

Parameters

• confidence_level — Confidence level in order to calculate confidence intervals. Float.

Returned values

Tuple with two or four elements (if the optional confidence_level is specified)

• calculated t-statistic. Float64.
• calculated p-value. Float64.
• calculated confidence-interval-low. Float64.
• calculated confidence-interval-high. Float64.

Example

Input table:

┌─sample_data─┬─sample_index─┐
│        20.3 │            0 │
│        22.1 │            0 │
│        21.9 │            0 │
│        18.9 │            1 │
│        20.3 │            1 │
│          19 │            1 │
└─────────────┴──────────────┘

Query:

SELECT welchTTest(sample_data, sample_index) FROM welch_ttest;

Result:

┌─welchTTest(sample_data, sample_index)─────┐
│ (2.7988719532211235,0.051807360348581945) │
└───────────────────────────────────────────┘

See Also

• Welch's t-test
• studentTTest function

welchTTest

Introduced in: v21.1

Applies Welch's t-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 means of populations are equal. Normal distribution is assumed. Populations may have unequal variance.

Syntax

welchTTest([confidence_level])(sample_data, sample_index)

Parameters

• confidence_level — Optional. Confidence level in order to calculate confidence intervals. Float

Arguments

• sample_data — Sample data. Int* or UInt* or Float* or Decimal*
• sample_index — Sample index. Int* or UInt*

Returned value

Returns a Tuple with two or four elements (if the optional confidence_level is specified): calculated t-statistic, calculated p-value, and optionally calculated confidence-interval-low and confidence-interval-high. Tuple(Float64, Float64) or Tuple(Float64, Float64, Float64, Float64)

Examples

Basic Welch's t-test

CREATE TABLE welch_ttest (sample_data Float64, sample_index UInt8) ENGINE = Memory;
INSERT INTO welch_ttest VALUES (20.3, 0), (22.1, 0), (21.9, 0), (18.9, 1), (20.3, 1), (19, 1);

SELECT welchTTest(sample_data, sample_index) FROM welch_ttest;

┌─welchTTest(sample_data, sample_index)──────┐
│ (2.7988719532211235, 0.051807360348581945) │
└────────────────────────────────────────────┘

With confidence level

SELECT welchTTest(0.95)(sample_data, sample_index) FROM welch_ttest;

┌─welchTTest(0.95)(sample_data, sample_index)─────────────────────────────────────────┐
│ (2.7988719532211235, 0.051807360ec7e104a, -0.026294346671631885, 4.092961013338302) │
└─────────────────────────────────────────────────────────────────────────────────────┘