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72 lines
2.4 KiB
Markdown
72 lines
2.4 KiB
Markdown
---
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slug: /en/sql-reference/aggregate-functions/reference/welchttest
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sidebar_position: 301
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sidebar_label: welchTTest
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---
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# welchTTest
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Applies Welch's t-test to samples from two populations.
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**Syntax**
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``` sql
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welchTTest([confidence_level])(sample_data, sample_index)
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```
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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.
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The null hypothesis is that means of populations are equal. Normal distribution is assumed. Populations may have unequal variance.
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**Arguments**
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- `sample_data` — Sample data. [Integer](../../../sql-reference/data-types/int-uint.md), [Float](../../../sql-reference/data-types/float.md) or [Decimal](../../../sql-reference/data-types/decimal.md).
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- `sample_index` — Sample index. [Integer](../../../sql-reference/data-types/int-uint.md).
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**Parameters**
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- `confidence_level` — Confidence level in order to calculate confidence intervals. [Float](../../../sql-reference/data-types/float.md).
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**Returned values**
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[Tuple](../../../sql-reference/data-types/tuple.md) with two or four elements (if the optional `confidence_level` is specified)
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- calculated t-statistic. [Float64](../../../sql-reference/data-types/float.md).
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- calculated p-value. [Float64](../../../sql-reference/data-types/float.md).
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- calculated confidence-interval-low. [Float64](../../../sql-reference/data-types/float.md).
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- calculated confidence-interval-high. [Float64](../../../sql-reference/data-types/float.md).
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**Example**
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Input table:
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``` text
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┌─sample_data─┬─sample_index─┐
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│ 20.3 │ 0 │
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│ 22.1 │ 0 │
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│ 21.9 │ 0 │
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│ 18.9 │ 1 │
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│ 20.3 │ 1 │
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│ 19 │ 1 │
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└─────────────┴──────────────┘
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```
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Query:
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``` sql
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SELECT welchTTest(sample_data, sample_index) FROM welch_ttest;
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```
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Result:
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``` text
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┌─welchTTest(sample_data, sample_index)─────┐
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│ (2.7988719532211235,0.051807360348581945) │
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└───────────────────────────────────────────┘
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```
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**See Also**
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- [Welch's t-test](https://en.wikipedia.org/wiki/Welch%27s_t-test)
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- [studentTTest function](studentttest.md#studentttest)
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