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71 lines
2.8 KiB
Markdown
71 lines
2.8 KiB
Markdown
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---
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toc_priority: 303
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toc_title: meanZTest
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---
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# meanZTest {#meanztest}
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Applies mean z-test to samples from two populations.
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**Syntax**
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``` sql
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meanZTest(population_variance_x, population_variance_y, 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 and the variances are known.
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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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- `population_variance_x` — Variance for population x. [Float](../../../sql-reference/data-types/float.md).
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- `population_variance_y` — Variance for population y. [Float](../../../sql-reference/data-types/float.md).
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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 four elements:
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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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│ 21.9 │ 0 │
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│ 22.1 │ 0 │
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│ 18.9 │ 1 │
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│ 19 │ 1 │
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│ 20.3 │ 1 │
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└─────────────┴──────────────┘
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```
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Query:
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``` sql
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SELECT meanZTest(0.7, 0.45, 0.95)(sample_data, sample_index) FROM mean_ztest
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```
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Result:
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``` text
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┌─meanZTest(0.7, 0.45, 0.95)(sample_data, sample_index)────────────────────────────┐
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│ (3.2841296025548123,0.0010229786769086013,0.8198428246768334,3.2468238419898365) │
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└──────────────────────────────────────────────────────────────────────────────────┘
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```
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[Original article](https://clickhouse.com/docs/en/sql-reference/aggregate-functions/reference/meanZTest/) <!--hide-->
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