welch_test()

Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Computes the p_value of the Welch-test function

Syntax

welch_test(mean1, variance1, count1, mean2, variance2, count2)

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
mean1	real or long	✔️	The mean (average) value of the first series.
variance1	real or long	✔️	The variance value of the first series.
count1	real or long	✔️	The count of values in the first series.
mean2	real or long	✔️	The mean (average) value of the second series.
variance2	real or long	✔️	The variance value of the second series.
count2	real or long	✔️	The count of values in the second series.

Returns

From Wikipedia:

In statistics, Welch's t-test is a two-sample location test that's used to test the hypothesis that two populations have equal means. Welch's t-test is an adaptation of Student's t-test, and is more reliable when the two samples have unequal variances and unequal sample sizes. These tests are often referred to as "unpaired" or "independent samples" t-tests. The tests are typically applied when the statistical units underlying the two samples being compared are non-overlapping. Welch's t-test is less popular than Student's t-test, and may be less familiar to readers. The test is also called "Welch's unequal variances t-test", or "unequal variances t-test".

Example

Run the query

// s1, s2 values are from https://en.wikipedia.org/wiki/Welch%27s_t-test
print
    s1 = dynamic([27.5, 21.0, 19.0, 23.6, 17.0, 17.9, 16.9, 20.1, 21.9, 22.6, 23.1, 19.6, 19.0, 21.7, 21.4]),
    s2 = dynamic([27.1, 22.0, 20.8, 23.4, 23.4, 23.5, 25.8, 22.0, 24.8, 20.2, 21.9, 22.1, 22.9, 20.5, 24.4])
| mv-expand s1 to typeof(double), s2 to typeof(double)
| summarize m1=avg(s1), v1=variance(s1), c1=count(), m2=avg(s2), v2=variance(s2), c2=count()
| extend pValue=welch_test(m1,v1,c1,m2,v2,c2)
// pValue = 0.021