Welch's t-Test Task

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A Welch's t-Test Task is a statistical hypothesis testing task used to describe an Welch's t-test.

Null hypothesis: "the difference of the means is equal to zero" ⇒ [math]\displaystyle{ H_0:\; \mu_{nonathlete} - \mu_{athlete} = 0 }[/math]
Alternative hypothesis: "the difference of the means is not equal to zero" ⇒ [math]\displaystyle{ H_1:\; \mu_{nonathlete} - \mu_{athlete} \neq 0 }[/math]


References

2017a

  • (Wikipedia, 2017) ⇒ http://en.wikipedia.org/wiki/Welch's_t-test
    • In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means. Welch's t-test is an adaptation of Student's t-test,[1] that is, it has been derived with the help of Student's t-test and is more reliable when the two samples have unequal variances and unequal sample sizes.[2] These tests are often referred to as "unpaired" or "independent samples" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. Given that Welch's t-test has been less popular than Student's t-test and may be less familiar to readers, a more informative name is "Welch's unequal variances t-test" or "unequal variances t-test" for brevity.

2017

2014


  1. Welch, B. L. (1947). "The generalization of "Student's" problem when several different population variances are involved". Biometrika 34 (1–2): 28–35. doi:10.1093/biomet/34.1-2.28. MR19277. 
  2. Ruxton, G. D. (2006). "The unequal variance t-test is an underused alternative to Student's t-test and the Mann–Whitney U test". Behavioral Ecology 17: 688–690. doi:10.1093/beheco/ark016.