Mathematics > Statistics Theory
[Submitted on 29 Oct 2022 (v1), last revised 8 Nov 2022 (this version, v2)]
Title:Te Test: A New Non-asymptotic T-test for Behrens-Fisher Problems
View PDFAbstract:The Behrens-Fisher Problem is a classical statistical problem. It is to test the equality of the means of two normal populations using two independent samples, when the equality of the population variances is unknown. Linnik (1968) has shown that this problem has no exact fixed-level tests based on the complete sufficient statistics. However, exact conventional solutions based on other statistics and approximate solutions based the complete sufficient statistics do exist.
Existing methods are mainly asymptotic tests, and usually don't perform well when the variances or sample sizes differ a lot. In this paper, we propose a new method to find an exact t-test (Te) to solve this classical Behrens-Fisher Problem. Confidence intervals for the difference between two means are provided. We also use detailed analysis to show that Te test reaches the maximum of degree of freedom and to give a weak version of proof that Te test has the shortest confidence interval length expectation. Some simulations are performed to show the advantages of our new proposed method compared to available conventional methods like Welch's test, paired t-test and so on. We will also compare it to unconventional method, like two-stage test.
Submission history
From: Chang Wang [view email][v1] Sat, 29 Oct 2022 02:56:22 UTC (883 KB)
[v2] Tue, 8 Nov 2022 03:16:32 UTC (883 KB)
Current browse context:
math.ST
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.