Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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USING A SIMPLE LINEAR MODEL TO PROVE THAT THE CLASSICAL $t$-TEST IS THE UNIFORMLY MOST POWERFUL (UMP) TEST FOR COMPARING TWO MEANS

Authors

  • David Sotres-Ramos

Keywords:

t-test, linear model, uniformly most powerful test.

DOI:

https://doi.org/10.17654/0973563125008

Abstract

The classical t-test for comparing two means plays an important role in statistical applications and is widely presented in most introductory statistics textbooks. Despite this, a formal demonstration of its optimality in hypothesis testing is often overlooked. In this article, we show that the classical t-test is the Uniformly Most Powerful (UMP) test among all invariant tests for comparing two means at a given significance level  To achieve this, we use a simple linear model. This approach allows us to establish the theoretical foundations of the t-test’s optimality, reinforcing its validity and importance in statistical inference.

Received: April 22, 2025
Accepted: May 8, 2025

References

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Published

05-06-2025

Issue

Vol. 27 No. 1 (2025)

Section

Articles

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How to Cite

USING A SIMPLE LINEAR MODEL TO PROVE THAT THE CLASSICAL $t$-TEST IS THE UNIFORMLY MOST POWERFUL (UMP) TEST FOR COMPARING TWO MEANS. (2025). Far East Journal of Mathematical Education, 27(1), 63-69. https://doi.org/10.17654/0973563125008