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Statistical hypothesis testing using deep learning: Focusing on two sample t-test
Journal of the Korean Data & Information Science Society 2021;32:25-35
Published online January 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.1.25
© 2021 Korean Data and Information Science Society.

Sangwoong Kim1 · Junmo Song2

12Department of Statistics, Kyungpook National University
Correspondence to: 1Graduate student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea.
2Corresponding author: Associate professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: jsong@knu.ac.kr

This research was supported by the Research Grants of Korea Forest Service (Korea Forestry Promotion Institute) project (No.2019149B10-2023-0301) and the National Research Foundation of Korea (NRF-2019R1I1A3A01056924).
Received December 28, 2020; Revised January 15, 2021; Accepted January 21, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Hypothesis testing is a process of deciding whether to reject the null hypothesis. When the null hypothesis is rejected, the alternative hypothesis is accepted. Since hypothesis testing chooses one between the null and alternative hypotheses, it can be viewed as a classification problem in machine learning. In this study, we investigate deep neural network as a classifier for classifying the null and alternative hypotheses. Particularly, focusing on testing for equality of two population means, we train deep neural network and then evaluate its performance compared to two sample t-test. Through simulations, we demonstrate that our DNN trained in this study shows similar performance to level 5% two sample t-test. Additionally, we discuss some of the issues that arise when using DNN in hypothesis testing.
Keywords : Classification, deep learning, deep neural network, statistical hypothesis testing, testing for equality in two means, two sample t-test.