Testing for signal-to-noise ratio in linear regression: a test under large or massive sample

Abstract

This paper proposes a test for the signal-to-noise ratio applicable to a range of significance tests and model diagnostics in a linear regression model. It is particularly useful when sample size is large or massive, where, as a consequence, conventional tests frequently lead to inappropriate rejection of the null hypothesis. The test is conducted in the context of the traditional F-test, with its critical values increasing with sample size. It maintains desirable size properties under a large or massive sample size, when the null hypothesis is violated by a practically negligible margin. The test is widely applicable to many empirical studies in business and management. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.