Sample size calculation for method validation using linear regression

Abstract

In this article, we present a method for sample size calculation for studies involving both the intercept and slope parameters of a simple linear regression model. Some methods have been proposed in the literature to determine the adequate sample size. However, they are usually based on the line slope only. We propose a method based on the F statistic that involves both the intercept and the slope parameters of the model. The validation process is conducted by fitting a simple linear regression model and by testing a zero intercept and unity slope hypothesis. Compared to a traditional method and using Monte Carlo simulations, encouraging results attest for the clear superiority of the proposed method. The article ends with a real-life example showing the value of the new method in practice.

Keywords:

• ℱ distribution
• Measurement method
• Non-central parameter
• Type II error

Acknowledgements

The research of Prof. Enrico Colosimo has been partially funded by the CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) of the Ministry for Science and Technology of Brazil, grant 300582/2003-0. The research of prof. Frederico Cruz has been partially funded by the CNPq, grants 201046/1994-6, 301809/1996-8, 307702/2004-9, 472066/2004-8, and 472877/2006-2, the FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais), grants CEX-289/98 and CEX-855/98, and PRPq-UFMG, grant 4081-UFMG/RTR/FUNDO/PRPq/99.