Statistical comparison of the slopes of two regression lines: A tutorial

Abstract

Comparing the slopes of two regression lines is an almost daily task in analytical laboratories. The usual procedure is based on a Student's t-test although literature differs in whether the standard errors of the slopes or the standard errors of the regressions should be employed to get a pooled standard error. In this work fundamental concepts on the use of the Student's test were reviewed and Monte Carlo simulations were done to ascertain whether relevant differences arise when the two options are considered. It was concluded that for small sample sets (as it is usual in analytical laboratories) the Student's t-test based on the standard error of regression models must be used and special attention must be paid on the equality of the models variances. Finally, alternative approaches were reviewed, with emphasis on a simple one based on the analysis of the covariance (ANCOVA).

Keywords: Analysis of covariance; Calibration; Comparison of slopes; Monte Carlo; Quality control.