Reliability Analysis of Non‐Parametric Statistical Tests for the Evaluation of Linear Drift in Experimental Data

Abstract

Abstract: During usual data gathering, the statistical analysis efficiency strongly depends on the noise level superimposed on the signal. It has been found that some well known statistical tests, commonly utilised in data acquisition in order to detect the presence of drift, can fail under some conditions. Thus, a statistical procedure for the predictive reliability estimation of the utilised statistical method could be useful in the design of experimental analysis. This paper reports the results of a simulation study carried out to evaluate the performance in drift detection of non‐parametric tests such as the Wald‐Wolfowitz run test, in comparison with the Mann‐Whitney, reverse arrangement test. In order to detect the sensitivity of the tests to evaluate a monotonous drift, a simulation program was developed. In the program a Gaussian raw data sequence with a linear pattern of variable slope and with variable variance was simulated and given as the input to the tests. The capability to detect the presence of drift as a function of angular coefficient and variance of the noise superimposed on the signal was verified. The obtained data were synthesised in graphs so that the experimentalist could determine preliminarily the effectiveness of each of the considered statistical methods in terms of percentage of success in detecting the presence of drift phenomena as a function of drift relevance and the noise amplitude. Finally, the graphs permitted the elucidation of the causes of contradictory failing results observed in long term experimental analysis.