Signal content index (SCI): a measure of the effectiveness of measurements and an alternative to p -value for comparing two means

Abstract

The purpose of a measurement is essentially to extract a signal from a mixture of signal and noise involved in the measurement process. We refer to signal as the true value (an unknown constant) of a quantity of interest and to noise as the unexplained variation that is found within a measurement and/or between measurements. A measurement result is an estimate of the true value, which contains both signal and noise. It is intuitive that the greater the amount of signal contained in a measurement result, the more effective the measurement. This paper presents a measure of the effectiveness of measurements: the signal content index (SCI). SCI is defined as the ratio between the signal energy and the total energy of signal and noise, based on the law of conservation of energy. In principle, SCI ranges between 0 and 1, which makes its interpretation intuitive, simple, and meaningful. A high SCI value (e.g. close to 1) indicates that the estimate is mostly attributable to signal, and therefore, the measurement is highly effective. A low SCI value (e.g. close to 0) indicates that the estimate is mostly attributable to noise, and therefore, the measurement is highly ineffective. The notion of SCI is universal and can be applicable to all measurements. In particular, SCI can be used for comparing the mean of a sample against a known mean or comparing the means from two independent samples. The SCI analysis provides an alternative method to the long-existing controversial t-tests and overcomes the shortcomings of the traditionally used p -values. Moreover, the SCI analysis unifies the comparison of two means (which deals with one or two samples) and the assessment of heterogeneity in interlaboratory studies or meta-analyses (which deals with multiple samples).