Misapplication of the parametric statistics to calculate the uncertainties when calibrating commercial spectrocolorimeters

Abstract

Nowadays, when calibrating spectrocolorimeters, the uncertainties are calculated based on the premise that the obtained measurements have a Gaussian distribution, but there is no certainty that the latter is completely true. The aim of this work is to show that, when measuring reference materials with different spectrocolorimeters, most of the results do not have, for all the points in the visible spectrum of the spectral curve, a Gaussian distribution. Also, this distribution is not present in measurements of the chromatic coordinates of these materials. These measurements were performed with two integrating sphere spectrocolorimeters; a Minolta 2600d r (portable) and a Gretag Macbeth 7000 r (bench) equipment, under the same measurement parameters and conditions of repeatability, as well as controlled environmental conditions, i.e., 20 ± 1 ◦C. Since a Gaussian distribution is needed to use parametric statistics to calculate the combined uncertainties and consequently, the expanded ones, the statistical method currently used is erroneous. Thus, parametric statistics should not be used to calculate the spectrocolorimeters’ uncertainties.