Abstract

This paper describes a fundamental procedure for deriving “within” and “between” variances and co-variances in the spectral tristimulus values. The within variances are based on the replications of color-mixture data by an observer. The between variances are based on differences among the color-mixture data of individual observers. A statistical model for the system in which the experimental data are obtained is given, expected values (means), variances, and co-variances are developed, and the method by which these variances and co-variances may be distributed among the sources of uncertainties in the experimental data is presented. There is developed a procedure for determining the uncertainties in the constants of a linear transformation to a system analogous to the present CIE system. The formulas for variances and co-variances after linear transformation are given for an arbitrary choice of transformation constants. The complete set of variances and co-variances derived from an arbitrary transformation is listed for 20 mµ intervals. This set, together with the mean spectral tristimulus values, forms a complete standard observer system. The between-observer variabilities are found to be about 10% of the averages of the color-mixture data and the average ratio of the between-observer variabilities to the within-observer variabilities is found to be about 5.7.

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