This paper describes a fundamental procedure for deriving “within” and “between” variances and covariances 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 covariances are developed, and the method by which these variances and covariances 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 covariances after linear transformation are given for an arbitrary choice of transformation constants. The complete set of variances and covariances 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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