Nimeroff Isadore, Rosenblatt Joan R, Dannemiller Mary C
J Res Natl Bur Stand A Phys Chem. 1961 Nov-Dec;65A(6):475-483. doi: 10.6028/jres.065A.050. Epub 1961 Dec 1.
As the spectral tristimulus values of the CIE Standard Observer System for Colorimetry are measurable quantities, their variabilities should be known. This paper describes a procedure for deriving "within" and "between" variances and covariances in the spectral tristimulus values, based on color-matching data for individual observers. 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 is given for the system in which the experimental data are obtained. Formulas for expected values (means), variances, and covariances are developed. Variances and covariances belonging to different sources of uncertainties in the experimental data are considered. A procedure is developed 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 a rigorous empirically-based choice, and also for an arbitrary choice of transformation constants. The complete standard observer system for every 10 m consisting of means, variances, and covariances derived from an arbitrary transformation, is listed. The between-observer variabilities are found to be about 10 percent 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.
由于用于比色法的CIE标准观察者系统的光谱三刺激值是可测量的量，所以应该了解它们的变异性。本文描述了一种基于个体观察者的颜色匹配数据来推导光谱三刺激值中“内部”和“之间”的方差及协方差的程序。“内部”方差基于观察者对颜色混合数据的重复测量。“之间”方差基于个体观察者颜色混合数据之间的差异。给出了获取实验数据的系统的统计模型。推导了期望值（均值）、方差和协方差的公式。考虑了实验数据中属于不同不确定性来源的方差和协方差。开发了一种程序来确定到类似于当前CIE系统的系统的线性变换常数中的不确定性。给出了线性变换后方差和协方差的公式，包括基于严格经验的选择以及变换常数的任意选择。列出了由任意变换得出的均值、方差和协方差组成的每10米完整标准观察者系统。发现观察者之间的变异性约为颜色混合数据平均值的10%，并且观察者之间变异性与观察者内部变异性的平均比率约为5.7。
