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Testing the differences between two color measurement probability distributions using Hotelling's T2 test and the permutation test
Color Research and Application ( IF 1.4 ) Pub Date : 2020-01-13 , DOI: 10.1002/col.22468
Brian M. Gamm 1 , Patrick Gerard 2
Affiliation  

It is common practice in statistics to test the equality of two population means using, for example, the Student's t test, in the univariate case, or the Hotelling's T2 Test in the multivariate case. However, tests on the equality of population means are not well developed for testing the difference between two populations of color measurements. Methods for analyzing populations of spectral reflectance and L*a*b* measurements have been described for applications such as analyzing inter‐instrument agreement and repeatability. Methods have also been proposed for the analysis of color differences, but there are little written about techniques for testing whether two samples have the same probability distribution. This article focuses on testing the difference between color measurement probability distributions based on color difference. In addition, a metric is proposed called the threshold for color difference discrimination (TCDD, in units of ΔE), the color difference at which two populations can be considered to have different population distributions. A lower TCDD means smaller color differences between two samples can be resolved. Two parametric tests based on Hotelling's T2 test and a nonparametric permutation test were used to determine the TCDD for populations of color measurements with different variances and sample sizes. The TCDD was found to be smaller by tests using the Hotelling's T2 statistic, compared with a permutation test performed directly on color difference. It was also found, as expected, that larger sample sizes led to smaller TCDDs, as did smaller population variances.

中文翻译:

使用Hotelling的T2检验和置换检验检验两个颜色测量概率分布之间的差异

统计上的惯例是使用单变量情况下的Student t检验或Hotelling T 2检验两个总体均值的均等性 在多变量情况下进行测试。但是,关于总体均值均等性的测试尚未很好地开发来测试两个色彩测量总体之间的差异。已经描述了用于分析光谱反射率和L * a * b *测量值的方法,用于分析仪器间的一致性和可重复性。还提出了用于分析色差的方法,但是关于测试两个样本是否具有相同概率分布的技术的文献很少。本文着重测试基于色差的颜色测量概率分布之间的差异。此外,还提出了一种度量标准,称为色差判别阈值(TCDD,以ΔE为单位),可以认为两个种群具有不同种群分布的色差。较低的TCDD意味着可以解决两个样本之间较小的色差。基于Hotelling的两个参数测试 T 2检验和非参数置换检验用于确定具有不同方差和样本大小的颜色测量总体的TCDD。与直接对色差进行的置换检验相比,使用Hotelling的T 2统计量进行的检验发现TCDD较小。正如预期的那样,还发现,较大的样本量导致较小的TCDD,较小的总体差异也导致较小的TCDD。
更新日期:2020-01-13
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