The Application of Multivariate Analysis on Proficiency Test

• Main Authors: Pei-Chein Wu, 吳佩倩
• Other Authors: Chu-fang Wu
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/35131707756782775730

碩士 === 國立東華大學 === 應用數學系 === 93 === In this paper, we apply multivariate statistical analysis to interlaboratory comparison. If paired data follows a bivariate normal distribution, we can find a best fitted ellipse for the paired data. In Youden plot, even the best fitted ellipse is found, we can not separate systematic error and random error from total error with general model. When two materials have the same level, we can get more information based on the additive model. Furthermore, in order to estimate between-laboratory variance and within-laboratory variance, we shift, rotate and normalize the confidence ellipse and obtain a new confidence circle. Thus, the x-axis represents the systematic error and the y-axis represents the random error effect. Since NATA ( national association of testing authorities, Australia ) uses Z-Score based on robust summary statistics to statistically evaluate the results of participants, we can also compare normalized Youden plot and Z-Scores. Finally, we construct two confidence regions with the concept of multivariate statistical analysis. These two regions, the rectangle formed by simultaneous T²-confidence intervals and the rectangle formed by simultaneous Bonferroni confidence intervals, have different results for analyzing data. We also modify Youden model and Z-Score with weight functions which represent the different contributions from the laboratories.