Stöckl Dietmar, Thienpont Linda M
Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium.
Clin Chem Lab Med. 2008;46(11):1648-9. doi: 10.1515/cclm.2008.309.
Total error (TE) in analytical measurement is calculated as systematic error (SE) plus z-times random error (RE). The z-multiplier is typically chosen at the 95% probability level, being 1.96 in the absence of SE is of considerable magnitude (one-sided 95% probability). Up to now, no SE/RE ratio dependent z-values have been considered. Here, we present z-values for SE/RE ratios ranging from 0 to 1.
The z-multiplier (95% probability level) was empirically obtained by modulation of the standard normal distribution with the EXCEL NORMDIST function (Microsoft EXCEL 2002). In total, five distributions representing SE/RE ratios between 0 and 1 were calculated, so that the total probability outside a TE boundary +/- 1.96 sigma was in the order of 5.013%.
For distributions with SE/RE ratios ranging from 0 to 1 that satisfy the aforementioned total probability outside a TE boundary +/- 1.96 sigma, we found that the associated z-multipliers exhibit values from 1.96 (SE/RE = 0), 1.769 (SE/RE = 0.25), 1.68 (SE/RE = 0.5), 1.651 (SE/RE = 0.75) TO 1.645 (SE/RE = 1). The respective probability values beyond +/- 1.96 sigma were 2.5%/2.5%, 1.165%/3.849%, 0.368%/4.645%, 0.081%/4.934%, and 0.013%/5% for the SE/RE ratios of 0, 0.25, 0.5, 0.75, and 1.
The results show that at SE/RE ratios > 0.75 the one-sided 95% probability level is practically reached. The results allow a refined calculation of TE at specified SE/RE ratios and a general understanding of the relevance of two- and one-sided probabilities at different SE/RE ratios.
分析测量中的总误差（TE）计算为系统误差（SE）加上z倍随机误差（RE）。z乘数通常在95%概率水平下选取，在不存在显著系统误差时为1.96（单侧95%概率）。到目前为止，尚未考虑依赖于SE/RE比率的z值。在此，我们给出SE/RE比率范围从0到1的z值。
z乘数（95%概率水平）通过使用EXCEL NORMDIST函数（Microsoft EXCEL 2002）对标准正态分布进行调制凭经验获得。总共计算了代表SE/RE比率在0到1之间的五种分布，使得在TE边界±1.96标准差之外的总概率约为5.013%。
对于SE/RE比率范围从0到1且满足上述在TE边界±1.96标准差之外总概率的分布，我们发现相关的z乘数取值为从1.96（SE/RE = 0）、1.769（SE/RE = 0.25）、1.68（SE/RE = 0.5）、1.651（SE/RE = 0.75）到1.645（SE/RE = 1）。对于SE/RE比率为0、0.25、0.5、0.75和1的情况，超出±1.96标准差的各自概率值分别为2.5%/2.5%、1.165%/3.849%、0.368%/4.645%、0.081%/4.934%以及0.013%/5%。
结果表明，当SE/RE比率>0.75时，实际上达到了单侧95%概率水平。这些结果允许在指定的SE/RE比率下对TE进行精确计算，并能全面理解不同SE/RE比率下双侧和单侧概率的相关性。
