Question 14.11: What is the estimated relative standard deviation for the re...
What is the estimated relative standard deviation for the results of a collaborative study in which the sample is pure analyte (100 \% \mathrm{w} / \mathrm{w} analyte)? Repeat for the case in which the analyte’s concentration is 0.1 \% \mathrm{w} / \mathrm{w}.
When the sample is 100 \% \mathrm{w} / \mathrm{w} analyte (C=1), the estimated percent relative standard deviation is
R=2^{[1-0.5 \log (1)]}=2 \%
Thus, we expect that approximately 67 \% of the participants in the collaborative study ( \pm 1 \sigma) will report the analyte’s concentration within the range of 98 \% \mathrm{w} / \mathrm{w} to 102 \% \mathrm{w} / \mathrm{w}. When the analyte’s concentration is 0.1 \% \mathrm{w} / \mathrm{w}(C=0.001), the estimated percent relative standard deviation is
\mathrm{R}=2^{[1-0.5 \log (0.001)]}=5.7 \%
and we expect that 67 \% of the analysts will report the analyte’s concentration within the range of 0.094 \% \mathrm{w} / \mathrm{w} to 0.106 \% \mathrm{w} / \mathrm{w}.