Page 198 - Modern Analytical Chemistry

1400-CH07 9/8/99 4:03 PM Page 181

Chapter 7 Obtaining and Preparing Samples for Analysis 181

7
EXAMPLE .1
A quantitative analysis for an analyte gives a mean concentration of 12.6 ppm.
The standard deviation for the method is found to be 1.1 ppm, and that due to
sampling is 2.1 ppm. (a) What is the overall variance for the analysis? (b) By
how much does the overall variance change if s m is improved by 10% to 0.99
ppm? (c) By how much does the overall variance change if s s is improved by
10% to 1.9 ppm?
SOLUTION
(a) The overall variance is

2
2
2
2
2
s o = s m + s s = (1.1) + (2.1) = 1.21 + 4.41 = 5.62 » 5.6
(b) Improving the method’s standard deviation changes the overall variance to
2
2
2
s o = (0.99) + (2.1) = 0.98 + 4.41 = 5.39 » 5.4
Thus, a 10% improvement in the method’s standard deviation changes the
overall variance by approximately 4%.
(c) Changing the standard deviation for sampling
2
2
2
s o = (1.1) + (1.9) = 1.21 + 3.61 = 4.82 » 4.8
improves the overall variance by almost 15%. As expected, since s s is larger
than s m , a more significant improvement in the overall variance is realized
when we focus our attention on sampling problems.
2
To determine which step has the greatest effect on the overall variance, both s m
2
and s s must be known. The analysis of replicate samples can be used to estimate the
overall variance. The variance due to the method is determined by analyzing a stan-
dard sample, for which we may assume a negligible sampling variance. The variance
due to sampling is then determined by difference.

7
EXAMPLE .2
The following data were collected as part of a study to determine the effect of
sampling variance on the analysis of drug animal-feed formulations. 2
% Drug (w/w) % Drug (w/w)

0.0114 0.0099 0.0105 0.0105 0.0109 0.0107
0.0102 0.0106 0.0087 0.0103 0.0103 0.0104
0.0100 0.0095 0.0098 0.0101 0.0101 0.0103
0.0105 0.0095 0.0097

The data on the left were obtained under conditions in which random errors in
sampling and the analytical method contribute to the overall variance. The data
on the right were obtained in circumstances in which the sampling variance is
known to be insignificant. Determine the overall variance and the
contributions from sampling and the analytical method.