Instant Notes: Analytical Chemistry

Chloride/ppm Mean Estimated standard deviation

346 351.67 ppm 6.66 ppm

359

350

Using equation (6), and at the 95% probability level, t=4.3 for two degrees of

freedom, and the confidence limits are:

3 determinations CL(m)= 352 ± = 352 ± 17 ppm

The wider limits given by equation (6) when the standard deviation is estimated

with only three results reflects the much greater uncertainty associated with this

value, which in turn affects the confidence in the degree of accuracy. To demon-

strate good accuracy, the confidence interval, CI, should be as small as possible

and increasing the number of replicates will clearly achieve this. However, due

to the Nterm in the denominator, to reduce the interval by, say, a factor of

two requires an increase in the number of replicates by a factor of four as shown

by Example 3. Unfortunately, the law of diminishing returns applies here, so if

the CI is to be halved again, the number of replicates must be increased from

fourto sixteen. Similarly, in Example 4, the number of replicates would have to

be increased from three to twelve to halve the CI, which would represent an

unacceptable amount of time and money for most analytical laboratories.

4.3×6.66

 3 

B2 – Assessment of accuracy and precision 33