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Example 5ASSESSMENT OF THE ACCURACY OF AN ANALYTICAL DATA SET

Question Calculate the confidence intervals at the 50%, 95% and 99% confidence levels of the

fasting serum glucose concentrations given in the previous worked example.

Answer Accuracy in this type of situation is expressed in terms of confidence intervals

that express a range of values over which there is a given probability that the ‘true’

value lies.

As previously calculated, x¼2.42 mM ands¼0.16 mM. Inspection of Table 1.8

reveals that for four degrees of freedom (the number of experimental values minus

one) and a confidence level of 50%,t¼0.741 so that the confidence interval for the

population mean is given by:

confidence interval¼ 2 : 42 

ð 0 : (^741) pÞð 0 : 16 Þ
5
¼ 2 : 42  0 : 05 mM
For the 95% confidence level and the same number of degrees of freedom,t¼2.776,
hence the confidence interval for the population mean is given by:
confidence interval¼ 2 : 42 
ð 2 : 776 Þð 0 : 16 Þ
p
5
¼ 2 : 42  0 : 20 mM
For the 99% confidence level and the same number of degrees of freedom,t¼4.604,
hence the confidence interval for the population mean is given by:
confidence interval¼ 2 : 42 
ð 4 : 604 Þð 0 : 16 Þ
p 5
¼ 2 : 42  0 : 33 mM
DiscussionThese calculations show that there is a 50% chance that the population mean lies in
the range 2.37 to 2.47 mM, a 95% chance that the population mean lies within the
range 2.22 to 2.62 mM and a 99% chance that it lies in the range 2.09 to 2.75 mM.
Note that as the confidence level increases the range of potential values for the
population mean also increases. You can calculate for yourself that if the mean and
standard deviation had been based on 20 measurements (i.e. a four-fold increase in
the number of measurements) then the 50% and 95% confidence intervals would
have been reduced to 2.420.02 mM and 2.420.07 mM respectively. This
re-emphasises the beneficial impact of multiple experimental determinations but at
the same time highlights the need to balance the value of multiple determinations
against the accuracy with which the experimental mean is required within the
objectives of the individual study.
26 Basic principles