Analytical Chemistry

Table 2.5 Some practical problems with relevant statistical tests

Practical problems Relevant tests

One result in a replicate set differs rather widely from the rest. Is it a

significant result?

Examine for gross error. Apply Q-test

(equation (2.6))

Two operators analysing the same sample by the same method obtain results

with different spreads. Is there a significant difference in precision between

the results?

Examine data for unreliable results. Apply

F-test (equation (2.8))

A new method of analysis is being tested by the analysis of a standard sample

with an accurately known composition. Is the difference between the

experimental value and the accepted value significant?

Examine data for unreliable results. Apply

t-test (equation (2.9))

Two independent methods of analysis have been used to analyse a sample of

unknown composition. Is the difference between the two results significant

and thus indicative of an error in one method?

Examine data for unreliable results.

Establish that both sets have similar

precisions by F-test. Apply T-test (equation

(2.10))

With what confidence can the mean of a set of experimental results be quoted

as a measure of the true mean?

Calculate the confidence interval (equation

(2.7))

If the standard deviation for a method is known, how many results must be

obtained to provide a reasonable estimate of the true mean?

Use the confidence interval method

(equation (2.7))

Is a determinate error fixed or proportional? Graphical plot of results against sample

weight (Figure 2.1)

Comparison with critical values in Table 2.2 shows Qcrit for 6 results to be 0.56. Thus Qexp < Qcrit and 7.01

is retained.

Example 2.3

The accepted value for the chloride content of a standard sample obtained from extensive previous
analysis is 54.20%. Five analyses of the same sample are carried out by a new instrumental procedure,
54.01, 54.24, 54.05, 54.27, 54.11% being the results obtained. Is the new method giving results
consistent with the accepted value?

(a) A preliminary examination shows no unreliable results.

(b) The mean and the standard deviations are then calculated (equation (2.2)).

x

54.01 –0.13 0.0169 s = (0.0528/4)1/2 = 0.115

54.24 +0.10 0.0100^

54.05 –0.09 0.0089^

54.27 +0.13 0.0169^

54.11 –0.03 0.0009^

Σx = 270.68^

= 0.0528^