keeping the others nominally constant is neither efficient nor necessarily successful. This point is well
illustrated in Chapter 4 where the optimization of chromatographic separations is discussed (p. 140).
A sample may be characterized by the determination of a number of different analytes. For example, a
hydrocarbon mixture can be analysed by use of a series of UV absorption peaks. Alternatively, in a
sediment sample a range of trace metals may be determined. Collectively, these data represent patterns
characteristic of the samples, and similar samples will have similar patterns. Results may be compared
by vectorial presentation of the variables, when the variables for similar samples will form clusters.
Hence the term cluster analysis. Where only two variables are studied, clusters are readily recognized in
a two-dimensional graphical presentation. For more complex systems with more variables, i.e. n, the
clusters will be in n-dimensional space. Principal component analysis (PCA) explores the
interdependence of pairs of variables in order to reduce the number to certain principal components. A
practical example could be drawn from the sediment analysis mentioned above. Trace metals are often
attached to sediment particles by sorption on to the hydrous oxides of Al, Fe and Mn that are present.
The Al content could be a principal component to which the other metal contents are related. Factor
analysis is a more sophisticated form of principal component analysis.
Problems
(1) Define the terms precision and accuracy as they are used in analytical chemistry. Indicate how they
may be estimated quantitatively. To what extent is the estimate of accuracy dependent upon precision?
(2) In an experiment the following replicate set of volume measurements (cm^3 ) was recorded:
(a) Calculate the mean of the raw data.(b) Using the rejection quotient (Q-test) reject any questionable results.(c) Recalculate the mean and compare it with the value obtained in 2(a).(3) Calculate the absolute standard deviation and the relative standard deviation (%) of the following
replicate set of data. Comment upon the precision of the measurement.
Weight of component/g:
(4) The three sets of replicate results below were accumulated for the analysis of the same sample. Pool
these data to obtain the most efficient estimate of the mean analyte content and the standard deviation.
Lead content/ppm:
Set 1 Set 2 Set 3
9.76 9.87 9.85
9.42 9.64 9.91
9.53 9.71 9.42
9.81 9.49