Page 177 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

THE VALUE OF STATlSTlCS 4.19

freedom as that for the Residual term, i.e. the 'within-titration' value. In
this example the number of degrees of freedom is 9, so the least significant
difference is given by
Jm J2/4 x 2.26 = 0.06 mL
x
If the titration means are arranged in increasing order, then X(B)<
X (A) < X (C), and X (C) - X (B) and X (A) - X (B) are both greater than 0.06,
whereas X (C) - X (A) is less than 0.06. Hence there is no significant difference
between analysts A and C, but the results of analyst B are significantly different
from those of both A and C.
It should be noted that in this example the performance of only one variable,
the three analysts, is investigated and thus this technique is called a one-way
ANOVA. If two variables, e.g. the three analysts with four diferent titration
methods, were to be studied, this would require the use of a two-way ANOVA.
Details of suitable texts that provide a solution for this type of problem
and methods for multivariate analysis are to be found in the Bibliography,
page 156.

4.19 THE VALUE OF STATlSTlCS
Correctly used, statistics is an essential tool for the analyst. The use of statistical
methods can prevent hasty judgements being made on the basis of limited
information. It has only been possible in this chapter to give a brief resumé of
some statistical techniques that may be applied to analytical problems. The
approach, therefore, has been to use specific examples which illustrate the scope
of the subject as applied to the treatment of analytical data. There is a danger
that this approach may overlook some basic concepts of the subject and the
reader is strongly advised to become more fully conversant with these statistical
methods by obtaining a selection of the excellent texts now available.
In addition there is the rapidly developing subject of Chemometrics, which
may be broadly defined as the application of mathematical and statistical
methods to design and/or to optimise measurement procedures, and to provide
chemical information by analysing relevant data. Space does not permit an
inclusion in this book of such topics as experimental design and instrumental
optimisation techniques or more sophisticated subjects as pattern recognition.
There is no doubt however, that a knowledge of the scope of Chemometrics
will be increasingly important for any competent analytical chemist. Details of
some useful texts, both introductory and more advanced, are given in the
Bibliography (Section 5.8). The reader should be aware, however, that some
signal-processing techniques are included in this book, e.g. information will be
found on derivative spectroscopy (Section 17.12) and Fourier transform
methods (Section 19.2).

For References and Bibliography see Sections 5.7 and 5.8.

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