Chemometrics

1
Chemometrics

• "Chemometrics has been defined as the application
  of mathematical and statistical methods to
  chemical measurements.
• " B. Kowalski, Anal. Chem. 1980, 52, 112R-122R.
• "Chemometrics is the chemical discipline that
  uses mathematical and statistical methods for the
  obtention in the optimal way of relevant
  information on material systems." I. Frank and B.
  Kowalski, Anal. Chem.,1982, 54, 232R-243R.

2
Chemometrics

• "Chemometrics developments and the accompanying
  realization of these developments as computer
  software provide the means to convert raw data
  into information, information into knowledge and
  finally knowledge into intelligence." M. Delaney,
  Anal. Chem. 1984, 261R-277R.
• ...research in chemometrics will contribute to
  the design of new types of instruments, generate
  optimal experiments that yield maximum
  information, and catalog and solve calibration
  and signal resolution problems. All this while
  quantitatively specifying the limitations of each
  instrument as well as the quality of the data it
  generates." L. S. Ramos et al., Anal. Chem. 1986,
  58, 294R-315R.

3
Chemometrics

• "Chemometrics, the application of statistical and
  mathematical methods to chemistry..." S. Brown,
  Anal. Chem., 1986, 60, 252R-273R.
• "Chemometrics is the discipline concerned with
  the application of statistics and mathematical
  methods, as well as those methods based on
  mathematical logic, to chemistry." S. Brown,
  Anal. Chem. 1990, 62, 84R-101R.

4
Chemometrics

• "Chemometrics is the use of mathematical and
  statistical methods for handling, interpreting,
  and predicting chemical data."
• Malinowski, E.R..  (1991)  Factor Analysis in
  Chemistry, Second Edition,   page 1.
• "Chemometrics is the discipline concerned with
  the application of statistical and mathematical
  methods, as well as those methods based on
  mathematical logic, to chemistry." S. Brown et
  al., Anal. Chem. 1992, 64,22R-49R.
•  

5
Chemometrics

• "Chemometrics can generally be described as the
  application of mathematical and statistical
  methods to 1) improve chemical measurement
  processes, and 2) extract more useful information
  from chemical and physical measurement data." J.
  Workman, P. Mobley, B. Kowalski, R. Bro, Appl.
  Spectrosc. Revs. 1996, 31, 73-124.
• "Chemometrics is an approach to analytical and
  measurement science based on the idea of indirect
  observation. Measurements related to the chemical
  composition of a substance are taken, and the
  value of a property of interest is inferred from
  them through some mathematical relation."
  B.Lavine, Anal. Chem. 1998, 70, 209R-228R.

6
Chemometrics

• "Chemometrics is a chemical discipline that uses
  mathematics, statistics and formal logic
• (a) to design or select optimal experimental
  procedures
• (b) to provide maximum relevant chemical
  information by analyzing chemical data and
• (c) to obtain knowledge about chemical
  systems."
• Massart, D.L., et al..  (1997)  Data Handling
  in Science and Technology 20A Handbook of
  Chemometrics and Qualimetrics Part A,   page 1.
• "The entire process whereby data (e.g., numbers
  in a table) are transformed into information used
  for decision making." Beebe, K. R., Pell, R. J.,
  and M. B. Seasholtz.  (1998) Chemometrics A
  Practical Guide,   page 1.

7
Chemometrics

• Chemometrics (this is an international
  definition) is the chemical discipline that uses
  mathematical and statistical methods,
• (a) to design or select optimal measurement
  procedures and experiments and
• (b) to provide maximum chemical information by
  analyzing chemical data.
• Bruce Kowalski, in a formal CPAC
  presentation, December 1997

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CHEMOMETRICS IS NOT A UNITARY SUBJECT LIKE
ORGANIC CHEMISTRY ORGANIC CHEMISTRY IS BASICALLY
A KNOWLEDGE BASED SUBJECT certain basic skills
and then increase the knowledge. CHEMOMETRICS IS
MORE A SKILLED BASED SUBJECT not necessary to
have a huge knowledge of named methods, a very
few basic principles but one must have hands-on
experience to expand ones problem solving
ability.
9
DIFFERENT GROUPS HAVE DIFFERENT BACKGROUNDS AND
EXPECTATIONS AS TO HOW CHEMOMETRICS SHOULD BE
INTRODUCED Statisticians want to start with
distributions, hypothesis tests etc. and build up
from there. They are dissatisfied if the maths is
not explained. Chemical engineers like to start
with linear algebra such as matrices, and expect
a mathematical approach but are not always so
interested in distributions etc.
10
Computer scientists are often most interested in
algorithms. Analytical chemists often know a
little statistics but are not necessarily very
confident in maths and algorithms so like to
approach this via statistical analytical
chemistry. Difficult group because the ability to
run instruments is not necessarily an ability in
maths and computing. Organic chemists do not
like maths and want automated packages they can
use. They often require elaborate courses that
avoid matrices. The course an organic chemist
would regard is good is one a statistician would
regard as bad.
11
Errors in quantitative analysis

• No quantitative results are of any value unless
  they are accompanied by some estimate of the
  errors inherent in them
• 24.69
• 24.73
• 24.77
• 25.39 (outlier)

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Types of errors

• Based on laboratory measurements
• Instrumental
• Methodology
• Theoretical
• Data treatment
• Based on their effect on the evaluation of the
  result
• Systematic-mostly instrumental
• Random
• Personal
• Gross

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• Random errors cause replicate results to differ
  from one another so that the individual results
  fall on both sides of the average values even
  when all other errors are allowed for.
• The deviation would be slight otherwise it could
  have been investigated
• The total effects of the causes would yield a
  significant deviation
• Systematic errors cause all the results to be in
  error in the same sense
• Instrumental errors are the most important
• Insufficient chemical purity
• Imperfect standard calibration and
  standardization
• Bias of the measurement is the total systematic
  error (some sources cause ve and others cause
  ve results)

14

• Personal errors
• The results depend to some extent on the
  physical peculiarities of the observer (under
  otherwise equal conditions). These can be both
  systematic and random.
• Gross errors
• Errors that are so serious that there is no
  real alternative t abandoning the experiment and
  making a completely fresh start (external
  influences that cause completely inaccurate
  results such as reading 20.0 and writing 30.0.

15
Absolute and relative errors

• Absolute error
• Relative error
• Reduced relative error

16

• Accuracy (according to ISO International
  Standards Organization) the closeness of
  agreement between a test result and the accepted
  reference value of the analyte
• Precision reproducibility and repeatability
• Precision describes random error, bias describe
  systematic error and the accuracy incorporates
  both types of errors.
• Repeatability
• Within-run-precision
• Reproducibility
• Between-run-precision

17
Random and systematic errors in titrimetric
analysis

• It involves about 10 separate steps
• 1. Making up a standard solution of one of the
  reactants. This involves
• (a) weighing a weighing bottle or similar
  vessel containing some solid material,
• (b) transferring the solid material to a
  standard flask and weighing the bottle again to
  obtain by subtraction the weight of solid
  transferred (weighing by difference), and
• (c) filling the flask up to the mark with
  water (assuming that an aqueous titration is to
  be used).
• 2. Transferring an aliquot of the standard
  material to a titration flask with the aid of a
  pipette. This involves
• (a) filling the pipette to the appropriate
  marls, and
• (b) draining it in a specified manner into
  the titration flask.
• 3. Titrating the liquid in the flask with a
  solution of the other reactant, added from a
  burette. This involves
• (a) filling the burette and allowing the
  liquid in it to drain until the meniscus is at a
  constant level,
• (b) adding a few drops of indicator solution
  to the titration flask,
• (c) reading the initial burette volume,
• (d) adding liquid to the titration flask
  from the burette a little at a time until the
  end-point is adjudged to have been reached, and
• (e) measuring the final level of liquid in
  the burette.

18

• In principle, we should examine each step to
  evaluate the random and systematic errors that
  might occur.
• Amongst the contributions to the errors are the
  tolerances of the weights used in the gravimetric
  steps, and of the volumetric glassware
• Standard specifications for these tolerances are
  issued by such bodies as the British Standards
  Institute (BSI) and the American Society for
  Testing and Materials (ASTM).
• Tolerance for a grade A 250-ml standard flask is
  0.12 ml grade B glassware generally has
  tolerances twice as large as grade A glassware

19
Handling systematic errors

• Much of the remainder of topics will deal with
  the evaluation of random errors, which can be
  studied by a wide range of statistical methods.
• In most cases we shall assume for convenience
  that systematic errors are absent
• Many determinations have been made of the levels
  of (for example) chromium in serum
• Different workers, all studying pooled serum
  samples from healthy subjects, have obtained
  chromium concentrations varying from lt 1 to ca.
  200 ng/ ml. In general the lower results have
  been obtained more recently, and it has gradually
  become apparent that the earlier, higher values
  were due at least in part to contamination of the
  samples by chromium from stainless-steel
  syringes, tube caps, and so on.
• Methodological systematic errors of this kind are
  extremely common - incomplete washing of a
  precipitate in gravimetric analysis, and the
  indicator error in volumetric analysis

20

• Another class of systematic error that occurs
  widely arises when false assumptions are made
  about the accuracy of an analytical instrument.
• Experienced analysts know only too well that the
  monochromators in spectrometers gradually go out
  of adjustment, so that errors of several
  nanometres in wavelength settings are not
  uncommon, yet many photometric analyses are
  undertaken without appropriate checks being made.
  
• Very simple devices such as volumetric glassware,
  stop-watches, pH-meters and thermometers can all
  show substantial systematic errors, but many
  laboratory workers regularly use these
  instruments as though they are always completely
  without bias.
• Instruments controlled by microprocessors or
  microcomputers has reduced to a minimum the
  number of operations and the level of skill
  required of their operators. Yet such instruments
  are still subject to systematic errors.
• Systematic errors arise not only from procedures
  or apparatus they can also arise from human
  bias.
• Some chemists suffer from astigmatism or
  colorblindness (the latter is more common amongst
  men than women) which might introduce errors into
  their readings of instruments and other
  observations.
• A number of authors have reported various types
  of number bias, for example a tendency to favour
  even over odd numbers, or 0 and 5 over other
  digits, in the reporting of results.

21
Approaches to avoid systematic errors

• The analyst should be vigilant concerning the
  instruments functions, calibrations, analytical
  procedures and others.
• Handling the design of the experiment at every
  stage carefully.
• weighing by difference can remove some systematic
  gravimetric errors
• If the concentration of a sample of a single
  material is to be determined by absorption
  spectrometry, two procedures are possible. In the
  first, the sample is studied in a 1-cm
  path-length spectrometer cell at a single
  wavelength, say 400 nm, and the concentration of
  the test component is determined from the A ebc
  
• Several systematic errors can arise here. The
  wavelength might be (say) 405 nm rather than 400
  nm, thus rendering the reference value of e
  inappropriate this reference value might in any
  case be wrong the absorbance scale of the
  spectrometer might exhibit a systematic error
  and the path-length of the cell might not be
  exactly 1 cm. Alternatively, the analyst might
  take a series of solutions of the test substance
  of known concentration, and measure the
  absorbance of each at 400 nm.

22
Planning and design of experiments

• Statistical tests are not used only to assess the
  results of completed experiments but also they
  may be considered crucial in the planning and
  design of experiments.
• In practice, the overall error is often dominated
  by the error in just one stage of the experiment,
  other errors having negligible effects when all
  the errors are combined correctly. Again it is
  obviously desirable to try to identify, before
  the experiment begins, where this single dominant
  error is likely to arise, and then to try to
  minimize it.
• Although random errors can never be eliminated,
  they can certainly be minimized by particular
  attention to experimental techniques improving
  the precision of a spectrometric experiment by
  using a constant temperature sample cell would be
  a simple instance of such a precaution.
• Some times many experimental parameters should be
  taken into consideration, such as sensitivity,
  selectivity, sampling rate, cost, etc.). So the
  experiment should be designed in a way to
  optimize all parameters.

23
Calculators and computers in statistical
calculations

• The rapid growth of chemometrics is due to the
  ease with which large quantities of data can be
  handed, and complex calculations done, with
  calculators and computers.
• Personal computers (PCs) are now found in all
  chemical laboratories. Most modern instruments
  are controlled by PCs, which also handle and
  report the analytical data obtained.