By C. A. Rogers, J. E. Jayne et. al. (editors)
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Additional resources for Analytic Sets (London school 1978)
There are two coefficients in this equation, but five experiments have been performed. ’ This could be important to the experimenter. For example, there may be unknown interferents, or the instrument might be very irreproducible, or there may be nonlinearities at high concentrations. Hence not only must the experiments be used to determine the equation relating peak height to concentration but also to answer whether the relationship is truly linear and reproducible. The ability to determine how well the data fit a linear model depends on the number of degrees of freedom which is given, in this case, by D =N −P where N is the number of experiments and P the number of coefficients in the model.
Often 10 or more possible factors can be identified. Which are significant and should be studied or optimised further? • In linear calibration, is the baseline important? Are there curved terms; is the concentration too high so that the Beer–Lambert law is no longer obeyed? 24 CHEMOMETRICS • In the study of a simple reaction dependent on temperature, pH, reaction time and catalyst concentration, are the interactions between these factors important? In particular, are higher order interactions (between more than two factors) significant?
A lack-of-fit that is much less than the replicate error is not significant, within the constraints of the experiment. Most statistical packages produce ANOVA tables if required, and it is not always necessary to determine these errors manually, although it is important to appreciate the principles behind such calculations. However, for simple examples a manual calculation is often quite and a good alternative to the interpretation of the output of complex statistical packages. The use of ANOVA is widespread and is based on these simple ideas.
Analytic Sets (London school 1978) by C. A. Rogers, J. E. Jayne et. al. (editors)