A bit of statistics

Despite the conflicting philosophies between statisticians and chemometricians, it is an unavoidable fact that statistics provides a strong foundation for chemometrics. One could easily argue that without classical statistics there could be no chemometrics. 

In analytical chemistry, r often represents an approximation of the noise of a particular measurement. 

Although there are many useful statistical tools, there are two that have particular relevance to chemometrics the /-test and the /-test.20,21 The f-test is used to determine whether a single value is statistically different from the rest of the values in a series. Given a series of values, and the number of values in the series, the f-value for a specific value is given by the following equation  

A good way of remembering the /-value is that it is the number of standard deviations that the single value differs from the mean value. This f-value is then compared to the critical f-value obtained from a f-table, given a desired statistical confidence (i.e. 90, 95, or 99% confidence) and the number of degrees of freedom (typically N — 1), to assess whether the value is statistically different from the other values in the series. In chemometrics, the f-test can be useful for evaluating outliers in data sets. 

The /-test is similar to the f-test, but is used to determine whether two different standard deviations are statistically different. In the context of chemometrics, the /-test is often used to compare distributions in regression model errors in order to assess whether one model is significantly different than another. The /-statistic is simply the ratio of the squares of two standard deviations obtained from two different distributions  

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The philosophy of the factorial approach is attractive, so are there related techniques which are more appropriate to the special requirements of chemistry There is a number of other methods for experimental design but one that is becoming applied in several chemical applications is known as D-optimal design . The origin of the expression D-optimal is a bit of statistical jargon based on the determinant of the variance-covariance matrix. As will be seen in the next section on compound selection, a well-chosen set of experiments (or compounds) will have a wide spread in the... 

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