Other Statistical Techniques

There are many other statistical techniques in addition to those presented in the preceding sections of this paper which can be used to advantage by the food research worker. Many of these are concerned with enumeration data (i.e., data which arise by counting), and others are recently developed methods for dealing with measurement data. Examples of the latter are control chart techniques, sequential analysis, procedures involving the sample range in place of the sample standard deviation, and nonparametric and distribution-free techniques. Since these methods have as yet received little attention by food research workers, published examples are difficult if not impossible to find. However, we have mentioned these methods so that interested persons may consult appropriate references (Ostle, 1954 Snedecor, 1948 Goulden, 1939 and Dixon and Massey, 1951) for the details of operation of particular techniques. 

Especial attention should be paid, though, to statistical procedures designed for handling enumeration data, since these techniques have been widely used by food research workers for some time. Specifically, 

To illustrate the method of evaluation of due to chance alone in n independent trials consider the binomial theorem expansion  

if iTi is interpreted as the probability of a success in any one trial, we see that the first term on the right-hand side of Eq. (2) represents the probability of zero successes and n failures in n independent trials. Similarly, the second term represents the probability of one success and n — 1 failures in n independent trials, and so on, until the last term, which represents the probability of n successes and zero failures in n independent trials. Thus the probability of r or more successes in n independent trials is  

To evaluate this probability is often a tedious job, especially if there are many terms to be summed. In this regard, it is good to know a quick. 

---

Since that time thousands of QSARs, covering a wide and diverse range of end points, have been published [9] most of these have used MLR, but numerous other statistical techniques have also been used, such as partial least squares, principal component analysis, artificial neural networks, decision trees, and discriminant analysis [f4]. 

We also reviewed the method for estimating paleo-moist-enthalpy. To estimate paleoenthalpy from plant fossils, Forest et al. (1999) quantified a relationship between leaf physiognomy and enthalpy from present-day plants and their local climate. Using Canonical Correlation Analysis, mean annual moist enthalpy can be estimated with an uncertainty of 5.5 kJ/kg. The contribution to the uncertainty in altitude is 560 m and is comparable to using temperature alone. Other statistical techniques that improve the ability to estimate enthalpy could replace the current method. 

We have presented trace element data and statistical analyses using these data. The data base needs to be expanded with analyses of samples from the many additional known localities in North America. Other statistical techniques, such as the one used by Sigleo (2) for turquoise, will also be examined. It appears that the discriminant function d is an important tool for archaeologists in provenance studies and that K-means cluster analysis can be very helpful in studying the singularity of trace element patterns for given localities. 

Besides regie.ssion analysis, there are other statistical techniques used in drug design. These fit under the classificalinn nf multivariate statistics and include discriminant analysis. 

Several stochastic models, based on mutli-parametric regression, artificial neural networks, Kalman filter and other statistical techniques, were implemented for short-term forecast of air pollution episodes, namely high ozone concentrations (Czech Republic, Hungary, Poland, Slovenia). 

A range of other statistical techniques can be used in the formulation of a classification model. Since a detailed description of these is outside the scope of this chapter, those which have been used in the study of odour are listed below ... 

Analysis More and more data mining and other statistical techniques allow for automated analysis and representations that make the visualisation of the textual data easy to understand and attractive. ... 

To examine the changes that can occur over different time periods (e.g., minutes, hours, days), other statistical techniques that account for non-linear changes, differences in driver populations, and changing patterns of behaviour can be used. Applying these statistical techniques requires an understanding of their usefulness as well as the type of information to be gathered beforehand. 

Neural network classifiers. The neural network or other statistical classifiers impose strong requirements on the data and the inspection, however, when these are fulfilled then good fully automatic classification systems can be developed within a short period of time. This is for example the case if the inspection is a part of a manufacturing process, where the inspected pieces and the possible defect mechanisms are well known and the whole NDT inspection is done in repeatable conditions. In such cases it is possible to collect (or manufacture) as set of defect pieces, which can be used to obtain a training set. There are some commercially available tools (like ICEPAK [Chan, et al., 1988]) which can construct classifiers without any a-priori information, based only on the training sets of data. One has, however, always to remember about the limitations of this technique, otherwise serious misclassifications may go unnoticed. 

Most environmental sampling studies are not amenable to classical statistical techniques. Correlation among samples, non-normal distributions of measurements, and multivariate requirements are typical In environmental studies. The effective use of statistics In an environmental study thus depends on meaningful Interaction between statisticians and other environmental scientists. 

The target number of commodity samples to be obtained in the OPMBS was 500, as determined using statistical techniques. A sample size of 500 provided at least 95% confidence that the 99th percentile of the population of residues was less than the maximum residue value observed in the survey. In other words, a sample size of 500 was necessary to estimate the upper limit of the 95% confidence interval around the 99th percentile of the population of residues. 

Ad-hoc approaches—Methods of estimating should be borrowed from other problems whenever applicable. For example, statistical techniques for quality control theory can probably be applied to chemicals by viewing discharges as "faulty" production. 

The models which we have developed can be classified as follows. Some are intended to represent physicochemical processes and properties by mimicking quantitatively concepts which have become accepted by chemists in general. A simple example would be the transfer of electronic charge between two atoms of differing electronegativities. Other models are statistical in nature. We have applied parameters quantified by the physicochemical models to series of chemical data. The relationships thus derived by various statistical techniques, and their form, is such that they are readily applicable to the task of quantifying the evaluation process in EROS. Further discussion of these points is a major feature of this article. 

However, the graphical approach is not appropriate for finding the absolute accuracy between more than two properties. The well-established statistical technique of regression analysis is more pertinent to determining the accuracy of points derived from one property and any number of other properties. There are many instances in which relationships of this sort enable properties to be predicted from other measured properties with as good precision as they can be measured by a single test. It would be possible to examine in this way the relationships between aU the specified properties of a product and to establish certain key properties from which the remainder could be predicted, but that would be a tedious task. 

The likeness of samples within the class can be assessed by the proximity of samples to each other in plots derived from principal components models. The statistical technique of cross-validation (17) was used to... 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

---