Non-parametric statistical techniques

Non-parametric statistical techniques (i.e. those that make minimal assumptions about the error distribution) can be used to handle the raw data. Such methods are generally resistant towards the effects of extreme values, often because they use the median (see Section 6.2) as a measure of central tendency or measure of location. Such methods have the further advantage of extreme simplicity of calculation in many cases, but while popular in the behavioural sciences they are less frequently used in the analytical sciences. 

The O Connor (1998) paper used log-transformation, Spearman rank correlation and non-parametric statistical techniques to avoid skewing trends by unusually high or low data points. This paper will, however, point out some of the unusually high concentrations shown by given... 

Probability distribution models can be used to represent frequency distributions of variability or uncertainty distributions. When the data set represents variability for a model parameter, there can be uncertainty in any non-parametric statistic associated with the empirical data. For situations in which the data are a random, representative sample from an unbiased measurement or estimation technique, the uncertainty in a statistic could arise because of random sampling error (and thus be dependent on factors such as the sample size and range of variability within the data) and random measurement or estimation errors. The observed data can be corrected to remove the effect of known random measurement error to produce an error-free data set (Zheng Frey, 2005). 

Hypothesis testing techniques should include ANOVA, regression analysis, multivariate techniques and parametric and non-parametric statistics. 

Non-parametric statistical analysis (Bray-Curtis cluster analysis and multidimensional scaling ordination (MDS)) was performed on the GC-MS output to ascertain if any differences could be detected between the animals. MDS has been shown to be a useful technique for analysing chromatographic data, which can be difficult to analyse statistically (see Hayes et al., 2002, 2003). Each point in the MDS plot represents an individual lemur and points that are close together (clumped) correspond to... 

Specificity. Several attempts were made to develop a non-parametric statistical description of the specificity question, based on techniques from numerical linguistics. It was hoped that sets of very specific or very nonspecific uses would naturally emerge in the analysis. But it was found that a simple parametric statistic did far better than nonparametric ones the mean uses per compound for each use. The mean uses... 

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

We also make a distinction between parametric and non-parametric techniques. In the parametric techniques such as linear discriminant analysis, UNEQ and SIMCA, statistical parameters of the distribution of the objects are used in the derivation of the decision function (almost always a multivariate normal distribution... 

Two non-parametric methods for hypothesis testing with PCA and PLS are cross-validation and the jackknife estimate of variance. Both methods are described in some detail in the sections describing the PCA and PLS algorithms. Cross-validation is used to assess the predictive property of a PCA or a PLS model. The distribution function of the cross-validation test-statistic cvd-sd under the null-hypothesis is not well known. However, for PLS, the distribution of cvd-sd has been empirically determined by computer simulation technique [24] for some particular types of experimental designs. In particular, the discriminant analysis (or ANOVA-like) PLS analysis has been investigated in some detail as well as the situation with Y one-dimensional. This simulation study is referred to for detailed information. However, some tables of the critical values of cvd-sd at the 5 % level are given in Appendix C. 

Quite a variety of different methods can and have been apphed in QSAR work for the evaluation of classification rules [74]. These methods may roughly be divided into two categories, namely parametric or statistical and non-parametric or heuristic techniques. While class separation in the parametric techniques is... 

The classification methods discussed in the previous section are all based on statistical tests wliich require normal data distribution. If this condition is not fulfilled the so-called non-probabihstic , non-parametric or heuristic classification techniques must be used. These techniques are also frequently referred to as pattern recognition methods. They are based on geometrical and not on statistical considerations, starting from a representation of the compounds... 

What is the significance of these different scales of measurement As was mentioned in Section 1.5, many of the well-known statistical methods are parametric, that is, they rely on assumptions concerning the distribution of the data. The computation of parametric tests involves arithmetic manipulation such as addition, multiplication, and division, and this should only be carried out on data measured on interval or ratio scales. When these procedures are used on data measured on other scales they introduce distortions into the data and thus cast doubt on any conclusions which may be drawn from the tests. Non-parametric or distribution-free methods, on the other hand, concentrate on an order or ranking of data and thus can be used with ordinal data. Some of the non-parametric techniques are also designed to operate with classified (nominal) data. Since interval and ratio scales of measurement have all the properties of ordinal scales it is possible to use non-parametric methods for data measured on these scales. Thus, the distribution-free techniques are the safest to use since they can be applied to most types of data. If, however, the data does conform to the distributional assumptions of the parametric techniques, these methods may well extract more information from the data. 

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