Statistical test cluster analysis

R R-project A ficeware product for statistical calculation and graphics creation. R provides a wide range of tools (linear and nonlinear modeling, classical statistical tests, consistent analysis, classification, clustering) http //www.r-project.org/... 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

Analysis of variance in general serves as a statistical test of the influence of random or systematic factors on measured data (test for random or fixed effects). One wants to test if the feature mean values of two or more classes are different. Classes of objects or clusters of data may be given a priori (supervised learning) or found in the course of a learning process (unsupervised learning see Section 5.3, cluster analysis). In the first case variance analysis is used for class pattern confirmation. 

The application of methods of multivariate statistics (here demonstrated with examples of cluster analysis, multivariate analysis of variance and discriminant analysis, and principal components analysis) enables clarification of the lateral structure of the types of feature change within a test area. 

Finally, having performed a cluster analysis, statistical tests can be employed to assess the contribution of each variable to the clustering process. Variables found to contribute little may be omitted and the cluster analysis repeated. 

Any form of statistical methods exceeding simple descriptive statistics, such as statistical tests, correlations, regression analysis, factorial or cluster analysis, data mining techniques,. .. ... 

A detailed analysis of the approaches and methods used in experiments with mixtures can be found in Cornell (1990). The multivariate statistical methods, such as multivariate hypothesis testing, principal component analysis, cluster analysis, and discriminant analysis are discussed in Dillon and Goldstein (1984). 

In the analysis stage, appropriate parametric and non-parametric statistics were employed to identify significant changes and effect sizes. Residual gain analyses for both attitude and cognitive tests identified individual teacher outcomes. Similarities between teachers were explored by cluster analysis. Pupil results for each cluster were then examined with respect to the changes shown by their teachers. 

A second ICPMS analysis illustrates how variability can be addressed and quantitated. This report summarizes attempts to differentiate standard white office paper from several countries by using elemental analysis and simple statistical techniques, such as the f-test between means (Section 2.2.3). The authors evaluated a number of important considerations, such as differences between monthly batches and different rolls of paper produced on the same day. The results are summarized in Figures 14.3-14.6. In all elements analyzed, there was no significant difference in elemental concentrations between handled and unhandled paper. When several elements were evaluated, differences were seen between batches on the same day, as illustrated by cluster analysis, but principally between the first batch and all others. Overlaps between batches 2, 3, and 4 are evident. Variations between monthly batches are illustrated by means of cluster analysis and t-test results. These data show that the expected variation between batches is greater tiian that between different rolls produced on the same day. Also, data indicate a change in processing in May compared with the other months. This report is an excellent example of the need for meticulous and complete analytical work. Such backgroimd data are indispensable to the evaluation of evidentiary value, be it of paper, fibers, or any other type of evidence, esp>ecially mass-produced items. 

We looked at our data by sensor location and found that R2 contains bad data. We also found that L3 to be suspect, and it should be removed from analysis based upon not behaving as expected. Let us look at angle effects on our data. We will use cluster analysis here instead of hypothesis testing, or ANOVA, to show a different method from the Statistics Toolbox that can be used to identify differences in the data. 

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