Visualization statistical techniques

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

Principal Component Analysis (PCA) is performed on a human monitoring data base to assess its ability to identify relationships between variables and to assess the overall quality of the data. The analysis uncovers two unusual events that led to further investigation of the data. One, unusually high levels of chlordane related compounds were observed at one specific collection site. Two, a programming error is uncovered. Both events had gone unnoticed after conventional univariate statistical techniques were applied. These results Illustrate the usefulness of PCA in the reduction of multi-dimensioned data bases to allow for the visual inspection of data in a two dimensional plot. 

Analysis involves statistical techniques that may oversimplify wbWe producing compelling visual images. 

In all instances the weld should have a clean appearance, with discoloration of the base materials kept to a minimum. At least two weld spots should be made at each connection joint. When the weld is tested by pulling the two pieces apart, the weld must hold while the base metal tears. For tabs the weld diameter, as a rule of thumb, should be three to four times the tab thickness. For example, a 0.125-mm-thick tab should have a tear diameter of 0.375-0.5 mm. Statistical techniques of weld pull strength for process control are helpful, but a visual inspection of the weld diameter must accompany the inspection process. 

Statistical techniques are powerful tools, which can be used in the search for minor constituents in planetary spectra. Correlation analysis is particularly applicable to the detection of gases with many, generally weak spectral features. Correlation analysis is best applied when the signatures of a suspected constituent are of the same magnitude or possibly even less than the noise level of the instrument. Under such conditions visual inspection of a spectral region where known lines of a particular gas should appear may not be conclusive. The advantage of correlation analysis is that many spectral positions can be searched simultaneously. 

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... 

Visualization of results, their statistical validity, and analysis of results are becoming increasingly important. Several techniques are available to represent data and compact representations are increasingly being made by images. The ease of visualization, however, must always be tempered with the need to present data completely and in an accurate manner. In particular, two areas are of relevant important. The first is two-dimensional spectral representation to better understand spectral structure while the second is more useful for imaging. 

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