Confirmatory data analysis

From an analytical viewpoint, statistical approaches can be subdivided into two types Exploratory Data Analysis (EDA) and Confirmatory Data Analysis (CDA). Exploratory data analysis is concerned with pictorial methods for visualising data shape and for looking for patterns in multivariate data. It should always be used as a precursor for selection of appropriate statistical tools to confirm or quantify, which is the province of confirmatory data analysis. CDA is about applying specific tools to a problem, quantifying underlying effects and data modelling. This is the more familiar area of statistics to the analytical community. 

These EDA methods are essentially pictorial and can often be carried out using simple pencil and paper methods. Picturing data and displaying it accurately is an aspect of data analysis which is under utilised. Unless exploratory data analysis uncovers features and structures within the data set there is likely to be nothing for confirmatory data analysis to consider One of the champions of EDA, the American statistician John W. Tukey, in his seminal work on EDA captures the underlying principle in his comment that... 

If the aim of the data analysis or the question asked about the data is clearly fixed and the result is obtained the next question will be what is the cause of the structure found This in turn may lead to new hypotheses about the data. Hence, methods of confirmatory data analysis ( usual statistics ) may subsequently be necessary in the next step. Sometimes in recognition processes the problem of the adequate selection of objects will arise. Then an additional problem may consist in the proper choice of features to be measured in order to characterize the objects correctly. 

Statistical methodology expectations for confirmatory data analysis... 

This approach well denotes the conceptual shift from confirmatory data analysis, where a hypothesis and a distribution are assumed on the data, and statistical significance is used to test the hypothesis on the basis of the data (where the less reliable the results, the more the data divert from the postulated distribution), to EDA, where the data are visualized in a distribution-free... 

As in the case in the analysis of food samples, the introduction of relatively inexpensive MS detectors for GC has had a substantial impact on the determination of methylxanthines by GC. For example, in 1990, Benchekroun published a paper in which a GC-MS method for the quantitation of tri-, di-, and monmethylxanthines and uric acid from hepatocyte incubation media was described.55 The method described allows for the measurement of the concentration of 14 methylxanthines and methyluric acid metabolites of methylxanthines. In other studies, GC-MS has also been used. Two examples from the recent literature are studies by Simek and Lartigue-Mattei, respectively.58 57 In the first case, GC-MS using an ion trap detector was used to provide confirmatory data to support a microbore HPLC technique. TMS derivatives of the compounds of interest were formed and separated on a 25 m DB-% column directly coupled to the ion trap detector. In the second example, allopurinol, oxypurinol, hypoxanthine, and xanthine were assayed simultaneously using GC-MS. 

Exploratory data analysis, EDA, is an essential prerequisite of the examination of data by confirmatory methods. Time spent here can lead to a much greater appreciation of its structure and the selection of the most appropriate confirmatory technique. This has parallels in the analytical world. The story of the student s reply to the question Ts the organic material a carboxylic acid which was I don t know because the IR scan isn t back yet poses questions about the approaches to preliminary testing ... 

A study protocol is often supplemented with another very important document called the statistical analysis plan (sometimes referred to by similar names such as a data analysis plan or reporting analysis plan). The statistical analysis plan often supplements a study protocol by providing a very detailed account of the analyses that will be conducted at the completion of data acquisition. The statistical analysis plan should be written in conjunction with (and at the same time as) the protocol, but in reality this does not always happen. At the very least it should be finalized before the statistical analysis and breaking of the blind. In many instances (for example, confirmatory trials) it may be helpful to submit the final statistical analysis plan to the appropriate regulatory authorities for their input. 

Once this initial characterization has been completed, continuation of the microscopic analysis using the hot-stage accessory may proceed. As an initial analysis, the ramp rate utilized for the DSC experiment should also be used for the hot-stage analysis. Use of a consistent ramp rate permits direct comparison of the data previously collected by DSC and TGA. If transitions are observed in the thermal data up to 300°C, the hot-stage experiment should also be run to that temperature. Ultimately, the assay should be conducted to generate confirmatory data on all transitions of interest. If available, the color camera should be utilized so that images may be collected as documentation of the transitions observed. Once the experiment is completed, the analyst may be able to compare the DSC, TGA, XRD, optical, and HSM data and develop a comprehensive characterization of the material. 

For validity evidence based on internal structure, confirmatory factor analysis was performed in Mplus 5.2 to estimate how well the designed two-factor correlated structure for the instrament fits the responses obtained with the sample (L. Muthen B. Muthen, 2007). Fit indices such as chi-square ( ), Comparative Fit Index (CFI), and the Standardized Root Mean Square Residual (SRMR) were examined to assess the fitness of the model to the data, and item loadings were also evaluated. The criteria of CFI value greater than 0.95 and SRMR value less than 0.08 were used to indicate a good model fit and CFI >0.90 as acceptable fit (Bentler, 1990 Hu Bentler, 1995). 

Citing a paper by Bro et al. [2], it can very well be said that "usually, data analysis is performed as a confirmatory exercise, where a postulated hypothesis is claimed, data generated accordingly and the data analysed in order either to verify or reject this hypothesis. 

Next we determined that the nine theorized climate measures were intercorrelated and that student data could be aggregated. We then conducted a confirmatory factor analysis which yielded nine data-driven factors. We correlated these with the theorized measures to determine if the two sets of measures were related. Except for three factors from the data-driven results that did not distinctively capture specific theorized climate measures, over half (42) of the 81 zero-order correlations were at least moderate (.40 < r < 1.0) indicating that the results of the two factor analyses were comparable. For example. Factor 1 of the data-driven result included Involvement and Faculty Support of the theorized measures. 

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