Rank correlation analysis

T2 quantifies similarity by a rank correlation analysis and in comparison to Ti it takes more information into account ... 

Partial ordering is useful as technique for rank correlation analysis, where a simple and transparent mapping of a correlation profile is possible. The principle described in this chapter is supported by the software named Po Correlation presented by Sorensen et al. (2005) and the content of this chapter is based on that paper. Non-commercial use of the software for research and education is free if reference is given to Sorensen et al., (2005) and can be made available by contacting the first author of this chapter. Two other software products exist for application of Partial... 

Figure 10 Spearman rank correlation analysis of the differences in skew values and PD, values for methacholine after rapid and slow inhalation. (From Ref 18.)...

Examples of mathematical methods include nominal range sensitivity analysis (Cullen Frey, 1999) and differential sensitivity analysis (Hwang et al., 1997 Isukapalli et al., 2000). Examples of statistical sensitivity analysis methods include sample (Pearson) and rank (Spearman) correlation analysis (Edwards, 1976), sample and rank regression analysis (Iman Conover, 1979), analysis of variance (Neter et al., 1996), classification and regression tree (Breiman et al., 1984), response surface method (Khuri Cornell, 1987), Fourier amplitude sensitivity test (FAST) (Saltelli et al., 2000), mutual information index (Jelinek, 1970) and Sobol s indices (Sobol, 1993). Examples of graphical sensitivity analysis methods include scatter plots (Kleijnen Helton, 1999) and conditional sensitivity analysis (Frey et al., 2003). Further discussion of these methods is provided in Frey Patil (2002) and Frey et al. (2003, 2004). 

The limitation of the use of one atmosphere foaming experiments to rank order the predicted surfactant performance in permeable media rather than in quantitatively or semi-quantitatively predicting the actual performance of the surfactants under realistic use conditions has already been mentioned. Multiple correlation analysis has its greatest value to predicting the rank order of surfactant performance or the relative value of a physical property parameter. Correlation coefficients less than 0.99 generally do not allow the quantitative prediction of the value of a performance parameter for a surfactant yet to be evaluated or even synthesized. Despite these limitations, multiple correlation analysis can be valuable, increasing the understanding of the effect of chemical structure variables on surfactant physical property and performance parameters. 

If correlation analysis is used with the raw data, ideally both data types should have similar ranges and distributions. If data is directly linearly correlated, this can be neglected, but is rarely the case for metabolome and transcriptome data. Changes in gene expression may not alter metabolite pools significantly. Therefore, data have to be normalized in an appropriate way and correlation methods other than linear correlation have to be used (e.g., Spearman s rank-order correlation or Kendall rank correlation should be preferred over Pearson correlation). 

If, on the other hand, all elements of E (or FJ%) are isolated then the attributes should be checked for the degree of anti-correlation (Spearman rank correlation). It depends on the scientific question, whether such a trade-off among attributes (a decreasing sequence of values of one attribute is always accompanied by an increasing sequence of another attribute) should be maintained in the study. There are methods to deal with such cases, see the chapter by Simon et al., p. 221 and by Sorensen et al., p. 259. However, this shall not be further discussed here. The subsets d, e as well as a, b, c form nontrivial hierarchies. Hence, we have three order relations b < a, c < a, and e < d. The fact that the set E can thus be partitioned into three disjoint subsets is always of great interest with respect to the data structures. Further structural elements, which are of interest in the analysis of Hasse diagrams, are subsequently discussed ... 

The primary topic for the correlation analysis is to investigate the coincidence between the ranking of pesticides based on the measured variable set DetFreq and MedMax on one side (Set 1) and the usage variable set Dose and SpArea on the other side (Set 2). The variables DetFreq and MedMax are thus denoted the predicted variables while Dose and SpArea are denoted the predicting variables. 

Comparison of Immunoassay with GC/MS Analysis. The relation between atrazlne concentration determined by GC/MS analysis and trlazlne concentration determined from immunoassay analysis on 127 samples is shown in figure 3. Samples with immunoassay results larger than 5 ug/L are not plotted. Although the two determinations are highly correlated (rank correlation coefficient is 0.90 p<0.0001) the relation is not linear over the 0.2 ug/L to 5 ug/L range of the immunoassay results. Linear and multiple-linear regression models were fitted to the data to enable prediction of atrazlne concentrations from the immunoassay data. 

Statistic analysis. The Spearman rank correlation was used for correlations (17). 

First, we will present the results that were apphed to the data collected fiom Hospital M. We calculated a mean annual reporting rate over the three years 2004— 06 as well as a mean score for each safety culture factor (cf Tables 4.2-4.5) for each of 18 work units. A rank-based correlation analysis (Spearman s rho) was applied to these cross-unit data and the analysis of results is shown in Table 4.8. 

The product-moment correlation coefficient is widely used in bmriate data analysis to measure the extent of the correlation between two variables, but it is not clear that it is necessarily appropriate to measure the extent of the similarity between two objects. Other sorts of correlation coefficient are available, such as the Spearman rank correlation coefficient which has been used by Manaut et al. as a measure of electrostatic similarity, but these have not found extensive application in similarity searching systems. Similar comments apply to probabilistic coefficients, which are calculated from the frequency distribution of descriptors in a database, and which Adamson and Bush < found to give poor results when applied to 2D chemical structures. 

State-of-the-art calculations for correlations analysis are based on Bravais-Pearson (precondition bivariate normal distributed characteristics), Spearman and Kendall (rank based analysis independent of characteristic distribution models), explanation in (Sachs 2002). The results of the application of these correlation analyses show the interdependences of the product characteristics (step 3, Fig. 1). For this case study Spearman correlation, shown in equation 4, was used. 

Conover, W.J., Measures of rank correlation. In Practical Nonparametric Statistics (2nd edition). John Wiley Sons, New York, 1980, pp. 250-256 and pp. 256-263 (Chapter 5.4). Bevington, P.R., Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill Book Co., New York, 1969. 

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