Spearman Rank correlation analysis

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. 

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). 

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 ... 

Correlation can be done by plotting the specific activity for the new reaction vs the marker reaction (Figure 10.7). In principle, the correlation coefficient estimates the fraction of the variance attributable to the relationship between the two activities, that is, the fraction of the activity catalyzed by the particular enzyme (assuming that all of the marker activity is catalyzed by this enzyme). In some cases, excellent correlations have been reported - An alternative method of analysis is the Spearman rank plot, which has some deficiencies but avoids the overweighting of unusually high or low values. ... 

The post-intervention data were not distributed in a way that allowed transformation to normality. No information was collected on subjects that had been sampled multiple times, so it was not possible to account for this in analysis. Medians were reported and nonparametric Wilcoxon and Kruskal—Wallis tests were used to examine group differences, and the Spearman rank procedure for the analysis of correlations. 

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.)...

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

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. 

One-way analysis of variance (ANOVA) was used for assessment of the differences among groups and subgroups of subjects. Spearman s rank order correlations were used for analyses of the relationships between isoflavones and thyroid hormone parameters. 

For the statistical analysis, the results for each test specimen were coded either one for a pass (i.e., no liquid penetration) or zero for a failure. The effects of fabric type and challenge liquid on the liquid penetration of the fabrics were analyzed using separate two-way analyses of variance, Fisher s LSD post hoc comparison tests, and Spearman s rank order correlations. The level of statistical significance was set at 0.05. The statistical tables and raw data are available in the technical report (8). 

This technique is concerned with quantitative analysis of data when analysing a pair of variables. Data can be displayed using a scatter diagram, and numerically, using simple correlation and regression - the product-moment correlation coefficient measures the strength of a linear relationship between the variables. If variables are measured using an ordinal scale then Spearman s rank or Kendall s tau may be used to indi-... 

Spearman s ranked correlation tests were conducted on the data sets to compare the various sampling and analysis techniques (Spearman s ranked correlation coefficient = p). A significance level of p<0.05 was used throughout the study. 

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