Spearman rank correlation

The mechanistic simulation ACAT model was modified to account automatically for the change in small intestinal and colon k as a function of the local (pH-dependent) log D of the drug molecule. The rank order of %HIA from GastroPlus was directly compared with rank order experimental %HIA with this correction for the log D of each molecule in each of the pH environments of the small intestine. A significant Spearman rank correlation coefficient for the mechanistic simulation-based method of 0.58 (p < 0.001) was found. The mechanistic simulation produced 71% of %HIA predictions within 25% of the experimental values. 

A robust, nonparametric (distribution free) measure for the correlation of variables is the Spearman rank correlation (symbol pjk, in M r Spearman). It is not limited to linear relationships, but measures the continuously increasing or decreasing... 

Kendall s tau correlation r Kendall) also measures the extent of monotonically increasing or decreasing relationships between the variables. It is also a nonparametric measure of association. It is computationally more intensive than the Spearman rank correlation because all slopes of pairs of data points have to be computed. Then Kendall s tau correlation is defined as the average of the signs of all pairwise slopes. The range of r is —1 to +1 the method is relatively robust against outliers for many applications p and r give similar answers. 

Trace element contents in rocks intersected by drill holes WB-08-03 to WB-08-06 are associated with altered rhyolite Spearman rank correlation coefficients for Ag, Mo and S with Au are moderate to high. Correlation coefficients for Au with As, Cu, Sb and Mo in drill hole WB08-11 (vuggy quartz) are moderate to high. These element correlations suggest that mineralization may be related to an epithermal system (Panteleyev 1995). 

For each IC50 bin, the percentage of compounds that list the ADR was calculated as percent ADR positive. For each group of seven IC50 bins, a Spearman rank correlation coefficient was calculated for the percent ADR positive relative to the bin rank. A strong Spearman correlation indicates a dose response in the ADR association. 

Apparently the oldest nonparametric measure of the strength of association between two factors [26], the Spearman rank correlation coefficient... 

While the Youden plot (Figure 3) indicates that there is systematic error in the various laboratories, a test by Spearmans rank correlation coefficient (Table Vb) is ambiguous. The ranking is significant at the 0.05 level but not at the 0.01 level thus a correlation of the ranks of the laboratories such as we see here would appear less than five times in 100 by chance but more than one time in 100. I prefer to look at these results in terms... 

As above represented it is necessary to test the ruggedness of FA against deviations from the normal distribution FA was, therefore, conducted on the basis of the SPEARMAN rank correlation coefficient [WEBER, 1986]. The obtained factor loading matrix... 

Several authors used the Spearman rank correlation coefficient as a MEP-SI in similarity investigations [112, 114, 115] ... 

Spearman rank correlation coefficient simiiarity/diversity... 

Figure 17.1 Correlation of rank order for ADMET Risk and human intestinal absorption (H IA%). The ADMET Risk score ranged from 0 to 5, with 5 being compounds with the greatest risk of having poor ADMET properties. Within a single ADMET Risk number, the compounds were ranked according to ascending estimated human jejunal permeability (ADMET Predictor, Simulations Plus, Inc.). Spearman rank correlation coefficient was 0.7 (pcO.OOl).

Figure 17.2 Correlation of rank order for 43 compounds that are known substrates for influx or efflux transporters. Spearman rank correlation coefficient was 0.3.

Moreover, if only one criterion is used or all the criteria have a Spearman rank correlation equal to one, that is, all the variables provide the same ordering, then a complete or total order is obtained, and all the alternatives are comparable. 

Spearman rank correlation coefficient statistical indices ( correlation measures)... 

The Spearman rank correlation coefficient, denoted as ps, is a widely used correlation measure between two ranked variables defined as... 

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 ... 

Another quick and dirty test for heteroscedasticity suggested by Carroll and Ruppert (1988) is to compute the Spearman rank correlation coefficient between absolute studentized residuals and predicted values. If Spearman s correlation coefficient is statistically significant, this is indicative of increasing variance, but in no manner should the degree of correlation be taken as a measure of the degree of heteroscedasticity. They also suggest that a further refinement to any residual plot would be to overlay a nonparametric smoothed curve, such as a LOESS or kernel fit. 

Relationships were tested with the non-parametric Spearman rank correlation coefficient, while the translocation capacity was tested with the ratio Ce/Cr, where Ce and Cr are the antimony contents in an epigeal compartment (shoots, leaves, etc.) and in the roots, respectively. The effects of plant traits were tested with the Mann-Whitney /-test in each sampling site for which a sample size no smaller than four observations was possible. The null hypothesis was not rejected when an overlap of observations between small samples occurred. 

Sometimes geochemical data cannot strictly be used in product-moment correlation of the type described above for they do not fuliil the requisite conditions. For example, some populations are not normally distributed and others include oudiers. An alternative, therefore, to Pearson s product-moment coefficient of linear correlation is the Spearman rank coefficent of correlation, usually designated r. This type of correlation is applicable to major or trace element data measured on a ranking scale rather than the equidistant scale used in Pearson s product-moment correlation. The Spearman rank correlation coefficient is calculated as follows ... 

The particular advantages of the Spearman rank correlation coefficient are (1) they alone are applicable to ranked data and (2) they are superior to the product- moment correlation coefficient when applied to populations that are not normally distributed and/or include outfiers. A further advantage 1 that the Spearman rank correlation coefficient (r,) is speedy to calculate and may be used as a quick approximation for the product-moment correlation coefficient (r). 

The O Connor (1998) paper used log-transformation, Spearman rank correlation and non-parametric statistical techniques to avoid skewing trends by unusually high or low data points. This paper will, however, point out some of the unusually high concentrations shown by given... 

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