Correlation coefficient Spearman s rank

Fields can be utilized in virtual screening applications for assessing the similarity (alignment) or complementarity (docking) of molecules. Two similarity measures have achieved the most attention. These are the so-called Garbo- [195] and Hodgkin indexes [196] respectively. Others are Pearson s product moment correlation coefficient [169] and Spearman s rank correlation coefficient [169]. 

III.2. Comparison with Spearman s Rank Correlation Coefficient... 

In an alternative approach, critical values of Spearman s rank correlation coefficient, tabulated as a function of observation size and significance probability [32], are employed. The 5% critical value is 0.738 when N = 8, hence rs = 0.369 is not significant (not even at the 10% level, with critical value 0.643). 

Slope and intercept with CIs are provided together with Spearman s rank correlation coefficient. A software program is required for the procedure. 

The correlation between the two rankings (rexp, rmoci) can then be evaluated by Spearman s rank correlation coefficient rs, according to the following expression ... 

Typical scattergrams for no correlation, positive correlation and negative correlation are illustrated in Figure 12.12. It is also possible to calculate a numerical value for correlations without drawing a scattergram. The appropriate measure for correlations involving accident data is Spearman s Rank Correlation Coefficient . ... 

The precondition with regard to the RAPP approach is the correlation between the progression of the analysed failure mode variable and the chosen life span variable. This can be verified with the help of the Spearman s rank correlation coefficient (Sachs 2002). 

This part of the research work focuses on the impact of the fibre thickness on the durability of the fibres. Durability is represented quantitatively by the number of cycles of the flex abrasion test. The impact is presented in form of the Spearman s rank correlation coefficient. The correlation coefficient gives a value between -1 and 1 inclusively, where -1 is total negative, 1 is total positive and 0 is no correlation. Spearman s rank correlation is a nonparametric tool which describes the linear dependency between two variables, and can be defined as ... 

Figure 4. Comparision of the important dental drill characteristics and their correlation influences on each other determined with Spearman s rank correlation coefficient (schematic visualisation). 

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. 

Table 4 Spearman s Ranked Correlation Coefficients of Proportions of Five Volatile Flavor Compounds ...

Rank from testing under Duhring Chambers using 25% shampoo solutions. Spearman s rank correlation test provides a correlation coefficient of 1.0 and a Z value of 2.0, indicating a significant relationship between in vivo irritation and calculated ranks. 

Correlation coefficient Spearman s Rank Correlation Kendall Tau Coefficient gamma Chi square Phi coefficient Fisher exact test Kendall coefficient of concordance... 

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). 

The 28 toxoplasma-positive sera that had been titrated for antibody by FA were titrated by RIA, and the titers of the two tests were correlated, using Spearman s rank-order correlation test. The correlation coefficient was 0.68, and probability that this value differs from zero (no correlation) by chance alone was <0.001. Thus there was reasonably good agreement between the titers obtained in the two tests. 

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. 

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 ... 

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-... 

N mi s is the number mi sc 1 ass ified, and the figure in parentheses after the value of N mis is the number misclassified by two grades and Rg is the Spearman rank correlation coefficient for recognition by use of "the leave-one-out technique. 

Spearman Rank Correlation Coefficient n Also known as Spearman s rho or SRCC and usually designated by r or p, is a widely used nonparametric measure of the correlation between two variables. It is generally used when the values of the variables are ambiguous or hard... 

Fischer (30) reported that airborne respirable endotoxin levels correlate (Spearman s coefficient of rank correlation) with the counts of gram-negative rods, with the percent of the total material processed that is Memphis cotton, and with the decrease in FEV, if these data are calculated only on mills where the carding areas are separate from the spinning areas. 

Pearson s product-moment correlation coefficient (r) is the most commonly used correlation coefficient. If both variables are normally distributed, then r can be used in statistical tests to test whether the degree of correlation is significant. If one or both variables are not normally distributed you can use Kendall s coefficient of rank correlation (t) or Spearman s coefficient of rank correlation (rs). They require that data are ranked separately and calculation can be complex if there are tied ranks. Spearman s coefficient is said to be better if there is uncertainty about the reliability of closely ranked data values. 

In many cases, instead of linear, the relation between inputs and outputs is monotonic. Then, it is convenient to transform inputs and outputs into their ranks. This way, the same tools (renamed as Spearman s correlation coefficient. Partial Rank Regression Coefficients -PRCC- and Standardised Rank Regression Coefficients -SRRC-) are used to assess the importance of each input parameter. The reliability of the results obtained via linear regression depends on the Coefficient of Determination (R ) of the regression model obtained. If is close to 1 the results are very reliable, if it is close to 0, it means that this SA method is not able to address all the complexity of the system model at hand. 

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