Spearman correlation

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. 

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 ... 

Table 3.6 Rank order correlations (Spearman) between time and competence ratings for learning phases 1 and 2...

Rank order correlations (Spearman) between time and... 

Table 1 Correlation (Spearman) between impedance and pressure catheter parameters in rats anesthetized with Ketamine, baseline records ( =60)...

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 ... 

On occasion you need to obtain correlation coefficients between two variables. Correlation coefficients are a way of measuring linear relationships between two variables. A correlation coefficient of 1 or -1 indicates a perfect linear relationship, and a coefficient of 0 indicates no strong linear relationship. Pearson correlation coefficients are useful for continuous variables, while Spearman correlation coefficients are useful for ordinal variables. For example, look at the following SAS code ... 

The first PROC CORR sends the Pearson correlation coefficients to a data set called pearson for the continuous variables Age and Weight, while the second PROC CORR sends the Spearman correlation coefficients to a data set called spearman for the categorical variables Race and Treatment Success. The correlation coefficients are found where the TYPE variable is equal to CORR in the pearson and spearman data sets. 

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. 

The results have been statistically processed by means of Spearman s non-parametrical correlation analysis and by multiple regression analysis to assess the complex effects induced by toxic and essential elements (Evstafyeva, Slusarenko, 2003 Evstafyeva et al., 2004). 

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... 

The range of p is — 1 to +1 the value is invariant to variable transformations that keep the sequence of the values that means that for instance a logarithmic transformation has no influence. Because the Spearman correlation is based on ranks, it is relatively robust against outliers. 

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. 

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]. 

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). 

Ag exhibits a strong Spearman s Rank correlation with Pb, Zn, Cd, and Sb reflecting its cogenetic nature with these elements as they are controlled by free energies, dissolved metal species, and degree of saturation. 

The number of circulating blood platelet is markedly reduced by injection of a lethal dose of toxin-LR into mice ( 7 ). The time course of the decrease of the blood platelets is closely paralleled by the increase in fresh weight of the liver. The sharp rise in Spearman s rank correlation between platelet count and liver weight 30 minutes after injection indicates that thromocytopenia and hepatomegaly were almost concurrent. 

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. 

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

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

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... 

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