Pearson correlation analysis

Table 4 Pearson correlation analysis for phosphates in water...

The first step to develop an MLR in order to predict the density of ternary mixtures of ionic liquid consists on performing a Pearson correlation analysis to determine which variables can be better fitted to the linear model (Table 21.1). 

TABLE 21.1 Pearson Correlation Analysis Results for Ternary Mixtures of Ethanol +Water + Ionic Liquid for 283 Cases... 

Correlation analysis quantifies the degree to which the value of one variable can be used to predict the value of another. The most frequently used method is the Pearson product-moment correlation coefficient. 

Fig. 5.3 Correlation between total ginsenoside content and log-transformed IC50 values. The IC50 values of different ginseng products were plotted against their total ginsenoside content. Only products quantified by HPLC-DAD were included in the analysis. Pearson correlation yielded a value of r = -0.997...

Lastly, it is desirable that parameters are able to discriminate between positive and negative conditions in a variety of experimental conditions. In other words they should be robust and reproducible. For this purpose, the Pearson correlation coefficient between all experimental repeats using control wells is calculated. Robust parameters have high Pearson correlation coefficients (above 0.7) in pairwise comparisons of experimental repeats. For this analysis we have developed another R template in KNIME to calculate the Pearson correlation coefficient between experimental runs. 

Deciding on an appropriate analysis is at this point subjective, but additional information such as the average Pearson correlation of profiles in a cluster or simply how positive controls cluster can be useful for judging the result of any clustering method. 

The results of the seven studies were analyzed using the statistical method of meta-analysis. Homogeneity of the studies was checked with an appropriate statistical test, while combined Pearson correlation coefficients were estimated with four different methods. The main findings were ... 

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 dose response curves performed in PBS 7.6 buffer and in a non-medicated poultry feed extract solution are shown in Figure 5. The two curves are significantly different in optical density responses but the slopes appear to be similar. A preliminary analysis of broiler feed extract by ELISA indicated that a non-medicated feed extact standard curve must be used for computing the values of unknown feed extracts. The same feed extract samples were analyzed by HPLC-F. The comparison is shown in Table II. The data indicates that the ELISA method of analysis for maduramicin in broiler feed correlates well with the HPLC-F method with a Pearson correlation coefficient of 0.973. 

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). 

Fig. 1 Dendrogram based on cluster analysis of digitized (GTG)j-PCR fingerprints of type, reference and Bryndza cheese strains. The dendrogram was constructed using the Unweighted Pair Group Method with Arithmetic Mean (UPGMA) using correlation levels expressed as percentage values of the Pearson correlation coefficient. Numbered clusters (1-9) correspond to identified species of Enterococcus sp. and Lactococcus sp.

Fig. 2.15. The result of cluster analysis for IC influencing factors in Liaodong Bay sediments (Dendrogram nsing average linkage between groups, Pearson correlation)...

Results from ex vivo assays performed at ABG and at William Harvey Research Limited were compared with a 2-tailed Pearson correlation test analysis was performed twice, once for each Cox isoenzyme, using data pooled from both NSAIDs (ibuprofen and celecoxib) together. For Cox-1, R squared was 0.67 (p <0.01) and for Cox-2, R squared was 0.92 (p <0.001). 

ABSTRACT This paper quantitatively analyzed effect of production performance on organizational accidents using Pearson correlation and regression model analysis. Results showed that coal mine output have significant effects on safety. Specifically, this paper posits that there is a U-shaped curve relativity between production yields and accident rate, along with yields increase, death toll occurred in accidents initially decrease, then increase. 

The Pearson correlation coefficient is used to represent the scale of a dendrogram constructed with TreeView after phylogenetic analysis with Cluster. For a pairwise comparison, a coefficient of 1 indicates absolute identity and zero indicates complete independence. 

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