Pearson coefficient

Note that in data analysis we divide by n in the definition of standard deviation rather than by the factor n - 1 which is customary in statistical inference. Likewise we can relate the product-moment (or Pearson) coefficient of correlation r (Section 8.3.1) to the scalar product of the vectors (x - x) and (y - y) ... 

Fig. 1. Analysis of fluorescence colocalizafion Pearsons coefficient standard deviation (/ =6) for colocalizafion of rhodamine fluorescence (liposomal marker) with Mitofluor green fluorescence (mitochondrial marker) obfained with Imaged. Open bars indicate nonfargefed liposomes, shaded bars n(i ca e STPP liposomes. (Asferfs/rindicates a Pvalue of <0.005). (Reproduced wifh permission from ref. 8)...

Confocal fluorescence micrographsobtained upon incubation of cells with STPP liposomes (see Note 5) are subjected to fluorescence colocalization analysis using ImageJ. Pearsons coefficient values obtained for STPP liposomes are compared to non-targeted liposomes prepared by replacing 1.5% STPP with 1.5%DOTAP(Fig.l). 

Table 2.21. Correlation (Pearson) coefficient matrices between the hydrous metal contents and grain proportion of the core sediments in the Dagu Estuary (Qin et al., 2006) (With permission from Qin YW)...

Calculate colocalization between proteins using the Pearson coefficient Colocolization Finder plugin in ImageJ. 

During the second session, the consumers retained 65 terms to evaluate the six manual transmissions. Among these terms, 46 were not linearly correlated (nonsignificant Pearson coefficient at a = 5%), 71% of the evaluated attributes. The test drivers retained 103 terms. Only 47 attributes were not linearly correlated for the test drivers (46% of the evaluated attributes). Figure 20.1 shows the results assessor by assessor. A first result is that consumers obviously managed to generate and to evaluate sensory terms while driving. 

Independency The correlations among L, a, b, h, C, Sl, Sa, Sb, Sh, and Sc are analyzed using matrix plots, a two-dimensional matrix of individual plots and Pearson coefficient generated by MINITAB 17. 

FIGURE 10.10 (a) Release profiles of ibuprofen from microemulsions of different composition, given in Table 10.2. Lines zero-order release kinetics. Pearson coefficients are given next to the symbols in the legend, (b) Correlation between release parameters (O) amount of released ibuprofen after 8 h and (A) ibuprofen release rate as function of the water weight ratio in the microemulsion (see Table 10.2). 

A high positive correlation coefficient implies a strong linear response of the target output to an increase in the parameter. For example, for the case shown in Fig. 5.1 la above, r = 0.9815. For nonlinear responses, however, the Pearson coefficient is not a useful measure of parameter importance. For nonlinear cases the... 

The relative statistical power, as defined by Eq. (3.112), does not always parallel the Pearson coefficient or the relative correlation factors, as is evident from Tables 3.22 and 3.23. However, because it includes more statistical information, we consider a model as relevant when it has greater individual output of this newly introduced statistical index. In particular, neither the linear nor the multilinear QSAR framework provides a good fit between the statistical correlation and the relative statistical power using the structural... 

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