Average correlation coefficient

Figure 44.6 Average correlation coefficients between estimated 24 h urinary iodine excretion and serum TSH in 15 healthy men grouped according to average annual estimated 24 h urinary iodine exoretion. Pearson s correlation coefficients on In-transformed data were used. From Andersen et al., (2001), reproduoed with permission.

The average correlation coefficient for the families of hydrocarbons studied is 0.984 which confirms a good agreement with theory. This manner of treating solutions is very sensitive to the number of [substituents of the solute molecule i.e. to the molecular shape of solute. 

Fig. 19.24 Example of time-averaged correlation coefficient (left) and the quadrant analysis for a local correlation value (right)...

We are interested in < E (0[,(t)i)E3(62,, where <> means the average over the ensemble of surfaces, the subindexes 1 and 2 refer to two different points of observation and the subindexes A and B belong to two different conditions of illumination, which for example arise from two different wavelengths, two different incident angles, etc.. If A = B and 1 = 2, the above expression gives the angular distribution of the mean scattered intensity, otherwise it turns to be the intensity correlation coefficient y from < E Eb >, assuming that we deal with fully developed speckle. 

Color Difference Evaluation. Shade evaluation is comparable in importance to relative strength evaluation for dyes. This is of interest to both dye manufacturer and dye user for purposes of quaUty control. Objective evaluation of color differences is desirable because of the well-known variabihty of observers. A considerable number of color difference formulas that intend to transform the visually nonuniform International Commission on Illumination (CIE) tristimulus color space into a visually uniform space have been proposed over the years. Although many of them have proven to be of considerable practical value (Hunter Lab formula, Friele-MacAdam-Chickering (FMC) formula, Adams-Nickerson formula, etc), none has been found to be satisfactorily accurate for small color difference evaluation. Correlation coefficients for the correlation between average visually determined color difference values and those based on measurement and calculation with a formula are typically of a magnitude of approximately 0.7 or below. In the interest of uniformity of international usage, the CIE has proposed two color difference formulas (CIELAB and CIELUV) one of which (CIELAB) is particularly suitable for appHcation on textiles (see Color). 

At the simplest level the orientational correlation of molecular pairs can be characterised by the averages of the even Legendre polynomials Pl(cos J ij) where is the angle between the symmetry axes of molecules i and j separated by a distance r. This correlation coefficient is denoted by... 

Here, Yx m( j) denotes a spherical harmonic, coj represents the spherical polar angles made by the symmetry axis of molecule i in a frame containing the intermolecular vector as the z axis. The choice of the x and y axes is arbitrary because the product of the functions being averaged depends on the difference of the azimuthal angles for the two molecules which are separated by distance r. At the second rank level the independent correlation coefficients are... 

However, it is not proper to apply the regression analysis in the coordinates AH versus AS or AS versus AG , nor to draw lines in these coordinates. The reasons are the same as in Sec. IV.B., and the problem can likewise be treated as a coordinate transformation. Let us denote rcH as the correlation coefficient in the original (statistically correct) coordinates AH versus AG , in which sq and sh are the standard deviations of the two variables from their averages. After transformation to the coordinates TAS versus AG or AH versus TAS , the new correlation coefficients ros and rsH. respectively, are given by the following equations. (The constant T is without effect on the correlation coefficient.)... 

Comp. Vol/km km/mm Tire Life (km) Rating Average Road Rating Correlation Coefficient... 

They include simple statistics (e.g., sums, means, standard deviations, coefficient of variation), error analysis terms (e.g., average error, relative error, standard error of estimate), linear regression analysis, and correlation coefficients. 

Figure 3.3a-c shows graphs of correlation coefficient r versus p2 f°r different pj in WEG, FAN, and PAR. The curves are limiting values of r evaluated as described in Appendix 3B. The symbols are the average r s from 1000 simulations of 500 random correlated coordinates for different pj and p2. The agreement is excellent, except for r < 0.1. The small deviation probably is caused by minor imperfections in the random number generator. 

FIGURE 3.3 Graph of linear correlation coefficient r versus /J2 f°r various Pi in (a) WEG, (b) FAN, and (c) PAR. Curves are predictions points are simulation averages. 

The errors that result from the use of average transport coefficients are not particularly serious. The correlations that are normally employed to predict these parameters are themselves determined from experimental data on packed beds. Therefore, the applications of the correlations and the data on which they are based correspond to similar physical configurations. 

Fig. 2 Plot of P-Cl distances (in A) vs average P-N distances (in A) for P-chloro-NHPs (diamonds) and for all compounds (R2N)2PC1 (except P-chloro-NHPs) listed in the CSD data base (open squares). The solid and dashed lines represent the result of linear regression analyses. R2 is the square of the correlation coefficient in the regression analysis. (Reproduction with permission from [55])...

Because of the large difference in the behavior of the thin plywood and the gypsum board, the type of interior finish was the dominant factor in the statistical analysis of the total heat release data (Table III). Linear regression of the data sets for 5, 10, and 15 min resulted in squares of the correlation coefficients R = 0.88 to 0.91 with the type of interior finish as the sole variable. For the plywood, the average total heat release was 172, 292, and 425 MJ at 5, 10, and 15 min, respectively. For the gypsum board, the average total heat release was 25, 27, and 29 MJ at 5, 10, and 15 min, respectively. 

A linear calibration curve for carvedilol in plasma was constructed over a range of 1 to 80 ng/mL. The correlation coefficient exceeded 0.999. Intra-day and inter-day coefficients of variation were 1.93 and 1.88%, respectively. The average carvedilol recovery was 98.1%. The limit of quantification was 1 ng/mL. This high-throughput method enabled the analysis of more than 600 plasma samples without significant loss of column efficiency. 

Calibration curves for voriconazole were constructed in concentration ranges of 0.1 to 10 jUg/mL. Correlation coefficients exceeded 0.9998. Intra-day and inter-day coefficients of variation were less than 3.8 and 6.1%, respectively. The average extraction recovery was 94.6%. The limit of detection and the limit of quantification were 15 and 50 ng/mL, respectively. 

A calibration curve for everolimus was obtained in a concentration range of 1 to 50 /.ig/mL with a correlation coefficient of 0.999. Between-day coefficient of variation was less than 8.6%. The limit of quantification was 1.0 /.ig/mL. Absolute recoveries averaged from 76.8 to 77.3%. 

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