Compound Standard Error

In Eq. (14) "est stands for the calculated (estimated) response, exp" for the experimental one, and n and m are the numbers of objects in the training set and the test set respectively. CoSE stands for Compound Standard Error. As an option, one can employ several test sets, if needed. 

Two models of practical interest using quantum chemical parameters were developed by Clark et al. [26, 27]. Both studies were based on 1085 molecules and 36 descriptors calculated with the AMI method following structure optimization and electron density calculation. An initial set of descriptors was selected with a multiple linear regression model and further optimized by trial-and-error variation. The second study calculated a standard error of 0.56 for 1085 compounds and it also estimated the reliability of neural network prediction by analysis of the standard deviation error for an ensemble of 11 networks trained on different randomly selected subsets of the initial training set [27]. 

For the extraction of rubber and rubber compounds a wide variety of solvents (ethyl acetate, acetone, toluene, chloroform, carbon tetrachloride, hexane) have been used [149]. Soxtec extraction has also been used for HDPE/(Tinuvin 770, Chimassorb 944) [114] and has been compared to ultrasonic extraction, room temperature diffusion, dissolution/precipitation and reflux extraction. The relatively poor performance of the Soxtec extraction (50% after 4h in DCM) as compared with the reflux extraction (95% after 2-4 h in toluene at 60 °C) was described to the large difference in temperature between the boiling solvents. Soxtec was also used to extract oil finish from synthetic polymer yam (calibration set range of 0.18-0.33 %, standard error 0.015 %) as reference data for NIRS method development [150]. 

Houben [256] has compared the determination of flame-retardant elements Br, P, S, K, Cl and F in polycarbonate using commercial (X40 and UniQuant ) software. For the X40 method, a calibration line for each element in PC or PC/ABS blends was mapped for the conversion of intensities to concentrations. With the universal UniQuant method, sensitivity factors (ks) were calibrated with pure standards. The X40 method turned out to be more reliable than UniQuant for the determination of FRs in PC and PC/ABS blends, even in the case of calibration of k values with PC standards. Standard errors of 5 % were achieved for Br, P, S and K, and 20% for Cl and F the latter element could not be determined by means of UniQuant (Table 8.44). GFR PC cannot be quantified with these two methods, because of the heterogeneous nature of the composites. Other difficult matrices for XRF analysis are PBT, PS and PP compounds containing both BFRs and Sb203 (10-30wt %) due to self-absorption of Sb and interelement effects. 

Compound Identification Number IC50 (pM) Standard Error (SE) of Fit or Standard Deviation (SD) from Multiple, Independent Determinations Hill Coefficient Maximum % Inhibition Attained Comments... 

Figure 3 Migration inhibition assessment of ECRF24 and MDA-MB-231 cells after exposure to compound 1 and 3. Wound closure in ECRF24 cultures after 7 h of incubation with concentration ranges of 1 (A) and 3 (B). (C) Typical images of the wound at the beginning of the experiment (culture medium as a control) and after 7 h of incubation with 3, 60 pM. Error bars represent standard error of the mean. P < 0.05.

For each compound, means standard error (SEM) were calculated and differences were assessed by ANOVA. Calculated p values < 0.05 were considered to be significantly different. The statistical procedures were performed with the software programme Instat Version 3 (Graphpad Software Inc.). 

Values represent mean concentration in J.g/g or jog/ml (expressed as parent compound) plus or minus the standard error of the mean of duplicate determinations on six animals. 

Of values in the right column of Table 1, the specified parameters are coefficients of z in formulae 45, 46 and 47, pertaining to vibrational and rotational g factors and adiabatic corrections respectively, with atomic centres B = Ga and A = H for this particular compound. Apart from the value of that was constrained to zero in the ultimate fit because preliminary fits indicated that its standard error much exceeded its magnitude, values of other parameters beyond cg, and Wg in their respective series, and also all and are not... 

Marne of Compound kj. (liter mln mole ) Standard Error ( )... 

COMPOUNDING OF ERRORS. Data collected in an experiment seldom involves a single operation, a single adjustment, or a single experimental determination. For example, in studies of an enzyme-catalyzed reaction, one must separately prepare stock solutions of enzyme and substrate, one must then mix these and other components to arrive at desired assay concentrations, followed by spectrophotometric determinations of reaction rates. A Lowry determination of protein or enzyme concentration has its own error, as does the spectrophotometric determination of ATP that is based on a known molar absorptivity. All operations are subject to error, and the error for the entire set of operations performed in the course of an experiment is said to involve the compounding of errors. In some circumstances, the experimenter may want to conduct an error analysis to assess the contributions of statistical uncertainties arising in component operations to the error of the entire set of operations. Knowledge of standard deviations from component operations can also be utilized to estimate the overall experimental error. 

For example, compounding the error of three operations, each with standard deviations of in concentration, say 2.0 mM, 1.1 mM, and 1.4 mM, would yield an overall standard deviation ... 

Survival after 24 h and the number of aphids feeding were determined at 4 mM compound in the diet. Reproductive index (number of nymphs/ average number of adults) was determined at 0.15 mM compound in the diet. Values are the average of three samples of ten aphids each. For reproduction studies five samples were used. Standard errors were always less than 10%. DIMBOA 2,4-Dihydroxy-7-methoxy-1,4-benzoxazin-3-one. 

Biological assays were performed with 6 mM compound in the diet. The reproductive index of aphids fed with 12 mM of glycine-betaine was 5.1 after 72 h of feeding. Values shown are the average ( standard error) of three samples of ten aphids each. Reproduction studies were performed with five samples. 

In 2008, Yan et al. [54] made prediction for a data set of 552 compounds for which HIA experimental data are available. Molecular descriptors were calculated by ADRIANA.Code and Cerius 2 as well. A set of models were constructed with PLS and SVM regression. The best model, which developed with SVM regression, had correlation coefficient of 0.89 and standard error of 16.35%. 

The approach of Hansch and Leo (1995) uses a small number of fragment values derived from very accurate partition coefficient measurements of a relatively small number of compounds, and requires a large number of correction factors. Some of the coefficient values are given in table 5.15. This approach has been designed for an automatic computer program that will do all the coefficients and corrections, called the CLOG. Hansch and Leo reported that for 7500 compounds tested, the correlation has a standard error of 0.336 and an = 0.978. 

An estimate of compound random errors is obtained from the square root of the sum of the squares of the RSDs attributed to each component or operation in the analysis. If the analysis of paracetamol described in Box 1.3 is considered then, assuming the items of glassware are used correctly. Assuming the items of glassware are used correctly the errors involved in the dilution steps can be simply estimated from the tolerances given for the pipette and volumetric flasks. The British Standards Institution (BS) tolerances for the grade A glassware used in the assay are as follows ... 

Tumor inhibition at three levels of Camptothecin (CI T), ellagic acid, and MV-extract tested in the Agrobacterium tumefaciens-induced tumor system. DMSO was used in the same concentrations as that used to test its respective dosage for each test compound. Error bars are indicative of 1 standard error, n = 15. 

Nelson and Jurs [41] have developed models for three sets of compounds (1) hydrocarbons, (2) halogenated hydrocarbons, and (3) alcohols and ethers. Each model correlates log[C (mol L-1)] with nine molecular descriptors that represent topological, geometrical, and electronic molecule properties. The standard error for the individual models is 0.17 log unit and for a fourth model that combines all three compound sets, the standard error is 0.37 log unit. 

In eq. 14.3.2, 1xv is the index for the heteroatom-containing molecule and (1Xv) p is the index for the corresponding, nonpolar (np) hydrocarbon equivalent. Bahnick and Doucette [20] demonstrate the calculation of these descriptors for 2-chloroacetani-lide. A ]xv accounts for nondispersive molecular interaction. Testing this model on a validation set of 40 structurally diverse compounds resulted in a standard deviation for the experimental versus estimated values of 0.37. The comparison of this value with the standard error of estimate (5 = 0.34) from the regression model suggests this model can be used confidently within the range of these structures. 

AQ/Qo = (Q - Qo)/Qo, where Q0 is charge consumption without analyte and Q is that at certain thrombin, concentration. An example of calibration curve for two independently prepared electrodes is shown in Fig. 47.3. It is seen, that results are well reproducible. Statistical analysis, performed earlier [4] revealed that standard error is approximately 11%. Interferences of this aptasensor with other compounds, human serum albumine (HSA) and human IgG are relatively low. An example is shown in Fig. 47.4, where calibration curve for thrombin is compared with those for HSA and IgG. Please note, that concentrations of HSA and IgG are much higher in comparison with that of thrombin. 

Table 11 Mean concentrations or range of perfluorinated compounds (ng/L) in water from the Great Lakes and their tributaries (standard error is in parentheses)... 

Table 14 Mean concentrations of perfluorinated compounds ( xg/kg or xg/L) in fish from the Great Lakes (standard error in parentheses)...

Authors found a root mean square error of 28.3°C with one derivation set of 979 compounds with no hydrogen bonding (Yalkowsky et al., 1994). A standard error of 28.1 K was reported for the 1,425-compound derivation set including hydrogen bonding compounds. A separate test set of 39 compounds yielded an average absolute error of 23.9 K (6.6%) (Walters et al., 1995). 

The standard error of regression equation (derived from data on 114 compounds) is 3.3 K. Root mean square errors on three test sets of decreasing similarity to derivation set were 17.1, 38.7, and 100 K, respectively. 

---