Confidence curves

Hopefully, we make our point. The confidence curve is NOT fashioned out of granite - it has to be applied with understanding and circumspection. It will always have the same basic shape but we have to be prepared to take a view on how wide it should be in every individual situation Matters become a great deal more complex when we come up against structures that are sterically crowded (i.e., structures where bond constraints force various moieties into close proximity with one another). 

Note also that the concept of the confidence curve is equally applicable when considering coupling data. That is What size coupling should I be looking for in this system or that Is it too big Too small ... 

As we pointed out earlier, it is a good idea if you can eliminate peaks from common solvents and impurities before getting into the real interpretation (note how chemical shifts can vary in different solvents - another factor which helps define the breadth of the confidence curve). Table 5.1 can be very helpful in this regard. 

Figure 14-18 Simulated example with positive and negative differences in the low and high range, respectively A, Bland-Altman plot. B, An x-y plot with diagonal (dotted straight line) and estimated Deming regression line fso//d //ne) with 95% confidence curves (dashed lines).

The method of standard additions would give the true result if there were no experimental errors. Practically, this is never the case and, so, a weakness of the method appears concerning the reliability of the provided result (unknown concentration). Effectively, the use of extrapolation of a calibration cmve is always less conformable and reliable than interpolation, especially concerning the errors on predicted values.The problem is even more explicit when the result is expressed along with its confidence interval. Confidence curves of the regression line must, thus, be used. Their expression is... 

HCLPp. A value for the selected parameter representing an external event, chosen on a median capacity curve of a structure, system or component, with and random variables with unit medians, representing the inherent randomness of the median and the uncertainty in the median value respectively. Assuming that both and % are log-normally distributed with logarithmic standard deviations and pu, respectively, the variables A, and determine a family of fragility curves representing various levels of confidence. The point on the 95% confidence curve that corresponds to a 5% Pp is commonly referred to as the high confidence of a low probability of failure (HCLPp) value, therefore ... 

Confidence Intervals for Normal Distribution Curves Between the Limits p zo... 

The second complication is that the values of z shown in Table 4.11 are derived for a normal distribution curve that is a function of O, not s. Although is an unbiased estimator of O, the value of for any randomly selected sample may differ significantly from O. To account for the uncertainty in estimating O, the term z in equation 4.11 is replaced with the variable f, where f is defined such that f > z at all confidence levels. Thus, equation 4.11 becomes... 

Relationship between confidence intervals and results of a significance test, (a) The shaded area under the normal distribution curves shows the apparent confidence intervals for the sample based on fexp. The solid bars in (b) and (c) show the actual confidence intervals that can be explained by indeterminate error using the critical value of (a,v). In part (b) the null hypothesis is rejected and the alternative hypothesis is accepted. In part (c) the null hypothesis is retained. 

Construct an appropriate standard additions calibration curve, and use a linear regression analysis to determine the concentration of analyte in the original sample and its 95% confidence interval. 

Statistically, a similar Indication of precision could be achieved by utilising the 95% probability level if the results fell on a "Gaussian" curve, viz., the confidence would lie within two standard deviations of the mean. R 2 x SD = 56.3 24.8... 

Fig. 12. The relationship between the mean oceanic residence time, T, yr, and the seawater—cmstal rock partition ratio,, of the elements adapted from Ref. 29. , Pretransition metals I, transition metals , B-metals , nonmetals. Open symbols indicate T-values estimated from sedimentation rates. The sohd line indicates the linear regression fit, and the dashed curves show the Working-Hotelling confidence band at the 0.1% significance level. The horizontal broken line indicates the time required for one stirring revolution of the ocean, T. ...

Figure 1.4.3-1 does not reflect the uncertainties in the analysis Figure 1.4.3-2 addresses this deficiency by presenting envelopes at the 5, 50, and 95% confidence levels. Of course, including confidence intervals on all curves, e.g.. Figure 1.4.3-1 would be confusing. 

The lower bound confidence limit is the probability that a parameter, x, is less than some value x . The upper bound confidence limit is the probability that a parameter, x, is greater than some value x . Figure 2.5-1 shows that confidence may be obtained from the discrete curve by simply adding the probabilities below or above x, for the lower or upper bound confidence respectively. If the curve is continuous it must be integrated above or below x. These results are normalized, by dividing the partial integral or partial sum by the full integral of the curve or complete sum. 

Calculations of the confidence intervals about the least-squares regression line, using Eq. (2-100), reveal that the confidence limits are curved, the interval being smallest at Xj = x. 

To.xicity values for carcinogenic effects can be e.xprcsscd in several ways. The slope factor is usually, but not always, the upper 95th percent confidence limit of the slope of the dose-response curve and is e.xprcsscd as (mg/kg-day). If the extrapolation model selected is the linearized multistage model, this value is also known as the ql. That is ... 

FIGURE 6.6 Schilcl regression for pirenzepine antagonism of rat tracheal responses to carbachol. (a) Dose-response curves to carbachol in the absence (open circles, n = 20) and presence of pirenzepine 300 nM (filled squares, n = 4), 1 jjM (open diamonds, n=4), 3j.lM (filled inverted triangles, n = 6), and 10j.iM (open triangles, n = 6). Data fit to functions of constant maximum and slope, (b) Schild plot for antagonism shown in panel A. Ordinates Log (DR-1) values. Abscissae logarithms of molar concentrations of pirenzepine. Dotted line shows best line linear plot. Slope = 1.1 + 0.2 95% confidence limits = 0.9 to 1.15. Solid line is the best fit line with linear slope. pKB = 6.92. Redrawn from [5],... 

This value is identified in F tables for the corresponding dfc and dfs. For example, for the data in Figure 11.13, F = 7.26 for df=6, 10. To be significant at the 95% level of confidence (5% chance that this F actually is not significant), the value of F for df = 6, 10 needs to be > 4.06. In this case, since F is greater than this value there is statistical validation for usage of the most complex model. The data should then be fit to a four-parameter logistic function to yield a dose-response curve. 

Competitive antagonists affinity of, 261-264 description of, 75 IC50 correction factors for, 223 Schild analysis, 261-264 Concentration-dependent antagonism, 99 Concentration-response curve, 13 Confidence intervals, 228-229 Conformations, 13-14 Constitutive activity of receptors description of, 49—51 receptor density and, 56 Schild analysis, 108-111 Context-dependent biological effect, 188 Correction factors, 211-213, 223 Correlational research, 231 CP320626, 128... 

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