Concentration confidence limit

Da.ta. Ana.lysls. First, the raw data must be converted to concentrations over an appropriate time span. When sample periods do not correspond to the averaging time of the exposure limit, some assumptions must be made about unsampled periods. It may be necessary to test the impact of various assumptions on the final decision. Next, some test statistics (confidence limit, etc) (Fig. 3) are calculated and compared to a test criteria to make an inference about a hypotheses. 

Acute toxicity studies are often dominated by consideration of lethaUty, including calculation of the median lethal dose. By routes other than inhalation, this is expressed as the LD q with 95% confidence limits. For inhalation experiments, it is convenient to calculate the atmospheric concentration of test material producing a 50% mortaUty over a specified period of time, usually 4 h ie, the 4-h LC q. It is desirable to know the nature, time to onset, dose—related severity, and reversibiUty of sublethal toxic effects. 

The model of simple competitive antagonism predicts that the slope of the Schild regression should be unity. However, experimental data is a sample from the complete population of infinite DR values for infinite concentrations of the antagonist. Therefore, random sample variation may produce a slope that is not unity. Under these circumstances, a statistical estimation of the 95% confidence limits of the slope (available in most... 

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],... 

The LC50 refers to the wastewater concentration which results in 50 percent mortality under the test conditions (see text). It is an extrapolated value with varying confidence limits. In the work summarized here confidence limits were quite variable and often could not be calculated due to insufficient data points. Nevertheless the data satisfies the primary intent of the tests as a screening tool. 

Figure 2.8. The slopes and residuals are the same as in Figure 2.4 (50,75,100, 125, and 150% of nominal black squares), but the A -values are more densely clustered 90, 95, 100, 105, and 110% of nominal (gray squares), respectively 96, 98, 100, 102, and 104% of nominal (white squares). The following figures of merit are found for the sequence bottom, middle, top the residual standard deviations +0.00363 in all cases the coefficients of determination 0.9996, 0.9909, 0.9455 the relative confidence intervals of b +3.5%, +17.6%, 44.1%. Obviously the extrapolation penalty increases with decreasing Sx.x, and can be readily influenced by the choice of the calibration concentrations. The difference in Sxx (6250, 250 resp. 40) exerts a very large influence on the estimated confidence limits associated with a, b, Y(x), and X( y ).

The Production Department was not amused, because lower values had been expected. Quality Control was blamed for using an insensitive, unse-lective, and imprecise test, and thereby unnecessarily frightening top management. This outcome had been anticipated, and a better method, namely polarography, was already being set up. The same samples were run, this time in duplicate, with much the same results. A relative confidence interval of 25% was assumed. Because of increased specificity, there were now less doubts as to the amounts of this particular heavy metal that were actually present. To rule out artifacts, the four samples were sent to outside laboratories to do repeat tests with different methods X-ray fluorescence (XRFi °) and inductively coupled plasma spectrometry (ICP). The confidence limits were determined to be 10% resp. 3%. Figure 4.23 summarizes the results. Because each method has its own specificity pattern, and is subject to intrinsic artifacts, a direct statistical comparison cannot be performed without first correcting the apparent concentrations in order to obtain presumably true... 

At each concentration xj the relative confidence limits 100 t Sy/ymeanj found for the group of Mj repeat determinations is plotted and connected (dashed lines). Because file VALID2.dat contains only duplicate determinations at each concentration, n = 2 and / = 1, thus t(f, p = 0.05) = 12.7, the relative CL are mostly outside the 30% shown. By pooling the data for all 6 days it can be demonstrated that this laboratory has the method under control. 

The mean, the standard deviation, and the confidence limits of the population at each concentration with multiple measurements are calculated and tabulated. 

FIGURE 9.4 Relationship between scope for growth and whole tissue concentration of 2-and 3-ring aromatic hydrocarbons in Mytilus edulis (mean 95% confidence limits). A, Data from Solbergstrand mesocosm experiment, Oslo Fjord, Norway. , Data from Sullom Voe. Shetland Islands (Moore et al. 1987). 

Develop a table of R values for various concentrations that span the range of concentrations of Interest. (A similar approach makes use of confidence limits based on the standard deviation rather than the range.)... 

Rather than have one antibody that can detect a class, a third approach is to analyze a sample using multiple immunoassays, each with a known cross-reactivity spectrum, and determine the concentration of the analytes and confidence limits... 

By making replicate analytical measurements one may estimate the certainty of the analyte concentration using a computation of the confidence limits. As an example, given five replicate measurement results as 5.30%, 5.44%, 5.78%, 5.00%, and 5.30%. The precision (or standard deviation) is computed using equation 73-1,... 

A deviation from linearity is observed in the calibration curve at higher lead concentrations. The estimated value for the original sample was found to be 0.51 xg/l, with confidence limits at the 95% confidence level of 0.036 pg/1, compared with a value of 0.65 0.08 ig/l obtained by anodic scanning voltammetry. This value is well within the normal range reported in the literature for the natural lead content of unpolluted seawater. A detection limit of 0.03 ng ml"1 was obtained. 

Where the test is conducted as a limit test, the specimen is determined to be positive or negative to the test judged against the endotoxin concentration specified in the individual monograph. Where the test is conducted as an assay of the concentration of endotoxin, with calculation of confidence limits of the result obtained, the specimen is judged to comply with the requirements if the result does not exceed (1) the concentration limit specified in the individual monograph and (2) the specified confidence limits for the assay. In either case the determination of the reaction endpoint is made with parallel dilutions of redefined endotoxin units. 

FIG.2 95% confidence limits for odour concentration as a function of panel size and number of replicates... 

Minimize the confidence limit or variance of a given parameter, such as a Michaelis constant. This requires picking a point or points in concentration space where the value of the parameter is maximally sensitive to the experimental result obtained, i.e., a kinetic constant basically representing the binding of a small... 

FIGURE 11-6 Ozone concentration vs. duration of exposure required to produce a S% response in three diffinent plant susceptibility groupings. The curves were generated by developing 95% confidence limits around the equations for all plants in each susceptibility grouping from Table 11-25. Qirves a > sensitive plants, b intermediate ants, c > resistant plants. 

Selected entries from Methods in Enzymology [vol, page(s)] Generation, 240, 122-123 confidence limits, 240, 129-130 discrete variance profile, 240, 124-126, 128-129, 131-133, 146, 149 error response, 240, 125-126, 149-150 Monte Carlo validation, 240, 139, 141, 146, 148-149 parameter estimation, 240, 126-129 radioimmunoassay, 240, 122-123, 125-127, 131-139 standard errors of mean, 240, 135 unknown sample evaluation, 240, 130-131 zero concentration response, 240, 138, 150. 

Geometric means of estimates of concentrations of immunoglobulins (lU/ml with 95% confidence limits)... 

Confidence intervals nsing freqnentist and Bayesian approaches have been compared for the normal distribntion with mean p and standard deviation o (Aldenberg and Jaworska 2000). In particnlar, data on species sensitivity to a toxicant was fitted to a normal distribntion to form the species sensitivity distribution (SSD). Fraction affected (FA) and the hazardons concentration (HC), i.e., percentiles and their confidence intervals, were analyzed. Lower and npper confidence limits were developed from t statistics to form 90% 2-sided classical confidence intervals. Bayesian treatment of the uncertainty of p and a of a presupposed normal distribution followed the approach of Box and Tiao (1973, chapter 2, section 2.4). Noninformative prior distributions for the parameters p and o specify the initial state of knowledge. These were constant c and l/o, respectively. Bayes theorem transforms the prior into the posterior distribution by the multiplication of the classic likelihood fnnction of the data and the joint prior distribution of the parameters, in this case p and o (Fignre 5.4). 

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