Upper confidence level

Fig. 3. Confidence limits for exposure levels. A, noncompliance B, possible overexposure C, compliance. STD is the standard value, LCL and UCL represent lower and upper confidence levels, between which it is 95% certain that the tme exposure Hes, and and correspond to two separate...

The EPA uses the linearized multistage model (LMS)—illustrated in Figure 9.34—to conduct its cancer risk assessments. It yields a cancer slope factor, known as the ql (pronounced Ql-star), which can be used to predict cancer risk at a specific dose. The LMS assumes a linear extrapolation with a zero dose threshold from the upper confidence level of the lowest dose that produced cancer in an animal test or in a human epidemiology study. 

Once again, field blanks and spiked field blanks are repetitively analyzed. The LOQ is determined as the concentration at which the lower confidence level of the mean of the spiked sample responses is at least four times greater than the upper confidence level for the mean blank response. 

Cleanroom standard The US Federal Standard 209E, Airborne Particulate Cleanliness Classes in Clean-rooms and Clean Zones, is required for manufacturers who want to conform to quality system regulation. Via the industrial ISO European Community, it has been integrated with ISO. Among the more important recent changes are metrication, revision of upper confidence level (UCL) requirement, provisions for sequential sampling, and an alternative verification procedure based on determination of the concept of ultra-fine particles known as U descriptors. 

There will be incidences when the foregoing assumptions for a two-tailed test will not be true. Perhaps some physical situation prevents p from ever being less than the hypothesized value it can only be equal or greater. No results would ever fall below the low end of the confidence interval only the upper end of the distribution is operative. Now random samples will exceed the upper bound only 2.5% of the time, not the 5% specified in two-tail testing. Thus, where the possible values are restricted, what was supposed to be a hypothesis test at the 95% confidence level is actually being performed at a 97.5% confidence level. Stated in another way, 95% of the population data lie within the interval below p + 1.65cr and 5% lie above. Of course, the opposite situation might also occur and only the lower end of the distribution is operative. 

The confidence limits for the slope are given by fc where the r-value is taken at the desired confidence level and (A — 2) degrees of freedom. Similarly, the confidence limits for the intercept are given by a ts. The closeness of x to X is answered in terms of a confidence interval for that extends from an upper confidence (UCL) to a lower confidence (LCL) level. Let us choose 95% for the confidence interval. Then, remembering that this is a two-tailed test (UCL and LCL), we obtain from a table of Student s t distribution the critical value of L (U975) the appropriate number of degrees of freedom. 

In this chapter as a continuation of Chapters 58 and 59 [1, 2], the confidence limits for the correlation coefficient are calculated for a user-selected confidence level. The user selects the test correlation coefficient, the number of samples in the calibration set, and the confidence level. A MathCad Worksheet ( MathSoft Engineering Education, Inc., 101 Main Street, Cambridge, MA 02142-1521) is used to calculate the z-statistic for the lower and upper limits and computes the appropriate correlation for the z-statistic. The upper and lower confidence limits are displayed. The Worksheet also contains the tabular calculations for any set of correlation coefficients (given as p). A graphic showing the general case entered for the table is also displayed. 

Studies in rats reported renal tubular adenomas and adenocarcinomas in male and female animals at doses of 20 mg/kg/day (Kociba et al. 1977a). Metastasis to the lungs was observed. Combined incidences of renal tubular neoplasms in males (9/39, 23%) and in females (6/40, 15%) increased (p <0.05) over controls (males-1/90, females-0/90, 0%). The tumor incidence was not increased in the 0.2 and 2 mg/kg/day dose groups but there were some indications of hyperplasia in animals exposed to 2 m /kg/day. The EPA (1990f) evaluated these data and calculated a human potency factor of 7.8x10 (mg/kg/day) (qi ), representing 95% upper confidence limit of extra lifetime human risk. Based on this value, cancer risk levels of 10, 10, and 10 correspond to exposures of 0.001, 0.0001, 0.00001 mg/kg/day. 

In Figure 8.14, the Cold El mass spectrum of corticosterone in methanol solution is shown in the upper trace, and is compared with the standard NIST 98 El library mass spectrum shown in the lower trace. Note the similarity of the library mass spectrum to that obtained with the SMB apparatus. All the major high mass ions of m/z 227, 251, 269, and 315 are with practically identical relative intensity and thus good library search results are enabled with the NIST library-matching factor of 829, and the reversed matching factor of 854% and 86.5% confidence level (probability) in corticosterone identification. In addition, the molecular ion at m/z 346 is now clearly observed while it is practically missing in the library (very small in the shown mass spectrum and absent in the other three replicate mass spectra). 

Max., maximum level found L UCL, lower and upper confidence limits... 

These decision rules can be generalized to permit easy comparison between OSHA decisions and NIOSH decisions by defining several new terms. Let UAL represent the upper action level, which is to be used in place of the standard. Let OK represent an acceptable workplace and let NOT OK represent an unacceptable workplace. Let P indicate the probability that the indicated decision is made. Thus, P( ) represents the probability that a decision cannot be made with sufficiently high confidence on the basis of one breathing zone sample. Under these definitions, the decision rules become ... 

The critical value of CVp has to be lower than the maximum permissible true value (e.g. lower than CVp 0.128 when there is no bias). The maximum permissible value of the true CVp will be referred to as its "target level". In order to have a confidence level of 95% that a subject method meets this required target level, on the basis of CVp estimated from laboratory tests, an upper confidence limit for CVp is calculated which must satisfy the following criterion reject the method (i.e. decide it does not meet the accuracy standard) if the 95% upper confidence limit for CVp exceeds the target level of CVp. Otherwise, accept the method. This decision criterion was implemented in the form of the Decision Rule given below which is based on assumptions that errors are normally distributed and the method is unbiased. Biased methods are discussed further below. 

As would be expected, in order to be able to have at least 95% confidence that the true CV p does not exceed its target level, we must suffer the penalty of sometimes falsely accepting a "bad" method (i.e. one whose true CV p is unsatisfactory). Such decision errors, referred to as "type-1 errors", occur randomly but have a controlled long-term frequency of less than 5% of the cases. (The 5% probability of type-1 error is by definition the complement of the confidence level.) The upper confidence limit on CV p is below the target level when the method is judged acceptable... 

Example Suppose you are attempting to observe a process that should produce 1 decay per week, and you observe no counts (with a 100% efficient detector) in 4 weeks. At the 95% confidence level, the upper limit on the decay rate is... 

To use the acceptance limits proposed by CuDAL, an acceptance limit table is generated to give the upper bound on the sample RSD for various values of the sample mean. For this example, the table was constructed for capsule content uniformity using a 90% confidence level with a lower bound (LBOUND) of 95%. A portion of the acceptance limit table is as follows ... 

For a 90 percent confidence level, the upper limit of the confidence interval is 104 mg/kg, still exceeding the action level. 

Student s t-test is frequently used in statistical evaluations of environmental chemical data. It establishes a relationship between the mean (x) of normally distributed sample measurements, their sample standard deviation (,v), and the population mean (p). Confidence intervals may be calculated based on Student s t-test (Equation 10). The upper limit of the confidence interval is compared to the action level to determine whether the sampled medium contains a hazardous concentration of a pollutant. If the upper confidence limit is below the action level, the medium is not hazardous otherwise the opposite conclusion is reached. 

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