Statistical analysis confidence limits

Further statistical procedures can be applied to determine the confidence limits of the results. Generally, only the values for the mean and standard deviation would be reported. The reader is referred to any good statistical text to expand on the brief analysis presented here. 

The models with insignificant overall model regression as indicated by the F -value and with meaningless parameter estimates (with confidence limits) as indicated by r-values should be rejected. If rejection of the parameter does not lead to a physically nonsensical model stmcture, repeat parameter estimation and statistical analysis. 

A brief study of the available data related to limits of inflammability in Part Two shows that these parameters are subject to high experimental uncertainty. For a large number of substances, the experimental values are widely dispersed. When they are submitted to quality estimation using statistical tools, in many cases they reveal that it is impossible to use them with confidence. The examples of difficulties raised by the statistical analysis of the LEL data can be multiplied. 

In any book, there are relevant issues that are not covered. The most obvious in this book is probably a lack of in-depth statistical analysis of the results of model-based and model-free analyses. Data fitting does produce standard deviations for the fitted parameters, but translation into confidence limits is much more difficult for reasonably complex models. Also, the effects of the separation of linear and non-linear parameters are, to our knowledge, not well investigated. Very little is known about errors and confidence limits in the area of model-free analysis. 

An approach for analyzing data of a quantitative attribute that is expected to change with time is to determine the time at which the 95% one-sided confidence limit for the mean curve intersects the acceptance criterion. If analysis shows that the batch-to-batch variability is small, it is advantageous to combine the data into one overall estimate by applying appropriate statistical tests (e.g., p-values for level of significance of rejection of more than 0.25) to the slopes of the regression lines and zero-time intercepts for individual batches. If it is inappropriate to combine data from several batches, the overall shelf life should be based on the minimum time a batch can be expected to remain within the acceptance criteria. 

These limitations on the statistical inference of species contributions to the particle light extinction coefficient raise several questions (i) Is the statistical analysis of filter data a valid method for determining species contributions to the extinction coefficient of atmospheric aerosols (ii) Can we place confidence limits on the quality of the statistical results and (iii) Can the quality of the statistical results be enhanced through improved sampling techniques ... 

VARICOMP. A method for evaluating the interface between fuze expl conponents in which it can be determined by statistical analysis and testing that the reliability and safety of a fuze expl train can be predicted at high-confidence levels with a small number of tests. This is done by varying the sensitivity of different expls that are then substituted into the expl train of interest to determine the safety and reliability limits under a penalty test situation... 

The previous discussion of standard deviation and related statistical analysis placed emphasis on estimating the reliability or precision of experimentally observed values. However, standard deviation does not give specific information about how close an experimental mean is to the true mean. Statistical analysis may be used to estimate, within a given probability, a range within which the true value might fall. The range or confidence interval is defined by the experimental mean and the standard deviation. This simple statistical operation provides the means to determine quantitatively how close the experimentally determined mean is to the true mean. Confidence limits (Lj and L2) are created for the sample mean as shown in Equations 1.6 and 1.7. 

Subtract the volume of titrant required for the blank from the titrant required for the sample. The difference represents the volume of DCIP that is equivalent to 0.50 mg of vitamin C. Calculate the standard deviation of your answer. What are the limits for 95°/o confidence Review Chapter 1, Section F for statistical analysis. 

APPENDIX VIII Values of t for Analysis of Statistical Confidence Limits 453... 

Accuracy. The more accurate the sampling method the better. Given the very large environmental variability, however, sampling and analytical imprecision is rardy a significant contribution to overall error, or width of confidence limits, of the final result. Even highly imprecise methods, such as dust count methods, do not add much to overall variability when the variability between workers and overtime is considered. An undetected bias, however, is more serious because such bias is not considered by the statistical analysis and can, therefore, result in gross unknown error. 

Data Analysis. 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. 

Again, the minimum and maximum loading configurations should be studied. Thermocouples will be placed both inside and outside the container at the cool spot location(s), in the steam exhaust line, and in constant-temperature baths outside the chamber. The F0 value will be calculated based on the temperature recorded by the thermocouple inside the container at the coolest area of the load. Upon completion of the cycle, the F0 value will indicate whether the cycle is adequate or if alterations must be made. Following the attainment of the desired time-temperature cycle, cycles are repeated until the user is satisfied with the repeatability aspects of the cycle validation process. Statistical analysis of the F0 values achieved at each repeated cycle may be conducted to verify the consistency of the process and the confidence limits for achieving the desired F0 value. 

Statistical analysis of the aroma and taste threshold values in Table I showed that within 95% confidence limits there was no difference between aroma and taste threshold values for all compounds but four. Octanal and citral had aroma threshold values significantly higher than the corresponding taste threshold values. Nonanal and trans-2-hexenal had higher taste threshold than aroma threshold values. 

Effective concentration of a test material in the test matrix (eg., growth medium) that is calculated to exhibit a specified non-lethal or lethal effect to x% of a group of test organisms during exposure over a specified period of time. The ECx and its 95% confidence limits are usually derived by statistical analysis of responses in several test concentrations. The particular effect must be specified as well as the exposure time (e.g., 48-h EC50 for immobilization). Volume 1(1,4,10). 

Stability data (not only assay but also degradation products and other attributes as appropriate) should be evaluated using generally accepted statistical methods. The time at which the 95% one-sided confidence limit intersects the acceptable specification limit is usually determined. If statistical tests on the slopes of the regression lines and the zero-time intercepts for the individual batches show that batch-to-batch variability is small (e.g., p values for the level of significance of rejection are more than 0.25), data may be combined into one overall estimate. If the data show very little degradation and variability and it is apparent from visual inspection that the proposed expiration dating eriod will be met, formal statistical analysis may not be necessary. 

An equivalence approach has been and continues to be recommended for BE comparisons. The recommended approach relies on (1) a criterion to allow the comparison, (2) a confidence interval (Cl) for the criterion, and (3) a BE limit. Log-transformation of exposure measures before statistical analysis is recommended. BE studies are performed as single-dose, crossover studies. To compare measures in these studies, data have been analyzed using an average BE criterion. This guidance recommends continued use of an average BE criterion to compare BA measures for replicate and nonreplicate BE studies of both immediate- and modihed-release products. 

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