Confidence interval length

The sets of technically and statistically acceptable results are represented in the form of bar-charts of which an example is given for Cu in Figure 3.1. The length of a bar corresponds to the 95 % confidence interval of the mean. The certified values... 

In this notation, N d is the number of independent samples contained in the trajectory, and fsim the length of the trajectory. The standard error can be used to approximate confidence intervals, with a rule of thumb being that + 2SE represents roughly a 95% confidence interval [26]. The actual interval depends on the underlying distribution and the sampling quality as embodied in Nfd fSimA/ see ref. 25 for a more careful discussion. 

Our considerations are valid only for error-free observations since with errors in A the inequalities (1.87) are not necessarily true. It is far from easy to extend this method to the real situation. In (ref. 19) the authors increased each observed A values by the half-length of the confidence intervals (for definition see Chapter 3), i.e., replaced (1.87) by inequalities... 

We can usually estimate or measure the random error associated with a measurement, such as the length of an object or the temperature of a solution. The uncertainty might be based on how well we can read an instrument or on our experience with a particular method. If possible, uncertainty is expressed as the standard deviation or as a confidence interval, which are discussed in Chapter 4. This section applies only to random error. We assume that systematic error has been detected and corrected. 

The subject population covariate plays a special role in PK similarity assessment, similar to that of formulation in BE assessment. That is, if the influence of formulation on the rest of the parameters Ka, V, CL, etc.) is not adequately represented in the model, then the model will underrepresent the formulation influence on the predictions of PK parameters and may bias the BE assessment results. To further illustrate this, the conventional model building procedure might find the formulation factor insignificant in the model, and if the final model contains no formulation factor, it will predict the AUC and Cmax ratios to be 1 with certainty, that is, producing confidence intervals of length 0. Thus, BE would have to be declared by default. This is clearly unacceptable from the standpoint of traditional BE assessment, which often finds the formulation term insignificant in ANOVA but always produces confidence intervals of positive lengths for the AUC and Cmax ratios. 

Kinjo et al. (1996) compared cancer death rates for a cohort (1,351 cases) of MD survivors with those of a referent population (5,667 subjects) who hved in the same region of Japan and consumed fish daily. After adjusting for age, gender, and length of follow-up period, they found no excess relative risk (RR) for overall mortality, all cancer deaths combined, or all noncancer deaths combined. Analysis of site-specific cancers found that Minamata survivors were less likely to die of stomach cancer than the referent population (RR, 0.49 95% confidence interval (Cl), 0.26-0.94). However, on Ae basis of five observed deaths, survivors were eight times more likely than the referent population to have died from leukemia (RR, 8.35 95% Cl, 1.61-43.3). 

With knowledge of the variances of the measured variables, one can compute the variance of the pressure drop per unit length. The computed variance can then be used to determine confidence intervals or perform hypothesis tests. 

Analysis of data obtained in experiments usually starts with the estimation of statistical measures that characterize the range, the mean value, the variance of the data, and their confidence intervals. Sometimes, when the experiment concerns the identification of changes in the distribution of the dependent factor, such as fibre length or fibre diameter distribution, the analysis continues with the estimation of the skewness and kurtosis, which are measures of the distribution symmetry and sharpness, respectively. Table 1.3 summarizes equations for the calculation of statistical measures. In this table Xi,X2,. ..,x . ..,x are individual measurements or observations for a sample of n measurements. 

It is clear from Equation 2.9 that the length of the confidence interval is linearly proportional to the population standard deviation, and inversely related to the square root of the sample size. If o were known. Equation 2.9 could be used to determine the minimum sample size required to obtain a confidence interval which will contain the unknown mean p, with a (1-cc) probability. An expression for the minimum sample size will, therefore, be... 

A practical approximation can be done considering the ratio L /S in Equation 2.14 and estimating the population mean for a given confidence interval, such that its length be equal to a certain multiple of S. In such a manner, an initial determination of the sample size is possible. By rearranging terms in Equation 2.14, the following relationship can be obtained ... 

Calculates the 100(1—alpha)% mean confidence intervals for the nonlinear function, Fun, given the values of x, x the estimated coefficients, beta the residuals, r and the covariance matrix, eovarb. The function returns the predicted y-values, y, and the half-width lengths, delta. This implies that the mean confidence interval will be given as y delta. 

Too Short Simulation Runs Attempting to save time makes even more dependent upon initial conditions. Therefore, correct length depends upon the accnracy desired (confidence intervals). 

Finally, the sample mean, X, constitutes a so-called point estimate of the mean, fi, of the population horn which the sample was selected at random. Instead of a point estimate, an interval estimate of p, may be required along with an indication of the confidence that can be associated with the interval estimate. Such an interval estimate is called a confidence interval, and the associated confidence is indicated by a confidence coefficient. The length of the confidence interval varies directly with the confidence coefficient for fixed values of n, the sample size the larger the value of n, the shorter the confidence interval. Thus, for fixed values of the confidence coefficient, the limits that contain a parameter with a probability of 95% (or some other stated percentage) are defined as the 95% (or that other percentage) confidence limits for the parameter the interval between the confidence limits is referred to as the aforementioned confidence interval. ... 

A prospective, observational study of 131 critically ill patients intubated with succinylcholine in an intensive care unit (ICU) showed that significant increase in potassium concentration (>=6.5 mmol/L) was related to the length of ICU stay (p<0.001) and the presence of acute cerebral pathology (p=0.047) [S -J.The threshold of 16days was found to be highly predictive of acute hyperkalaemia> 6.5 mmol/L with 37% (95% confidence interval 19-58%). 

To simulate the on-line RUL estimation problem, the actual time is gradually replaced by 30 h towards the failure. After each replacement, more information about the deterioration is achieved and the diagnostic and prognostic procedures are re-implemented. Figure 7 represents the mean value of the estimated RUL associated with the 95% confidence interval. It can be realized that, at the early instances, the lack of information due to the limited observations results inthe bias and large variance in the RUL estimation. However, the actual values always he within the 95% confidence interval. As the time passes, the length of the... 

Detailed testing plan test length, number of samples, confidence intervals, acceleration factors, test environment... 

Quantitative ATs are used to obtain information about the failure-time distribution and degradation in a relatively short period of time (usually weeks or months) by accelerating the use environment. In most cases a model to describe the relationship between failure mechanism and accelerating variables already exists. They are also well-suited for finding dominant failure mechanisms and are usually performed on individual assemblies rather than full systems. In order to set up a quantitative AT, severd different parameters must be known, for example test length, number of samples, desired confidence intervals, field and test environment, stress-life relationship and distribution model. 

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