Confidence range

This distribution belongs to a standard model, Dixon s test does not give rise to an unrealistic value (hence the normality). The calculation of the confidence range of the individual values in this sequence then leads to ... 

The residual standard deviation is Sr = 5.558, the forecast standard deviation is Sq = 5.63 in the middle of the experimental domain. The coefficient of the linear correlation is r = 0.9966. The table below gives some examples of estimations compared with the extreme experimental values found in literature. The confidence range at 95% of the forecast is added in order to show the quality of the estimate. 

The confidence range of the intercept (Cr aj) and slope (Cr bj) from the recovery curves are calculated for p = 0.05, as described in Fig. 5. These confidence ranges... 

The P value defined by limestones, dolostones, marbles and seawater is consistent with equilibrium fractionation between aqueous Mg and carbonate Mg (Fig. 8, Table 3). The best-fit P is 0.524 + 0.006 (2a) with the 95% confidence range of 0.517-0.531. The data included in the regression represent an eclectic group of rocks, including three samples of marble (with the lowest A Mg values near chondritic). However, there is some support for the equilibrium... 

Range - confidence range for the activity value, in log units... 

When required uncertainty should be reported (confidence range e.g. 95 %)... 

Figure 10.7 Simulated AUC at steady state for five potential clinical candidate compounds. Symbols give the mean prediction while lines indicate a 95% confidence range [6],...

Figure 6. Comparison of the concentrations of many oxides in ancient pottery and in modern pottery and clays from Teotihuacan. Average concentrations (—) and 95% confidence ranges ( ) of 23 ancient sherds. Average concentrations (%) in two modem pottery plus two clay specimens.

Note that the confidence range of the mean is much smaller than the confidence range of a single value. So the result is more useful, but as uncertain as before. 

By analogy with the confidence range of a single value or a mean, we can calculate a confidence interval for a single predicted value according to ... 

For a small sample size and a particular confidence level other than GAUSSian distribution, the STUDENT /-distribution has to be assumed. Furthermore, the confidence range for the estimate x is ... 

The points of intersection between the highest value of a random correlation and the lower limit of the confidence interval of the corresponding empirical model function according to Eq. 9-4 correspond to the lower limits of the confidence range of the critical distances between the sampling points. These values are represented in Tab. 9-2. 

Tab. 9-2. Critical distances, lcrit, between sampling points and estimated values of the lower limit of the confidence range, lcrit iom for a critical error probability of a = 0.05...

Such an iterative procedure has been worked out in detail by Drouen et al. [576]. Refinements of the method using the phase selection diagram discussed above include the use of normalized resolution products (see section 4.3.2), shifted compositions and confidence ranges. 

Confidence ranges may be defined around each experimental data point by the following equation ... 

Hence, in the initial situation the confidence ranges stretch from 0 to about 0.03 and from about 0.97 to 1. 

However, when more data points become available, the size of the confidence ranges quickly increases. From eqn.(5.19) we see that the confidence interval will equal Ax/2 when the square root equals zero, i.e. when... 

Although voice lessons help increase a chance of being chosen for a part in the community play, they look at other elements, including appearance, confidence, range and enunciation. 

Fig. 2. Relationship of observed AUQnf values for XYZ1234 plasma-profiles versus dose,with linear regression (bold line), and the 95 % confidence range (dashed line).

The confidence interval on the slope can be calculated from the variance of the slope in the same manner as was used to determine the confidence range for the mean. Thus for a 95 percent confidence interval on the slope... 

Example 14 Analysis of linear regression. What is the confidence range of the slope and the mean of the dependent variable for a 95 percent confidence level in Example 13 ... 

The analysis of a flue gas gives the following CO, volume content 23.8, 23.4, 24.1, 24.6, 23.9, and 23.1. What is the confidence interval for the true mean for a probability level of 0.95 and 0.99 How much could the confidence range be improved if the number of analyses were doubled assuming the original distribution remained unchanged ... 

The bond distances in solid P406 [1.653(3) A] are larger than those determined for gaseous P406 [1.638(3) A]. However, the confidence ranges for the bond length distributions still overlap. 

Fig. 6.3 97.5th percentile exposure estimate (with a 95% confidence range) for the three age groups for BADGE using the Food Standards Agency, Food Surveillance Information Sheet 9, November 2000. Median dietary exposure estimate 0.04 tg/kg bw/day (0.03-0.053 tg/kg bw/day) (Hohnes et al. 2005). 

---