A error

Interproton distances of 0-ceIIobiose (see Ref. 49) error 0.01 A. Interproton distances of 1,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.01 A. Interproton distances of -cellobiose octaacetate (see Ref. 49) error 0.05 A. Interproton distances of 2,3,4-tri-0-acetyl-l,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.05 A. Error calculations based on the errors of the measured quantities in Eqs. 18 and 21. Interproton distances calculated from the relaxation parameters of the methylene protons. 

Continuing from our previous discussion in Chapter 18 from reference [1], analogous to making what we have called (and is the standard statistical terminology) the a error when the data is above the critical value but is really from P0, this new error is called the [3 error, and the corresponding probability is called the (3 probability. As a caveat, we must note that the correct value of [3 can be obtained only subject to the usual considerations of all statistical calculations errors are random and independent, and so on. In addition, since we do not really know the characteristics of the alternate population, we must make additional assumptions. One of these assumptions is that the standard deviation of the alternate population (Pa) is the same as that of the hypothesized population (P0), regardless of the value of its mean. 

No definitive conclusions can be drawn concerning a possible role of rifaximin in preventing major complications of diverticular disease. Double-blind placebo-controlled trials with an adequate sample size are needed. However, such trials are difficult to perform considering the requirement of a large number of patients. Assuming a baseline risk of complications of diverticular disease of 5% per year [2], a randomized controlled trial able to detect a 50% risk reduction in complications should include 1,600 patients per treatment group considering a power of 80% (1 - (3) and an a error of 5%. 

The 11 points of the isochron diagram are drawn in Figure 5.13. Their respective error ellipse (1 a error) could be drawn using the method described in Section 2.4, but errors are too small for the ellipses to be clearly seen. 

This chapter has been divided into two different portions, namely (a) Errors in Pharmaceutical Analysis, and (b) Statistical Validation, which will be discussed individually in the following sections ... 

This type of error equates to box B and is variously described as a type I error, a false-positive error or the a error. A type I error in a study result would lead to the incorrect rejection of the null hypothesis. 

Nakatsuji and Yasuda [56, 57] derived the 3- and 4-RDM expansions, in analogy with the Green function perturbation expansion. In their treatment the error played the role of the perturbation term. The algorithm that they obtained for the 3-RDM was analogous to the VCP one, but the matrix was decomposed into two terms one where two A elements are coupled and a higher-order one. Neither of these two terms can be evaluated exactly thus, in a sense, the difference with the VCP is just formal. However, the structure of the linked term suggested a procedure to approximate the A error, as will be seen later on. 

Until now the focus has been on the construction algorithms for the 3- and 4-RDMs and the estimation of the A errors. However, the question of how to impose that the RDMs involved as well as the high-order G-matrices be positive must not be overlooked. This condition is not easy to impose in a rigorous way for such large matrices. The renormalization procedure of Valdemoro et al. [54], which was computationally economical but only approximate, acted only on the diagonal elements. 

Figure 3-28 H2O diffusion profile for a diffusion-couple experiment. Points are data, and the solid curve is fit of data by (a) error function (i.e., constant D) with 167 /irn ls, which does not fit the data well and (b) assuming D = Do(C/Cmax) with Do = 409 /im ls, which fits the data well, meaning that D ranges from 1 /rm /s at minimum H2O content (0.015 wt%) to 409 firn ls at maximum H2O content (6.2 wt%). Interface position has been adjusted to optimize the fit. Data are adapted from Behrens et al. (2004), sample DacDC3.

Suppose the truth is that = p,2> the treatments are the same. We would hope that the data would give a non-significant p-value and our conclusion would be correct, we are unable to conclude that differences exist. Unfortunately that does not always occur and on some occasions we will be hoodwinked by the data and get p < 0.05. On that basis we will declare statistical significance and draw the conclusion that the treatments are different. This mistake is called the type I error. It is the false positive and is sometimes referred to as the a error. 

The type I error was set at 5 per cent. Note in general the alternative phrases for the type I error significance level, a error, false positive rate. 

A. Error Bounds for the Response to a Damped Harmonic Perturbation. 85... 

Assume that the Student s /-test is applied to test whether or not there is an effect in one variable (for example, x4 = HOLE COUNT) of treatment with 0.05 mg/kg BHT compared with controls. The significance level 5% is then chosen, that is, 5% false positives (type I errors or a-errors) are accepted in the research. When one more measurement (x5 = HOLE TIME) is taken on the same set of data and Student s /-test is applied again to the data, the risk for at least one false positive is no longer 1.0 - 0.95 = 5% but 1.0 - 0.952 = 9.75%. When 10 variables are measured, as in the BHT 920 example, the risk is 1.0 - 0.9510 = 40.13% (a more detailed table has been published elsewhere [10]). This phenomenon is usually referred to as the increased risk of type I errors. 

Fig. 7.4. Deposition of particles in alveolar region (open symbols) and whole respiratory tract (closed symbols) (14 or 15 breaths/min by mouth, tidal volume 1.0 to 1.51). Experimental results of Chan Lippmann, 1980 (C>), Stahlhofen etal., 1980 ( ), Foord etal., 1978 (O), Pritchard etal., 1980 (A). Error bars are Is.e. Lines are theoretical calculations of Yu Diu, 1982.

Lorber A. Error propagation and figures of merit for quantification by solving matrix equations. Analytical Chemistry 1986, 58, 1167-1172. 

Here the only problematic parameter is the CCSD(T) FO bond length the DFT error was —0.051 A, still a bit outside our imposed 0.01-0.02 A error limits. The DFT geometry is fully high-quality. 

Fig. 35 Uranyl species in dependence on the measured pH value taking into account a error estimate (after Meinrath 1997)...

---