Standard deviation in time

The time constant (r) affects both the height and the width of the observed peaks. It can be shown [708,709] that (for r<0.2 ctc) the observed standard deviation in time units (a,) increases with r according to... 

For each of the columns in table 7.2 the hold-up time (t0) can readily be calculated from eqn.(7.6) using k=0. The standard deviation in time units follows from t0 after division by vN (eqn.1.16). Eqns.(7.35) and (7.36) then provide the maximum allowable detection time constant (r), the required sample frequency for digital data handling (/) and the required number of datapoints (Ndat) for recording a chromatogram (0 < k< 4). All these characteristics are shown for the different columns in the bottom part of table 7.2. 

Figure 5.5. A Gaussian zone emerges from a column. In the time r the zone is displaced one standard deviation or through the column end. Time r is thus the standard deviation in time units.

The degree of synchronization can be characterized by the standard deviation in time of the spatially averaged concentration... 

To determine an averaged value of the profile standard deviations in time units, consider an averaged value of the profile standard deviations in length unit... 

In Eq. (9-223), Cqh — 0Cboh) E known as the budgeted overhead-cost variance, 0(cboh oh). s the overhead-volume variance, and voh(Q Q ) 3.S the overhead-efficiency variance. The last is analogous to the labor-efficiency variance and is the standard overhead rate multiplied by the deviation in time taken to produce a given output. 

The closeness of agreement between independent results obtained with the same method on identical test material but under different conditions (different operators, different apparatus, different laboratories, and/or after different intervals of time). The measure of reproducibility is the standard deviation qualified with the term reproducibility as reproducibility standard deviation. In some contexts reproducibility may be defined as the value below which the absolute difference between two single test results on identical material obtained under the above conditions may be expected to lie with a specified probability. Note that a complete statement of reproducibility requires specification of the experimental conditions which differ. 

Figure 17 Permeability of uranine ( ), dextran 4.4K (O), and dextran 150K (A) through cross-linked poly(/V-isopropyl acrylamide-co-butyl methacrylate, 95 5 mol%) membrane. Error bars represent standard deviation in the slope of the curve of the receiver concentration of solute as a function of time at steady state. (From Ref. 37.)...

Tablets and capsules that became available on the market in the above time frame often showed 10-20% relative standard deviation in amounts dissolved. The FDA s St. Louis Laboratories results on about 200 different batches of drugs...

The changes are minimal the computation of the SVD, calculation of Yred, and using Yred and Ared for the computation of the standard deviations. Computation times are similar in fact, depending on the dimensions of the matrices, more time is wasted for the Singular Value Decomposition than gained by the data reduction. 

We need this standard deviation in dimensionless time units if we are to find D. Therefore... 

For the determination of the intralaboratory repeatability of the DR CALUX bioassay for sediment samples, two sediment extracts were analyzed 10 times. Each analysis was performed in triplicate. As a prerequisite for a correct triplicate analysis, the percentage standard deviation in the triplicate determination should be below 15%. This is in accordance with the harmonized quality criteria for eell-based bioassay analyses of PCDDs/PCDFs in feed and food as formulated by Behnisch et al. (Behnisch et al, 2001 a) and as detailed in European Union directive 2002/69/ EC and direetive 2002/70/EC. The repeatability for the low-2,3,7,8-TCDD-content sediment... 

Enter the measured mean value of y for replicate measurements of the unknown in cell B18. In cell B19, enter the number of replicate measurements of the unknown. Cell B20 computes the value of x corresponding to the measured mean value of v. Cell B21 uses Equation 4-27 to find the uncertainty (the standard deviation) in the value of x for the unknown. If you want a confidence interval for x, multiply sv times Student s t from Table 4-2 for n — 2 degrees of freedom and the desired confidence level. 

Starting with either 1-butene or 1-pentene the conversion (x) was measured as a function of time (t). Plots of log (xe — x) vs. t were linear (8) at all temperatures, demonstrating that the reactions were first order in time. From the slopes of these plots the sums (k2i + k31) were calculated, and when combined with the data plotted in Figure 1 (Z i/A x), they allowed the calculation of the absolute values of the rate constants. The values of k21 and k31 for each olefin are plotted against 1000/77 in Figure 2. The differences in activation energies (AEtj) and the absolute values of E2i and E i were calculated from the experimental points represented in Figures 1 and 2, respectively. These values and their standard deviations in kcal/mole, were obtained by a computer fit and are summarized in Table II. 

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