Sample size equivalence

All samples of l-14C-acetylated SRL and SRC were weighed in combustocones and mixed with cellulose to insure a slow and uniform oxidation. The samples were then oxidized in a Packard Model 306 automatic sample oxidizer for subsequent liquid scintillation measurement of 002 Problems such as sample solubility and color quenching usually experienced in liquid scintillation counting were eliminated by this procedure. Chemical quenching is minimized and chemllumlnesence is entirely eliminated. Because of this counting efficiency is increased and quench correction is unnecessary. For carbon-14 the oxidizer can accommodate a sample size equivalent up to 40 millimoles of CO2... 

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

More modern systems (diffractometers) follow the same principles but the diffracted X-rays are detected with a solid state detector, as described earlier. Typically, the X-ray source is static and the sample and detector are rotated, with the detector moving at twice the angular velocity of the sample to maintain the equivalent angle. Such instruments typically make use of relatively large samples compressed into the window of a 35 mm sample holder. However, where the sample size is restricted, as is common with archaeological applications, a smaller sample (a few mg) can be attached to a silica wafer. In all cases the sample needs to be hnely ground to ensure a uniform diffracted beam. 

Comparisons between AAS instruments and the Jerome show statistically equivalent results. The Jerome gives accurate results for samples with a mercury content of less than 1 ppb and requires less work space, set up time, chemical reagents and sample size. 

The sample size and sample allocation scheme is obtained in one of two ways. Either the cost is fixed and the variance of the mean is minimized or the variance is fixed and the cost is minimized. The first approach is used when the budget for sampling and analysis is determined in advance. The objective in this case is to use that budget to obtain an estimate with maximum precision (equivalently minimum variance). The second approach is used when the required precision of the estimator is specified in advance. Then the objective is to derive an estimator with the desired level of precision at the lowest possible cost. 

Thus, given an ensemble generated by a particular (non-ideal) simulation, possibly consisting of a great many "snapshots," the key conceptual question is To how many i.i.d. configurations is the ensemble equivalent in statistical quality The answer is the effective sample size [1,9,10] which will quantify the statistical uncertainty in every slow observable of interest — and many "fast" observables also, due to coupling, as described earlier. 

Although conventional p-values have no role to play in equivalence or noninferiority trials there is a p-value counterpart to the confidence intervals approach. The confidence interval methodology was developed by Westlake (1981) in the context of bioequivalence and Schuirmann (1987) developed a p-value approach that was mathematically connected to these confidence intervals, although much more difficult to understand It nonetheless provides a useful way of thinking, particularly when we come later to consider type I and type II errors in this context and also the sample size calculation. We will start by looking at equivalence and use A to denote the equivalence margins. 

A linear regression procedure (Figure 5) showed that 1-L batch LLE is equivalent to 1-L CLLE with and without humics present. Some compounds showed lower recoveries for 38-L CLLE than for 1-L CLLE, but statistical evaluation of this result was not possible because only one 38-L extraction was run for each condition (with and without humics). The third experiment was designed to address the effect of sample size on solute recovery and further investigate the effect of humic materials on solute recovery. 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

A response factor is a ratio of signal-to-sample size. There are two kinds of response factors. Some response factors are numbers used in calculating the quantities required in a chemical analysis. They can be in any convenient form, including the inverse, that is, sample size divided by signal. They may, if desired, involve an internal standard, take account of efficiency of sample workup, or be expressed in arbitrary units. The response factors considered here, however, are meant to characterize detectors. They should be independent of carrier flow, Fc and the units of sample size should reflect the way the detector works. For any particular detector, there are two ways to define response factor, depending on whether peak height, S, and peak width W, are measured, or whether an integrator makes areas. A, available. They can be shown to be equivalent to the extent that SW/2 = A. 

The sample volume is a critical factor in planning a gel chromatography experiment. If too much sample is applied to a column, resolution is decreased if the sample size is too small, the solutes are greatly diluted. For group separations, a sample volume of 10 to 25% of the column total volume is suitable. The sample volume for fractionation procedures should be between 1 and 5% of the total volume. Column total volume is determined by measuring the volume of water in the glass column that is equivalent to the height of the packed bed. 

Purify the reduced IgG by gel filtration using Sephadex G-25 or the equivalent. Perform the chromatography using 0.1 M sodium phosphate, 0.15 M NaCl, pH 7.2, containing 10 mM EDTA as the buffer. To obtain efficient separation between the reduced antibody and excess reductant, the sample size applied to the... 

A few values of the t-distribution are given in an accompanying table. We note that t values are considerably higher than corresponding standard normal values for small sample size but as n increases, the t-distribution asymptotically approaches the standard normal distribution. Even at a sample size as small as 30, the deviation from normality is small, so that it is possible to use the standard normal distribution for sample sizes larger than 30 (n>30) and in most cases, for n<30 t-distribution is used. This is equivalent to assuming that Sx is an exact estimate of ox at large sample sizes (n>30). 

In an experiment to determine the effects of sample size and amount ofliquid phase on the height equivalent to a theoretical plate (HETP) in gas chromatography, it was necessary to utilize solid support material from different batches. It was therefore imperative that the resulting data be checked for homogeneity prior to attempting to develop any quantitative expressions regarding the effects of these variables on HETP. Several sets of data points were selected at random and examined using Bartlett s test. 

Consider two examples from previous chapters that illustrate this. In Chapter 9, discussions of sample-size estimation emphasized that the process is indeed one of estimation rather than pure calculation. A calculation is certainly executed, but the values that are placed into the appropriate formula are chosen by the sponsor. On each occasion, the sponsor must consider the influences of the choices that are made and make the most appropriate decision in the specific context of that trial. In Chapter 11, equivalence and noninferiority designs were discussed. In addition to the calculations that are involved using the data collected in a trial, equivalence or noninferiority margins must be established before the trial commences. Their choice is a clinical choice, not a statistical choice, and subjectivity is necessarily involved in this choice. Thus, the discipline of Statistics certainly involves using informed judgments. Statistics really is an art as well as a science, a sentiment well expressed by Katz (2001) as cited in Chapter 13. 

Your instructor will weigh out 0.1 g of benzoic acid for sample size comparison. With your microspatula, take some sample equivalent to the preweighed sample (an exact quantity is not important here). Add the solid to a test tube (100 X 13 mm) along with... 

Before - identify the primary question, primary end-point and primary statistical analysis establish equivalence limits where necessary perform power and sample size calculations. 

Procedure Use a gas chromatograph equipped with a hotwire detector and a suitable sample-injection system or on-column injection. Under typical conditions, the instrument contains a 1/4-in. (od) x 6- to 8-ft column, or equivalent, maintained isothermally at 70° to 80°. The flow rate of dry carrier gas is 50 to 80 mL/min, and the sample size is 15 to 20 pL (for the hot-wire detector). The column selected for use in the chromatograph depends on the components to be analyzed and, to a certain extent, on the preference of the analyst. The columns 1, 2, 3, and 4, as described under Toluene, may be used as follows (1) This column separates acetone and methanol from their aqueous solution. It may be used for... 

---