Sample sizes

Sample Size. - The larger the sample, the more nuclei there are to detect, and hence the stronger the signal. The homogeneity of the magnetic field will, however, deteriorate over the whole sample volume, and resolution will be adversely affected. A further complication with solid samples is that the process of rapid spinning imposes very severe mechanical forces on the sample holder, and destruction thereof can become a problem. An optimum sample size is of the order of a few hundred milligrams. 

Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids , Oxford University Press, London, 1970. 

FIGURE 2.3 Comparison of three samples of indium, of varying mass, heated at 10°C/min. Hermetic pan with inverted lid. Nitrogen purge gas at 25 ml/min. Heat flow plotted against temperature. 

Summary of the Effect of Changing Sample Mass on the Transitions Measured by DSC 

Most previous studies have been carried out on samples that are too small to inspire confidence in the findings most have relied on samples of fewer than 20 cases. In the present investigation, more than 100 matched case-control pairs were compared. This provided an 80% chance of detecting a difference between groups of 0.40 standard deviations and a 90% chance of detecting a difference of 0.46 standard deviations, assuming that an effect exists. 

The final area of concern in the chromatographic process is the size of the fractions. Decreasing the fraction size does not increase the resolution of the column, but does allow realization of the full resolution capability of the column to be expressed. 

Resolution. Because of thermal gradients across a sample the faster the scan rate the lower the resolution, and the slower the scan rate the sharper the resolution. Thermal gradients can be reduced by reducing sample size and improving thermal contact with the pan by good encapsulation. 

Transition kinetics. Slow events such as a cure reaction may not complete if scaimed quickly and maybe displaced to a higher temperature where they can occur more rapidly. The kinetics of an event may need to be considered when choosing a scan rate. 

Time of analysis. Speed of analysis is an issue in many businesses, and higher rates speed up throughput. 

In many industrial areas, as well as food and agriculture, the amount of sample available to the analyst is not normally a limiting factor. However, in clinical chemistry the opposite applies, as no patient is willing to donate large volumes of blood for analysis Similarly in forensic work, the sample material may also be limited in size. Sample size is linked to the limit of detection. Improved detection levels can sometimes be achieved by taking a larger mass of sample. However, 

The numbers of animals used for a study is highly dependent upon the goals of the study, magnitude and direction of the measured effect, expected variation in the effect, desired significance level, and power (i.e., the probability of finding an effect—usually 80%) (Charan and Kantharia, 2013). For the purposes of this chapter, sample sizes for pharmacoge-netic studies will be the major focus. 

1 CC For the majority of studies conducted to date, panels of CC lines have been the standard model. Simulation analysis has proposed that an idealized minimum number of animals for a genetic study involving CC lines is 128 lines. For a QTL with additive effects, using 128 strains enables detection of a major QTL with an effect size of 0.25 and 90% power (Tsaih et al., 2005). For comparison, the same statistical model indicates that power is reduced to 60% when the CC panel is reduced to 64 strains. Another recent retrospective analysis included metrics of heritability, and the genetic coefficient of variation confirmed that it may be possible to identify a strong QTL that maps to a resolution as narrow as 1 Mb with as few as 100 CC lines (Iraqi et al., 2014). 

It should be mentioned that there are at least two types of genetic studies that have been proposed for CC lines. The 

MOUSE POPULATION-BASED TOXICOLOGY FOR PERSONALIZED MEDICINE AND IMPROVED SAFETY PREDICTION 

3 MDP The rule of thumb for MDP sample sizes is the more strains the better. In the past, successful studies have been completed using between 34 and 36 inbred strains (Harrill et al., 2009c). 

High-pressure, high-temperature solvent extraction 

---

Sample size is 100 ml and distillation conditions are specified according to the type of sample. Temperature and volume of condensate are taken simultaneously and the test results are calculated and reported as boiling temperature as a function of the volume recovered as shown in Table 2.1. 

MW frequency of 10 Hz. There are various considerations that influence the choice of the radiation frequency. Higher frequencies, which require higher magnetic fields, give inlierently greater sensitivity by virtue of a more favourable Boltzmaim factor (see equation (b 1.15.11)). However, several factors place limits on the frequency employed, so that frequencies in the MW region of the electromagnetic spectrum remain favoured. One limitation is the sample size at frequencies around 40 GHz the dimensions of a typical... 

Diffraction is not limited to periodic structures [1]. Non-periodic imperfections such as defects or vibrations, as well as sample-size or domain effects, are inevitable in practice but do not cause much difSculty or can be taken into account when studying the ordered part of a structure. Some other forms of disorder can also be handled quite well in their own right, such as lattice-gas disorder in which a given site in the unit cell is randomly occupied with less than 100% probability. At surfaces, lattice-gas disorder is very connnon when atoms or molecules are adsorbed on a substrate. The local adsorption structure in the given site can be studied in detail. 

In the next several sections, the theoretical distributions and tests of significance will be examined beginning with Student s distribution or t test. If the data contained only random (or chance) errors, the cumulative estimates x and 5- would gradually approach the limits p and cr. The distribution of results would be normally distributed with mean p and standard deviation cr. Were the true mean of the infinite population known, it would also have some symmetrical type of distribution centered around p. However, it would be expected that the dispersion or spread of this dispersion about the mean would depend on the sample size. 

Diagonal lines connecting the two axes show combinations of sample size and concentration of analyte containing the same absolute amount of analyte. As shown in Figure 3.6, for example, a 1-g sample containing 1% analyte has the same amount of analyte (0.010 g) as a 100-mg sample containing 10% analyte or a 10-mg sample containing 100% analyte. 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Sampling of a large population n = 900) of colored candies (M M s work well) is used to demonstrate the importance of sample size in determining the concentration of species at several different concentration levels. This experiment is similar to the preceding one described by Bauer but incorporates several analytes. 

Finally, we note that the size and shape of the particles of the packing, the packing technique, and column dimensions and configuration are additional factors which influence a GPC experiment. In addition, the flow rate, the sample size, the sample concentration, the solvent, and the temperature must all be optimized. Details concerning these considerations are found in analytical chemistry references, as well as in the technical literature of instrument manufacturers. 

Barcol Indenter. The Barcol hardness tester is a hand-held, spring-loaded instmment with a steel indenter developed for use on hard plastics and soft metals (ASTM D2583) (2). In use the indenter is forced into the sample surface and a hardness number is read direcdy off the integral dial indicator caUbrated on a 0 to 100 scale. Barcol hardness numbers do not relate to nor can they be converted to other hardness scales. The Barcol instmment is caUbrated at each use by indenting an aluminum ahoy standard disk suppHed with it. The Barcol test is relatively insensitive to surface condition but may be affected by test sample size and thickness. 

Numerous collections of herbicide analysis methods have been pubUshed (276—279). An increased emphasis has been placed on the first step in the environmental sampling process, that of obtaining a representative, uncontaminated sample. If this is to be accompUshed, consideration must be made of such factors as sample size and location (280—283). After the sample has been obtained, it must be stored in such a way as to minimize degradation. This generally consists of refrigeration, possibly preceded by some type of drying (284). 

Success Testing. Acceptance life tests ate sometimes planned with no failures allowed. This gives the smallest sample size necessary to demonstrate a rehabiUty at a given confidence level The rehabiUty is demonstrated relative to the test employed and the testing period. 

LLDPE can present a certain health hazard when it bums, since smoke, fumes, and toxic decomposition products are sometimes formed in the process. Exposure to burning LLDPE can cause irritation of the skin, eyes, and mucous membranes of the nose and throat due to the presence of acrolein and formaldehyde (81). Toxicity of LLDPE pyrolysis products depends on temperature, heating rate, and the sample size (82—84). 

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). 

The quantity of sample required comprises two parts the volume and the statistical sample size. The sample volume is selected to permit completion of all required analytical procedures. The sample size is the necessary number of samples taken from a stream to characterize the lot. Sound statistical practices are not always feasible either physically or economically in industry because of cost or accessibiUty. In most sampling procedures, samples are taken at different levels and locations to form a composite sample. If some prior estimate of the population mean, and population standard deviation. O, are known or may be estimated, then the difference between that mean and the mean, x, in a sample of n items is given by the following ... 

If the standard deviation of the lot caimot be estimated, a sampling program of greater sample size is required to generate an estimate of the standard deviation for future sampling operations. In some cases, sample size can be increased and sampling costs reduced by the use of automatic samplers. These offer a substantial reduction in labor costs but an increase in capital costs. 

Technique Detection limits, ppb Precision, % Sample size, mL Econ omy Multie lemen t Dyna mic range Matri X interfe rence Spectr al interfe rence Refrac tories... 

Instead of calculations, practical work can be done with scale models (33). In any case, calculations should be checked wherever possible by experimental methods. Using a Monte Carlo method, for example, on a shape that was not measured experimentaUy, the sample size in the computation was aUowed to degrade in such a way that the results of the computation were inaccurate (see Fig. 8) (30,31). Reversing the computation or augmenting the sample size as the calculation proceeds can reveal or eliminate this source of error. 

This separation technique has been employed primarily for preparative types of separations because detailed knowledge of the properties of the sample is required. Also, because this separation results in discrete zones of sample ions which are virtually pure, it makes sense to use this technique when the sample size is large. This technique is ineffective when the levels of impurities are small with respect to the target compound small amounts of sample ions do not form zones well and tend to mix with the target compound. Information on this technique is available (30). 

In applications sample sizes are usually small and O unknown. In these cases, the t distribution can be used where... 

Since the t distribution relies on the sample standard deviation. s, the resultant distribution will differ according to the sample size n. To designate this difference, the respec tive distributions are classified according to what are called the degrees of freedom and abbreviated as df. In simple problems, the df are just the sample size minus I. In more complicated applications the df can be different. In general, degrees of freedom are the number of quantities minus the number of constraints. For example, four numbers in a square which must have row and column sums equal to zero have only one df, i.e., four numbers minus three constraints (the fourth constraint is redundant). 

---