Experimental error sample size

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 experimentally, the sample size in the computation was allowed 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. 

The sampling of solution for activity measurement is carried out by filtration with 0.22 pm Millex filter (Millipore Co.) which is encapsuled and attached to a syringe for handy operation. The randomly selected filtrates are further passed through Amicon Centriflo membrane filter (CF-25) of 2 nm pore size. The activities measured for the filtrates from the two different pore sizes are observed to be identical within experimental error. Activities are measured by a liquid scintillation counter. For each sample solution, triplicate samplings and activity measurements are undertaken and the average of three values is used for calculation. Absorption spectra of experimental solutions are measured using a Beckman UV 5260 spectrophotometer for the analysis of oxidation states of dissolved Pu ions. 

We have successfully synthesized an inventory of polymers with this method. Table 7.4 summarizes viscosity and size data for select samples. The hydrodynamic radii (f h) measured by VIS and QELS agree within experimental error. 

The experimental design used was nested plots. Main plots had a total area of 100 m2 and were rectangular plots. The criterion used to determine sample size for each stratum was an estimation of AGB of trees with a diameter at breast height (dbh) >10 cm during pre-sampling (90% probability and 20% mean standard error). 

Figures 1 and 2 illustrate how the determination of false-positive and -negative inference errors varies with sample size. In Figure 1, the sample size is 50. To be 95 percent confident that an observed incidence difference between the experimental and control groups is really evidence of carcinogenicity rather than sampling variation, the difference in cancer rates between the two groups must be at least 23 percent.

In an earlier procedure applying universal calibration, viscosities of the four most concentrated fractions eluting about the peak were measured, and the intrinsic viscosities were plotted against count. The intrinsic viscosities of all the fractions were obtained by extrapolation of the plot for use in the calculations to obtain degree of polymerization (DP). In the present method the DP of each fraction is obtained from the relationship MW = (cod size/K)1/1+ derived from Benoit s concept and the Mark-Houwink equation. Results from the new procedure are in excellent agreement with those obtained independently on cotton by others. Anomalies in results obtained previously on some samples disappear while marked improvement is noted for others. The determination is speeded up greatly by computer processing of data, and experimental error is reduced. 

The steps of the analytical process are illustrated in Fig. 1-1. It is well known that in each step of this process experimental errors are possible. Furthermore, each analytical result contains at least some experimental error the relative size of this error increases considerably as the analyte concentration in the sample decreases. This general relationship is demonstrated in Fig. 1-6 for some selected environmentally relevant compounds. Because the majority of studies concerning the environment deals with trace or ultratrace analysis, this fact is very evident and important. 

With control of particle size and spacing as per annealing conditions, if one considers Eq. 3 it is possible to extract the critical superparamagnetic particle size. Figure 8 shows a plot of Hc as a function of particle size for FePt/C samples. As expected the coercivity asymptotically approaches a maximum value as the particle size increases. A fit to the data with Eq. 3 reveals that the superparamagnetic particle size for FePt is between 2 and 3 nm [6]. The value of the critical superparamagnetic size can be seen in the figure to be the same, within experimental error, for each of the volume fractions of carbon in the samples. 

Note that in this procedure the main decision required by the experimenter is the size of the dose. Of course, this will depend on the adsorption capacity of the sample and the number of experimental points desired. For a new, unknown sample, a first exploratory experiment with large doses is useful. Also, the fact that the final accuracy is an inverse function of the number of experimental points (because of the additivity of the errors made at each introduction of adsorptive) must be kept in mind. The introduction of the desired dose is made easier if the gas flow is restricted by a constriction or a needle valve. 

When two samples are veiy similar, t approaches zero when they are different, t approaches infinity. The value of f is used to calculate the P value using Student s f-test tables, given in the appendix of this book. The P value is tte probability that the two distribution means are the same that is, Aj = Ag. When the P value is greater than a critical accepted value (typically 5% [21] or the experimental error due to both sampling and size determination if it is lai ger) then the null hypothesis (Ho Aj = A2) is accepted (i.e., the two populations are considered to be the same). Ceramic powder size distributions are often represented by log-normal distributions and not by normal distributions. For this reason the t statistic must be augmented for use with lognormal distributions. Equation (2.59) can be modified for this purpose to... 

To examine the effect of phase separation on the loss modulus, a sample of a 50/50 chemical blend was phase separated by annealing at 130 C and then evaluated by DMS, Figure 8. Note that the unannealed 50/50 blend shows a broad transition similar to that obtained by DSC and by Hourston and Hughes (24). As compared to the unannealed blend, the annealed PVME/PS blend shows a broader transition. Similarly, the IPN has a still broader transition than the blend. However, the LA s for the three samples are relatively constant, 5%, agreeing also with theory. Table II. Note that overall experimental error is 10%. Also, it was observed that the phase separated blend has a milky white appearance whereas the IPN is slightly hazy. This indicates that the size of the phase separated domains in the IPN are smaller. 

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