Sample size reduction

Six samples were taken daily during three non-consecutive days within one week to achieve an average weekly composition. The sample size of every subsample of BA had to be defined based on considerations of a particulate pollutant (e.g., heavy metals) concentration rather than that of a diffusive pollutant distribution. A sample size reduction scheme (Fig. 1) was defined according to the study of Bunge Bunge (1999) depending on grain size and concentration of particulate pollutants. From the 18 collected subsamples,... 

Fig. 1. Sample size reduction scheme, considering particle size of particulate pollutants (e.g., Pb as metal droplet) and pollutant concentration of the bulk sample.

To acquire a representative sample, one must develop and implement a suitable sampling plan. A good sampling plan includes (i) population determination and sample size selection and (ii) sample collection procedure and sample size reduction method. In addition, one needs an infrastructure to maintain the integrity of the samples and sampled materials. To begin with, a brief introduction to the sampling theory and terminology is in order. 

When it is not possible to obtain samples comparable to the ideal size, appropriate sample size reduction techniques must be employed to obtain representative sample for analysis. For random mixtures, the sample variance is inversely proportional to the sample size. For a certain composition of noninteracting particulate and a given sample size, there exists a minimum theoretical value of standard deviation that can be achieved through random mixing. If the chosen sample size is very small, one must take a large number of samples to reduce the uncertainty in determination of mean mixture property (Student s t-test). 

Sample Size Reduction. The sample obtained from the sampler is generally larger than the sample required for analysis. If a small portion of this sample is arbitrarily scooped for analysis, it will introduce a bias. The sample size can be reduced to the analytical size using various sample reduction techniques (1) spinning riffler, (2) chute riffler, (3) ICI method, and so on. All these methods follow the golden rules for sampling. For details on these sample reduction techniques, see AUen (1981). 

E. Goodrich have burned a 10% tire chip mixture with coal (11—13). Tire grinding size reduction problems and deflvery costs have stymied projects based on combined tire and coal fuel. Transportation of tire scrap can cost 0.05 /kg, exclusive of grinding costs, thus tire-fired boilers are limited to areas with sample scrap tire suppHes, eg, large cities or tire manufacturers. The cost of burning one metric ton of tires per hour in an incinerator was ca 0.20—0.40 per tire in 1974, which increased to 0.35—0.70 per tire in 1987 (14). 

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. 

IAEA/AL/095 1996). Both methods were suitable, but needed to be repeated several times to produce the small particle size that was required. The particle size reduction, e.g. of IAEA-395 from a median size of 30 pm to 3.5 pm, improved the homogeneity of elements. Sampling constants (the minimum mass that can be used to achieve a random error of i % at the 65 % confidence level) improved from a factor of 1.2 for Sc, up to a factor of 800 for Au. The average improvement was about a factor of 2-10. (Ni Bangfa et al. 1996). From these initial experiences, it is dear that preparation of reference materials is critical with respect to the final particle size distribution, which should exhibit a low maximum (<50 pm) and a narrow range in particle sizes. Milling techniques to meet such criteria are available today, and materials that show intrinsic uniformity are particularly suitable to achieve the desired properties. 

To obtain representative samples from nonhomoge-neous sample materials, such as polymer compounds, particle-size reduction techniques need often to be applied (not for film) [50]. Also, for destructive inpolymer additive analysis it is advantageous to change the physical state of solid samples to provide a larger surface area per unit mass. Complete extraction is sometimes achieved only after grinding the sample. Typically, Perlstein [51] has reported recoveries of only 59 % for extraction of Tinuvin 320 from unground PVC after 16 h of Soxhlet extraction with diethyl ether while recoveries rise to 97 % for ground polymer. 

Miniaturisation of scientific instruments, following on from size reduction of electronic devices, has recently been hyped up in analytical chemistry (Tables 10.19 and 10.20). Typical examples of miniaturisation in sample preparation techniques are micro liquid-liquid extraction (in-vial extraction), ambient static headspace and disc cartridge SPE, solid-phase microextraction (SPME) and stir bar sorptive extraction (SBSE). A main driving force for miniaturisation is the possibility to use MS detection. Also, standard laboratory instrumentation such as GC, HPLC [88] and MS is being miniaturised. Miniaturisation of the LC system is compulsory, because the pressure to decrease solvent usage continues. Quite obviously, compact detectors, such as ECD, LIF, UV (and preferably also MS), are welcome. 

Purify the thiolated antibody by gel filtration using a desalting resin. Perform the chromatography using 0.1M sodium phosphate, 0.15M NaCl, pH 7.2, containing lOmM EDTA as the buffer. To obtain efficient separation between the reduced antibody and excess reductant, the sample size applied to the column should be at a ratio of no more... 

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%. 

Yamamoto et al. [33] applied this technique to the determination of arsenic (III), arsenic (V), antimony (III), and antimony (V) in Hiroshima Bay Water. These workers used a HGA-A spectrometric method with hydrogen-nitrogen flame using sodium borohydride solution as a reductant. For the determination of arsenic (III) and antimony (III) most of the elements, other than silver (I), copper (II), tin (II), selenium (IV), and tellurium (IV), do not interfere in at least 30 000-fold excess with respect to arsenic (III) or antimony (III). This method was applied to the determination of these species in sea water and it was found that a sample size of only 100 ml is enough to determine them with a precision of 1.5-2.5%. Analytical results for surface sea water of Hiroshima Bay were 0.72 xg/l, 0.27 xg/l, and 0.22 xg/l, for arsenic (total), arsenic (III), and antimony (total), respectively, but antimony (III) was not detected. The effect of acidification on storage was also examined. 

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