Subsample Size Research Articles

Preliminary assessment of homogeneity of new candidate agricultural/food reference materials

In an effort to bring to the analytical community new natural matrix reference materials (RM's) for elemental composition quality control, ten new agricultural/food candidate reference materials prepared previously, were characterized for homogeneity. The materials include bovine muscle powder, whole egg powder, corn bran, microcrystalline cellulose, wheat gluten, whole milk powder, corn starch and three wheat flours representing a wide range of matrix types and elemental composition. Characterization was for up to some twenty five major, minor, trace and ultratrace elements of nutritional, toxicological and environmental significance. Solid sampling electrothermal atomic absorption spectrometry was applied to the determination of copper and lead in sub-milligram subsamples. A variety of other analytical techniques via an interlaboratory cooperative effort was used to determine many other elements in 100–2000 mg subsample sizes. Good material homogeneity was observed for virtually all materials and analytes with the exception of Cr and Pb in limited instances. The materials were thus deemed suitable for detailed characterization of elemental concentration to lead to recommended values and to bring these biological products to reference material status.

Surname versus gene structure of a small isolate

A hierarchical partition of the Wright coefficient of inbreeding (F) is shown for an isolated population (about 2000 inhabitants) from a mountainous region of Tuscany (Italy) with regard to both surnames and genes. At total population level surname variation proves substantially consistent with the observed genetic differentiation of the isolate. Analysis of parental isonymy reveals that the population is structured in subunits and it is concluded that the unit population of the region may be very small, practically coinciding with the village (less than 500 inhabitants). The agreement of 'demographic' and genetic structures is less satisfactory at this level, partly because of subsample size, but we conclude that analysis of surnames may give at least a rough idea of the genetic structure of the population.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type 11 error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

A program for the computation of power and determination of sample size in hierarchical experimental designs

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the ‘ordinary’ case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Two-level Numerical Sampling Plans and Optimal Subsample Size Computations for Urophora affinis and Urophora quadrifasciata (Diptera: Tephritidae) on Spotted Knapweed

Taylor's power law analysis was performed on among- and within-subsample mean and variance estimates of the number of Urophora affinis Frauenfeld and Urophora quadrifasciata (Meigen) galls per spotted knapweed seed head. Highly significant correlation coefficients suggested that Taylor's power relationship fits the data well. A comparison of the b parameters from Taylor's analyses suggested that the spatial dispersion of U. affinis was more clumped than that of U. quadrifasciata. The spatial dispersion of U. quadrifasciata appeared to become more uniform in the presence of U. affinis. Means and estimated variances (among and within subsamples) were used to develop numerical sampling equations for the two fly species. A cost (work effort) analysis was performed on the among- and within-subsample units. Optimal subsample sizes calculated for overall mean gall densities of U. affinis and U. quadrifasciata (averaged over all sampling sites) were 18.95 and 21.86 seed heads per subsample, respectively. To protect against sampling low population sites, it is recommended that 15 subsamples of 25 seed heads each be collected per sampling site and used to assess population levels of the two fly species. Information presented in this paper should improve accuracy and efficiency in future sampling of U. affinis and U. quadrifasciata and aid in determining those sites warranting future releases of the flies.

Gender identity and gender transposition: longitudinal outcome study of 24 male hermaphrodites assigned as boys.

The longitudinal case histories of 24 male-assigned male hermaphrodites aged 18 or older were indexed and abstracted for the presence or absence of variables related to gender transposition, namely, bisexualism, homosexuality, or sex reassignment to live as a female. The sample was biased in favor of cases (N = 20) not showing signs of gender transposition. In these cases, there was no gender transposition even if the following variables were in evidence; neonatal ambivalence in announcing the sex; cosmetic inadequacy of masculine genital appearance; sitting posture for urination; and feminizing (N = 9) instead of virilizing (N = 11) puberty. Despite the small size of the minority subsample (N = 4), it showed a trend toward an association between gender transposition and sitting to urinate, and being stigmatized in childhood. This trend is consistent with the association between stigmatization and gender transposition found in a counterpart study of male hermaphrodites announced and reared as girls. Freedom from gender transposition did not prevent suicidal depression, drug or alcohol addiction, marital failure, or death from testicular cancer.

Determination of total tin in National Research Council of Canada marine reference materials

An intralaboratory determination of total Sn in three National Research Council of Canada reference materials, i.e., estuarine sediments BCSS-1 and MESS-1 and lobster hepatopancreas TORT-1 was undertaken. Samples were solubilized by acid mineralization and analyzed by stable isotope dilution inductively coupled plasma mass spectrometry, direct solution injection graphite furnace atomic absorption spectrometry (GFAAS), and hydride generation-GFAAS. The materials were homogeneous at the 500 mg subsample size. Good agreement was obtained amongst the results from the three instrumental methods of analysis. Certified values of total Sn in these materials are 1.85 ± 0.20 μg/g in BCSS-1, 3.98 ± 0.44 μg/g in MESS-1, and 139 ± 11 ng/g in TORT-1. The above uncertainties represent 95% tolerance limits for an individual (500 mg) subsample.

Predictive species-area relations and determination of subsample size for vegetation sampling in the Transvaal Waterberg

An expression for predicting the number of species in a given area is described. Derivatives of this expression, to increase sampling efficiency in a vegetation stand, include a minimum of four separate subsamples; a maximum number of subsamples when less than 10% increment in new species is achieved; and subsample size. It is also suggested that species diversity in terms of species per unit area can be more consistent when derived from this expression. ’n Uitdrukking om die aantal spesies vir ’n bepaalde gebied te voorspel word beskryf. Afleidings van hierdie uitdrukking, om doeltreffendheid by die monsterneming van ’n plantegroeistand te verbeter, sluit die volgende in: ’n minimum van vier afsonderlike submonsterpersele; ’n maksimum aantal submonsterpersele wanneer die nuwe spesiesaanwas minder as 10% is; en submonsterperseelgrootte. Dit word ook voorgestel dat spesies diversiteit, ooreenkomstig spesies per eenheidoppervlakte, meer konsekwent kan wees wanneer dit van hierdie uitdrukking afgelei word.

A generalized quantile estimator under censoring

Based on right-censored data from a lifetime distribution F0 a smooth alternative to the product-limit estimator as a nonparametric estimator of a population is proposed; The estimator is a generalized product-limit quantile obtained by averaging appropriate subsample product-limit quantiles over all subsamples of a fixed size. Under the random censorship model and some conditions on Fop it is shown that the estimator is consistent and has the same asymptotic normal distribution as the product-limit estimator. A small Monte Carlo simulation study shows that there exist some values of the subsample size for which the estimator performs better than the product-limit estimator in the sense of estimated mean squared errors.

Meiofaunal foraminiferans from the bathyal Porcupine Seabight (northeast Atlantic): size structure, standing stock, taxonomic composition, species diversity and vertical distribution in the sediment

Living benthic Foraminifera in Multiple Corer samples collected at 1320–1340 m in the Porcupine Seabight have been evaluated using standard meiofaunal techniques. The preponderance of tiny individuals (45–106 μm) is believed to reflect both the small subsample size (3.46 cm 2) and the examination of very fine sieve fractions. Standing crops (1246–2324 live specimens per 10 cm 2) are higher than normally reported from the deep sea. This is attributed to (a) the abundance of specimens in the rarely studied 45–62 μm size fraction, (b) the virtually undisturbed nature of the sediment-water interface collected by the Multiple Corer, and (c) the care taken to extract obscure, tectinous and agglutinated forms from the residues. Most of the important species have hyaline, calcareous tests (suborder Rotaliina) or multilocular or unilocular agglutinated tests (suborder Textulariina). However, forms with proteinaceous tests (suborder Allogromiina) and various hitherto unrecognized foraminiferans which occupy empty globigerinacean shells are also abundant. Diversity is high (94–124 species per subsample) but relatively few species are common, and about half are represented by single individuals, a pattern often found in the deep sea. Within the upper 5 cm of sediment, most foraminiferans (52.3–71.0%) occur in the top 1 cm, there being a steeper than linear decrease in density below this level. Unilocular agglutinated species are concentrated in the top 1 cm, hyaline, calcareous species are proportionally more abundant between 1 and 3 cm, and multilocular agglutinated species increase in relative abundance below 3 cm. Some of the abundant species are concentrated in the surface layer (0–1 cm), while others peak between 1 and 3 cm; a few rare species occur mainly below 3 cm. It is suspected that this tendency towards vertical segregation results from biotic interactions rather than the influence of chemical or physical factors.

The Choice of Subsample Size in Two-Stage Sampling

Abstract This article presents a simple method for choosing the subsample size m in two-stage sampling when the values of the relevant design parameters, the variance ratio and the cost ratio, are not known exactly but can only be assumed to lie within some specific range. Measuring the efficiency of a choice of m by its precision relative to the optimum choice, which depends on the parameters, it is proposed to choose m so that its minimum efficiency, over the specified range of parameters, is maximized. The value of m under this maximin criterion, and its minimum efficiency, are derived. A simple practical rule is also given. The usefulness of the method is discussed and illustrated with examples.

The Choice of Subsample Size in Two-Stage Sampling

Abstract This article presents a simple method for choosing the subsample size m in two-stage sampling when the values of the relevant design parameters, the variance ratio and the cost ratio, are not known exactly but can only be assumed to lie within some specific range. Measuring the efficiency of a choice of m by its precision relative to the optimum choice, which depends on the parameters, it is proposed to choose m so that its minimum efficiency, over the specified range of parameters, is maximized. The value of m under this maximin criterion, and its minimum efficiency, are derived. A simple practical rule is also given. The usefulness of the method is discussed and illustrated with examples.

Some tests for the constancy of regressions under heteroscedasticity

For testing the equality of coefficients of a linear regression model under heteroscedasticity, we suggest an F criterion conditioned on the posterior mean of the ratio of standard deviations of error terms in two subsamples. For pairable subsamples, and exact F test is derived. Sampling experiments show that the Chow test differs substantially from the nominal significance level when the two subsample sizes are unequal, and that the F test conditioned on the posterior mean is superior to other tests when sample sizes are small.

Subsampling program for the estimation of fish impingement

Federal regulations require operators of nuclear and coal-fired power-generating stations to estimate the number of fish impinged on intake screens. During winter months, impingement may range into the hundreds of thousands for certain species, making it impossible to count all intake screens completely. We present graphs for determinig the appropriate“optimal” subsample that must be obtained to estimate the total number impinged. Since the number of fish impinged tends to change drastically within a short time period, the subsample size is determined based on the most recent data. This allows for the changing nature of the species-age composition of the impinged fish. These graphs can also be used for subsampling fish catches in an aquatic system when the size of the catch is too large to sample completely.

Statistical consequences of reducing the number of rabbits utilized in eye irritation testing: Data on 67 petrochemicals

Data from 67 six-rabbit eye irritation tests were used to generate two-, three-, and four-rabbit Draize scores. The 15 two-rabbit, 20 three-rabbit, and 15 four-rabbit “subsample” scores for each of the 67 petrochemicals tested were used to establish prediction intervals for the original six-rabbit scores. Prediction interval length shortens with increasing sample size, is widest in the middle portion of the Draize scale, and can be used to select the minimum number of rabbits necessary to satisfy a required level of precision. Also, the ability of each subsample size to correctly classify the test materials according to an in-house irritation classification system was evaluated. Results indicate that subsamples of size 2, 3, 4, and 5 were 88, 93, 95, and 96% accurate, respectively (compared to six rabbits), at correctly classifying the irritation potential of the materials tested.

Estimation of the size of freshwater ciliate populations by a sub-sampling technique

A technique is described for the estimation of the size of ciliate populations based on replicated counts. Sample drops were taken by automatic pipettes of different volume from activated sludge and from a small oligotrophic stream. Specific aims were: 1) the estimation of the number of species; 2) the estimation of the number of individual in each species; 3) the selection of a suitable sub-sample size and number of replicates. For each volume the cumulative increase in species taken in successive sub-samples was determined. For each species the minimum permissible sub-sample volume and the number of replicates required for an allowable error of 10% and 25% were determined. Lastly, the relationship between the mean number of individuals counted for each species and the relative coefficient of variation was visualized.

Prescriptive relationship levels for juvenile delinquents in a psychotherapy analog

Prescriptive relationship levels for juvenile delinquents in a psychotherapy analog

Selection of Subsample Sizes for the Box-Scheffé Test of Homogeneity of Variance

Power and stability of Type I error rates are investigated for the Box-Scheffe test of homogeneity of variance with varying subsample sizes under conditions of normality and nonnormality. The test ...

Estimating the Population Sizes of Different Types of Organisms in a Plankton Sample

Estimation of the sample or population size N has recently been examined by several authors. We consider a problem related to the estimation of tlle binomial parameter N. Biologists are interested in estimating the population sizes of different types of organisms in a plankton sample from their counts in the subsamples. A method is presented for determining subsample sizes for the different types of organisms in the original sample. Also, the maximum likelihood estimators of the population sizes and their asymptotic properties are examined. Plankton ecologists find that often the organisms are not distributed randomly in the plankton sample but form clumps. We propose a test for investigating this clustering; also, the interval estimation problem of the organism count is examined when clustering is present. Finally, we illustrate the results using plankton samples from the Chesapeake Bay.

Apparatus for Measuring and Subsampling Digesta in Ruminants Equipped with Reentrant Intestinal Cannulas2

A completely automated device for quantitatively measuring and sampling digesta entering the proximal duodenum of cattle is described. The system operates according to volume of flow from intestinal reentry cannulas. Size of subsample, frequency of sampling and rate of digesta return may be varied according to experimental objectives. The apparatus has the following features: (1) digesta temperature control, (2) a rotary sample collector to obtain individual subsamples, and (3) an event recorder to indicate flow cycle time parameters. The system described was constructed for cattle and may be used with animals standing or lying in the special holding crate. The apparatus has logged in excess of 1,900 hr of continuous collection (53 periods of 36 hr each) with only minor malfunction. Repetitive sampling of pooled digesta has produced coefficients of variation for volume, dry matter flow and percentage dry matter in digesta samples of 2.68, 2.81 and 1.81%, respectively. On the basis of incomplete recovery (range 71 to 97%) of chromic oxide from animals during collection periods (24 hr fed vs 24 hr recovery at duodenum), it is suspected that some inhibition to normal flow through the cannula occurs during sampling. Experiments have been conducted in which several parameters of interest were measured and total collection of digesta was compared via spot sampling (500 ml digesta at 6-hr intervals for 48 hr). When corrected to 100% chromic oxide recovery, differences between techniques for estimates of total digesta flow, organic matter and nitrogen entering the duodenum were small and not significant.