Large Numbers Of Small Samples Research Articles

Testing the hypothesis of the normality of the falling number of oatmeal in small samples

Verification of the hypothesis of the normality of small samples is required to establish whether the empirical distribution obtained belongs to the theoretical distribution. The condition for testing the hypothesis of normality for a set of small independent samples is the presence of a sufficient number of them with the same volume. In this case, it is possible to test the hypothesis of the normality of the general aggregates from which the studied samples were taken, assuming that the parameters of these aggregates have different values. When testing the hypothesis of normality for a large number of small samples, only one value of the first, second, etc. measurements is randomly selected from each sample, thereby allowing simplification and random selection of data. The object of this study is small samples of the falling number of oat flour used in bakery production in the development of bakery products. The purpose of this work was to test the hypothesis of normality for small samples of the experiment using the nonparametric criterion of agreement ω2 of the smallest of each of the four definitions of the incidence number, since rounding the values of direct measurements excludes the random nature of the quantity or its normal distribution in favor of a uniform one. It was found that at a significance level of p = 0?05, the table value (nω2)1-p is greater than the calculated value of nω2 for all four definitions, hence the hypothesis of the normal distribution of small samples for all four definitions (as random variables) of the falling number of oatmeal does not deviate. The results obtained in this work are consistent with the generally accepted classical concepts of testing the statistical hypothesis of the normal distribution of samples. The statistical method provides sufficient accuracy of the studied indicator in technical systems and does not require the synthesis of a statistical criterion to test the hypothesis of the normality of small sample.

Nanotube abundance from non-negative matrix factorization of Raman spectra as an example of chemical purity from open source machine learning

The chemical purity of materials is important for semiconductors, including the carbon nanotube material system, which is emerging in semiconductor applications. One approach to get statistically meaningful abundances and/or concentrations is to measure a large number of small samples. Automated multivariate classification algorithms can be used to draw conclusions from such large data sets. Here, we use spatially-mapped Raman spectra of mixtures of chirality-sorted single walled carbon nanotubes dispersed sparsely on flat silicon/silicon oxide substrates. We use non-negative matrix factorization (NMF) decomposition in scikit-learn, an open-source, python language “machine learning” package, to extract spectral components and derive weighting factors. We extract the abundance of minority species (7,5) nanotubes in mixtures by testing both synthetic data, and real samples prepared by dilution. We show how noise limits the purity level that can be evaluated. We determine real situations where this approach works well, and identify situations where it fails.

Breeders' Sensory Test: A new tool for early selection in breeding for tomato (Solanum lycopersicum) flavour

AbstractFor several decades, improved flavour has not been a main focus in tomato breeding because it is difficult and expensive to evaluate. Sensory panels are designed to assess flavour, but they are not able to evaluate large sample numbers typical for early breeding generations. Selection in the first segregating generation could enhance breeding for flavour by preventing the loss of favourable alleles. The efficiency of early selection is unknown due to the polygenetic inheritance of flavour. To address these issues, F2 plants from 32 crosses and their parents (910 individuals) were evaluated for aroma, sweetness and sourness with the Breeders' Sensory Test (small team and large number of small samples from individuals), as well as for physicochemical traits (total soluble solids, titratable acidity and dry matter), and volatile compounds in low‐input organic and hydroponic cultivation. Corresponding physicochemical and sensory traits were significantly correlated. For most of the studied traits, it was possible to select between single plants in the F2 generation. Thus, the Breeders' Sensory Test can be used as a new tool in breeding for flavour.

A new sampling technique for larval lamprey population assessment in small river catchments

Larval lampreys were sampled in a small river using a new method modified from the Surber bottom sampler for invertebrates. This method uses a rectangular dredge to sample a constant and small surface of sediments in soft substrate areas. It was compared to a classical point abundance sampling by electrofishing. Both methods generated large numbers of small samples encompassing the spatial heterogeneity of ammocoete distributions. However, the bottom sampler provided samples with higher abundance and was more efficient for small individuals. Furthermore, the equipment is cheap and the method is cost-effective, since it can be operated by only two people. It could therefore be applied at a large scale to collect information on lamprey populations and contribute to knowledge of their distribution, abundance and, in fine, to devise better conservation measures.

Saddlepoint approximation methods for testing of serial correlation in panel time series data

The saddlepoint method is used to approximate the tail probabilities of the lag one serial correlation coefficient α, of a zero mean, first-order auto-regressive process, for both large and small numbers of small samples, and to test for serial correlation in a first-order non-zero mean process. The formula for the tail probability due to Lugannani and Rice is extended to the current problem. In the case of the zero mean process, approximate tail probabilities are computed using our results, and are compared with the Edgeworth and normal approximations. Unlike the other two approximations, the saddlepoint approximation performs uniformly well over the whole range of tail probability values considered. For the testing of serial correlation in the non-zero mean process, the saddlepoint method used to obtain the P-values performs in a similar manner to the asymptotic normal approximation method used by Cox and Solomon [Cox, D.R. and Solomon, P.J. (1988). On testing for serial correlation in large numbers of small samples. Biometrika, 75, 145–148].

A Note on Testing for Serial Correlation in Large Number of Small Samples Using Tail Probability Approximations

A method of testing for serial correlation in large number of independent replications from short, first order autoregressive type time series with zero mean is considered. We use an approach via the Edgeworth expansion to compute the tail probability in order to test the null hypothesis of zero serial correlation at lag 1. Approximate tail probabilities are computed using our results to justify the theory.

Multiplexed RT-PCR for streamlined detection and separation of barley and cereal yellow dwarf viruses

Two novel multiplexed RT-PCR assays that can efficiently detect and distinguish among different barley and cereal yellow dwarf viruses (B/CYDVs) are described. The basic multiplex can produce two fragments simultaneously, a ∼830-bp fragment indicating the presence of the BYDV-PAV, BYDV-MAV, or BYDV-SGV viruses and a ∼372-bp fragment indicating the presence of the CYDV-RPV, BYDV-RMV, or BYDV-GPV viruses. The enhanced multiplex produces two additional fragments, which further differentiate between BYDV-PAV, BYDV-MAV, and BYDV-SGV. These assays fulfill the critical need for a streamlined diagnostic procedure for B/CYDVs that can be cost-effectively applied to large numbers of small samples. The assays are useful not only in the basic diagnosis of B/CYDVs, but also for studies examining the ecological roles of B/CYDVs in natural systems and for longer-term epidemiological studies of grasses and cereals.

Quantitative Statistical Assessment of Conditional Models for Synthetic Aperture Radar

Many applications of object recognition in the presence of pose uncertainty rely on statistical models-conditioned on pose-for observations. The image statistics of three-dimensional (3-D) objects are often assumed to belong to a family of distributions with unknown model parameters that vary with one or more continuous-valued pose parameters. Many methods for statistical model assessment, for example the tests of Kolmogorov-Smirnov and K. Pearson, require that all model parameters be fully specified or that sample sizes be large. Assessing pose-dependent models from a finite number of observations over a variety of poses can violate these requirements. However, a large number of small samples, corresponding to unique combinations of object, pose, and pixel location, are often available. We develop methods for model testing which assume a large number of small samples and apply them to the comparison of three models for synthetic aperture radar images of 3-D objects with varying pose. Each model is directly related to the Gaussian distribution and is assessed both in terms of goodness-of-fit and underlying model assumptions, such as independence, known mean, and homoscedasticity. Test results are presented in terms of the functional relationship between a given significance level and the percentage of samples that wold fail a test at that level.

DISTINCTION BETWEEN CLOSELYRELATED APPLE CULTIVARS OF THE BELLE-FLEUR FAMILY USING RFLP AND AFLP MARKERS

The Belle-Fleur family is a group consisting of mainly three old and distinct apple cultivars: Belle-Fleur de Brabant, Belle-Fleur de France and Belle-Fleur Large Mouche. The distinction of the three cultivars requires an expert evaluation of phenological characters of the tree and the fruits. In our experiment, we tried to correlate the pomological identification of the three Belle-Fleur cultivars with the identification obtained via RFLP and AFLP markers. For this study, nine trees supposedly identified as belonging to the Belle-Fleur family were selected and analysed using RFLP and AFLP protocols previously established in our laboratory. Results of molecular analyses were confronted to pomological observations. The observations performed on trees and fruits in the field during several years allowed to identify three of the nine trees as belonging to the cultivar Belle-Fleur de France, one tree as Belle-Fleur de Brabant cultivar and two trees as Belle-Fleur Large Mouche. Pomological observations could exclude the three other trees from belonging to the Belle-Fleur group. Results of the RFLP analysis appeared to confirm the pomological classification based on morphological observations, except for one tree of Belle-Fleur de France which presents similar RFLP patterns to Belle-Fleur de Brabant. In contrast, the AFLP results seem to match more perfectly with the morphological observations with a perfect matching between classes obtained by molecular and morphological profiles. Therefore, the AFLP appears to be a more powerful tool for the distinction of closelyrelated apple cultivars than RFLP. The results obtained using this method seem to be in closer agreement with morphological observations than those obtained with the RFLP method. Moreover, the AFLP analysis is less work-and time-consuming than the RFLP method and allows the study of large numbers of small samples, making it particularly wellsuited for routine identification.

Interpreting recruitment limitation in forests

Studies of tree recruitment are many, but they provide few general insights into the role of recruitment limitation for population dynamics. That role depends on the vital rates (transitions) from seed production to sapling stages and on overall population growth. To determine the state of our understanding of recruitment limitation we examined how well we can estimate parameters corresponding to these vital rates. Our two-part analysis consists of (1) a survey of published literature to determine the spatial and temporal scale of sampling that is basis for parameter estimates, and (2) an analysis of extensive data sets to evaluate sampling intensity found in the literature. We find that published studies focus on fine spatial scales, emphasizing large numbers of small samples within a single stand, and tend not to sample multiple stands or variability across landscapes. Where multiple stands are sampled, sampling is often inconsistent. Sampling of seed rain, seed banks, and seedlings typically span <1 yr and rarely last 5 yr. Most studies of seeding establishment and growth consider effects of a single variable and a single life history stage. By examining how parameter estimates are affected by the spatial and temporal extent of sampling we find that few published studies are sufficiently extensive to capture the variability in recruitment stages. Early recruitment stages are especially variable and require samples across multiple years and multiple stands. Ironically, the longest duration data sets are used to estimate mortality rates, which are less variable (in time) than are early life history stages. Because variables that affect recruitment rates interact, studies of these interactions are needed to assess their full impacts. We conclude that greater attention to spatially extensive and longer duration sampling for early life history stages is needed to assess the role of recruitment limitation in forests.

A microtiter assay for determining protein, acetylcholinesterase activity, and G418 (neomycin) resistance in cultured cells

The Coomassie brilliant blue assay for the determination of protein has been extended to rapidly and conveniently measure the protein concentration of cells growing in culture in a 96-well microtiter format. Modifications of the standard assay include sodium hydroxide to solubilize the cells and ovalbumin, instead of bovine serum albumin, as a protein standard. The procedure allows a large number of small samples to be assayed simultaneously. Two examples of its use, enzyme-specific activity and drug resistance, are shown. An assay for acetylcholinesterase activity in the same culture plate is demonstrated. G418, an inhibitor of cell protein synthesis, is frequently used to select for cells transfected with the neomycin resistance gene. The required concentration of G418 can be easily determined with this protein assay.

Optimal Testing for Serial Correlation in a Large Number of Small Samples

AbstractIn recent years, there has been an increased awareness of the potential one‐sided nature of many testing problems in applied sciences. Usually, these testing problems can be reduced, either by conditioning on sufficient statistics or by invariant techniques. COX and SOLOMON (1988) considered testing the serial correlation coefficient of a stationary first order autoregressive process and concentrated on four independent samples, with each of size three. We outline a general method for testing the serial correlation coefficient, using locally best invariant, point optimal invariant and locally most mean powerful invariant test procedures. The first procedure optimizes power near the null hypothesis, the second optimizes it at a pre‐determined point away from the null while the third optimizes the average curvature of the power hypersurface in the neighbourhood of the null hypothesis.

A rapid screening technique for determining the lipid composition of soybean seeds

AbstractAn efficient method to determine the fatty acid composition of a large number of small seed tissue samples is needed to facilitate the genetic manipulation of seed lipid composition in soybean and other oilseeds. A rapid procedure has been developed to simultaneously extract and transmethylate the neutral lipids from soybean cotyledons at 90°C in a mixture of hexane and 1% H2SO4 in methanol (pretreatment of cotyledon pieces with hexane prior to methanolysis was found to improve yields). Fatty acid methyl esters were analyzed by capillary or packed column gas chromatography. The method required less than 10 mg of cotyledon tissue which could be taken from opposite the embryo axis so the sampled seed remained viable.This direct transmethylation method was compared to Soxhlet extraction and subsequent acid methanolysis and to methods requiring separate steps for extraction [with hexane alone, hexane:isopropanol (3:2) or chloroform:methanol (2:1)], washing, solvent removal and methanolysis. Determinations of fatty acid content and composition were similar among the four methods. Approximately 30 times more samples could be analyzed (more than 2000 samples per month) using the direct transesterification method than were possible with the Soxhlet procedure. This direct transmethylation method is more rapid, requires less tissue, and provides results comparable to other inexpensive methods. It should be especially useful in breeding studies where large numbers of small samples are encountered.

Testing distributions in large numbers of small samples

A weak convergence theorem is derived for the empirical distribution function of the residuals in a one-way classification (with equal numbers In the groups) as the. number of groups tends to infinity. A Kolmogorov-Smirnov test baaed on this is proposed and Its use illustrated.

Spatial Pattern Analysis of Seed Banks: An Improved Method and Optimized Sampling

Analysis of spatial pattern of the seed bank of an old field in Maryland showed that the seed bank was composed primarily of annual and short—lived perennial species. Tree and shrub species were poorly represented. Seed abundance decreased with depth in the soil. The seeds of all species generally had clustered distributions in the soil. However, there was no trend in mean cluster size within or among species, or at different soil depths. The lack of definite trends indicates that the spatial distributions of seeds are governed primarily by environmental factors, and to a lesser degree by biological factors. The method of spatial pattern analysis developed for this study represents a significant improvement over traditional contiguous quadrat methods. In this method, individuals' positions are mapped in the field using cartesian coordinates, and the quadrat data are subsequently derived mathematically. The resolution of pattern is greatly improved, and several problems that reduce the effectiveness of other methods are eliminated. This method can be used to advantage in any study in which spatial patterns analysis is performed, particularly if the objects can be mapped easily. A comparison of three sampling techniques revealed that the precision of seed—number estimates can be improved by taking a large number of small samples, or by subsampling large whole units with very small subunits. The smaller number of large samples favored by many seed—bank researchers generally results in imprecise seed estimates. This result has implications for spatial studies of any clustered organism.

On Testing for Serial Correlation in Large Numbers of Small Samples

On Testing for Serial Correlation in Large Numbers of Small Samples

On testing for serial correlation in large numbers of small samples

SUMMARY Methods are outlined for testing for serial correlation in large numbers of small samples, emphasis being placed on samples of size three. Some data on pulse rates are analysed in illustration.

A simple, inexpensive method for the salt-free concentration of proteins for analysis by two-dimensional gel electrophoresis.

A rapid, inexpensive method for the salt-free concentration of small quantities of proteins for analysis by two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) has been developed. Proteins adsorbed to diatomaceous earth are subsequently removed using either sodium dodecyl sulfate or urea solubilization reagents for 2D-PAGE analysis. This procedure has been found to concentrate proteins having wide ranges of molecular weight and charge. It is also valuable for the concentration of large numbers of small samples from cells cultured in vitro.

Improved extraction of lipids from strawberry

A high degree of variability in strawberry lipid content and fatty acid composition, previously observed after two extractions with chloroform-methanol-water following the Bligh and Dyer method, was reduced by extracting three times with larger volumes. The previously observed variation was caused by incomplete lipid extraction while the internal standard, methylheptadecanoate, was quantitatively extracted. The improved procedure caused by itself little variation in the lipid determination. The remaining variability was predominantly due to the heterogeneity of the strawberry population. Ripe fruit contained slightly more lipid than unripe fruit, and these lipids were richer in oleic acid and less rich in linoleic acid. The improved extraction procedure was however more cumbersome than three extractions with chloroform-methanol followed by evaporation to dryness and purification according to Bligh and Dyer in a small volume of chloroform-methanol-water. The latter procedure yielded a slightly larger amount of lipids and was more suitable to the analysis of a large number of small samples. In conclusion, equivalent extraction of internal standard and sample lipids should not be taken for granted.

Colorimetric microtiter plate assay of glucose and fructose by enzyme-linked formazan production: Applicability to the measurement of fructosyl transferase activity in higher plants

A rapid, enzyme-linked colorimetric assay, for the sequential determination of nanomole quantities of glucose and fructose in the same sample, has been developed for the measurement of fructosyl transferase activity in plant extracts. The assay extends the conventional dehydrogenase-linked assay for these sugars by utilizing the intermediary electron carrier, phenazine methosulfate, to couple NADP reduction to the production of a formazan dye from the tetrazolium salt, thiazolyl blue, in a form suitable for measurement using a microtiter plate reader. When the microtiter plate assay was used to measure the activities of yeast invertase and sucrose:sucrose fructosyl transferase from Lolium temulentum, results obtained were very similar to results obtained using the conventional procedure. The rapidity, small scale, and ease of execution of the method offers considerable advantages over the conventional hexose assay and is particularly suitable for screening of large numbers of small samples, exploiting both the speed of the microtiter plate reader and the facility of for microcomputer processing of data. The potential of this method for use with other enzyme systems and other metabolites is discussed.