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Journal articles

Academic literature on the topic 'Sample size approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "Sample size approximation"

1

Millar, Russell B., and Christopher D. Nottingham. "Improved approximations for estimation of size-transition probabilities within size-structured models." Canadian Journal of Fisheries and Aquatic Sciences 76, no. 8 (2019): 1305–13. http://dx.doi.org/10.1139/cjfas-2017-0444.

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Modelling annual growth of individuals in a size-structured model requires calculation of the size-transition probabilities for moving from one size class to another. This requires evaluation of two-dimensional integrals when there is individual variability in growth. For computational simplicity, it is common to approximate the integrals by setting all individuals in a size class to the midsize of that class or by ignoring the individual variability. We develop a more accurate approximation that assumes a uniform distribution in size within each size class. The approximation is fast and hence feasible for Bayesian models in which the matrix of transition probabilities must be computed for each posterior sample. The improved accuracy of the new approximation is shown to hold over a diverse range of formulations for incremental growth. For the New Zealand Paua 5A (Haliotis iris) stock assessment model, it was found to reduce the average approximation error of the size-transition probabilities by 86% and 98% compared with the midpoint and deterministic growth approximations, respectively. Moreover, the midpoint and deterministic approximations inflated the estimated maximum sustainable yield by 6% and 8%, respectively, and the current biomass by almost 30% in comparison with the more accurate approximation.

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2

Schwertman, Neil C., and Margaret A. Owens. "Simple approximation of sample size for the bivariate normal." Computational Statistics & Data Analysis 8, no. 2 (1989): 201–7. http://dx.doi.org/10.1016/0167-9473(89)90007-8.

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3

Ullah, Insha, Sudhir Paul, Zhenjie Hong, and You-Gan Wang. "Significance tests for analyzing gene expression data with small sample sizes." Bioinformatics 35, no. 20 (2019): 3996–4003. http://dx.doi.org/10.1093/bioinformatics/btz189.

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Abstract Motivation Under two biologically different conditions, we are often interested in identifying differentially expressed genes. It is usually the case that the assumption of equal variances on the two groups is violated for many genes where a large number of them are required to be filtered or ranked. In these cases, exact tests are unavailable and the Welch’s approximate test is most reliable one. The Welch’s test involves two layers of approximations: approximating the distribution of the statistic by a t-distribution, which in turn depends on approximate degrees of freedom. This study attempts to improve upon Welch’s approximate test by avoiding one layer of approximation. Results We introduce a new distribution that generalizes the t-distribution and propose a Monte Carlo based test that uses only one layer of approximation for statistical inferences. Experimental results based on extensive simulation studies show that the Monte Carol based tests enhance the statistical power and performs better than Welch’s t-approximation, especially when the equal variance assumption is not met and the sample size of the sample with a larger variance is smaller. We analyzed two gene-expression datasets, namely the childhood acute lymphoblastic leukemia gene-expression dataset with 22 283 genes and Golden Spike dataset produced by a controlled experiment with 13 966 genes. The new test identified additional genes of interest in both datasets. Some of these genes have been proven to play important roles in medical literature. Availability and implementation R scripts and the R package mcBFtest is available in CRAN and to reproduce all reported results are available at the GitHub repository, https://github.com/iullah1980/MCTcodes. Supplementary information Supplementary data is available at Bioinformatics online.

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4

Lin, Hung-Chin. "USING NORMAL APPROXIMATION ON TESTING AND DETERMINING SAMPLE SIZE FORCpk." Journal of the Chinese Institute of Industrial Engineers 23, no. 1 (2006): 1–11. http://dx.doi.org/10.1080/10170660609508991.

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5

Birnbaum, David. "Who Is at Risk of What?" Infection Control & Hospital Epidemiology 20, no. 10 (1999): 706–7. http://dx.doi.org/10.1086/501570.

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AbstractIf you have calculated the sample size required for an employee survey or an observational study of departmental practices but found that the number of observations required is larger than the number of employees, chances are the error is due to use of approximation formulae. Many of us unknowingly were taught to use approximations that fail to include the finite population correction factor. Depending on the objective of a study and the proportion of a population sampled, it may be necessary to consider this correction factor in order to estimate standard error and sample size accurately.

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6

Pagurova, V. I. "On the approximation accuracy for quantiles in a random-size sample." Moscow University Computational Mathematics and Cybernetics 32, no. 4 (2008): 214–21. http://dx.doi.org/10.3103/s0278641908040043.

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7

Madden, L. V., and G. Hughes. "An Effective Sample Size for Predicting Plant Disease Incidence in a Spatial Hierarchy." Phytopathology® 89, no. 9 (1999): 770–81. http://dx.doi.org/10.1094/phyto.1999.89.9.770.

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For aggregated or heterogeneous disease incidence, one can predict the proportion of sampling units diseased at a higher scale (e.g., plants) based on the proportion of diseased individuals and heterogeneity of diseased individuals at a lower scale (e.g., leaves) using a function derived from the beta-binomial distribution. Here, a simple approximation for the beta-binomial-based function is derived. This approximation has a functional form based on the binomial distribution, but with the number of individuals per sampling unit (n) replaced by a parameter (v) that has similar interpretation as, but is not the same as, the effective sample size (ndeff ) often used in survey sampling. The value of v is inversely related to the degree of heterogeneity of disease and generally is intermediate between ndeff and n in magnitude. The choice of v was determined iteratively by finding a parameter value that allowed the zero term (probability that a sampling unit is disease free) of the binomial distribution to equal the zero term of the beta-binomial. The approximation function was successfully tested on observations of Eutypa dieback of grapes collected over several years and with simulated data. Unlike the beta-binomial-based function, the approximation can be rearranged to predict incidence at the lower scale from observed incidence data at the higher scale, making group sampling for heterogeneous data a more practical proposition.

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8

Zhu, Hong, Song Zhang, and Chul Ahn. "Sample size considerations for split-mouth design." Statistical Methods in Medical Research 26, no. 6 (2015): 2543–51. http://dx.doi.org/10.1177/0962280215601137.

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Split-mouth designs are frequently used in dental clinical research, where a mouth is divided into two or more experimental segments that are randomly assigned to different treatments. It has the distinct advantage of removing a lot of inter-subject variability from the estimated treatment effect. Methods of statistical analyses for split-mouth design have been well developed. However, little work is available on sample size consideration at the design phase of a split-mouth trial, although many researchers pointed out that the split-mouth design can only be more efficient than a parallel-group design when within-subject correlation coefficient is substantial. In this paper, we propose to use the generalized estimating equation (GEE) approach to assess treatment effect in split-mouth trials, accounting for correlations among observations. Closed-form sample size formulas are introduced for the split-mouth design with continuous and binary outcomes, assuming exchangeable and “nested exchangeable” correlation structures for outcomes from the same subject. The statistical inference is based on the large sample approximation under the GEE approach. Simulation studies are conducted to investigate the finite-sample performance of the GEE sample size formulas. A dental clinical trial example is presented for illustration.

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9

Sterling, Grigoriy, Pavel Prikhodko, Evgeny Burnaev, Mikhail Belyaev, and Stephane Grihon. "On Approximation of Reserve Factors Dependency on Loads for Composite Stiffened Panels." Advanced Materials Research 1016 (August 2014): 85–89. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.85.

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We present two level approach to build accurate approximations for Reserve Factors dependency on loads for composite stiffened panels. Such dependency is continuous non-smooth function with complex form plateaux regions (i.e. regions where function has zero gradient), defined on low dimensional grids. The main problem that arises if one tries to construct global approximation in such case is the occurrence of Gibbs effect (i.e. harmonic oscillations of prediction) near the borders of plateaux that may significantly deteriorate approximation quality. Viable existing solution: approximation based on linear triangular interpolation avoids oscillations, but unlike the proposed approach it provides model that is not smooth outside plateaux regions and generally requires larger sample size to achieve same accuracy of approximation.

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10

Christoph, Gerd, and Vladimir V. Ulyanov. "Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting." Mathematics 8, no. 7 (2020): 1151. http://dx.doi.org/10.3390/math8071151.

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We consider high-dimension low-sample-size data taken from the standard multivariate normal distribution under assumption that dimension is a random variable. The second order Chebyshev–Edgeworth expansions for distributions of an angle between two sample observations and corresponding sample correlation coefficient are constructed with error bounds. Depending on the type of normalization, we get three different limit distributions: Normal, Student’s t-, or Laplace distributions. The paper continues studies of the authors on approximation of statistics for random size samples.

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