Assessment of the Effect of Six Methods of Analysis and Different Sample Sizes for Biomass Estimation in Grasslands of the State of Puebla, Mexico

In the assessment of natural resources, such as forests or grasslands, it is common to apply a two-stage cluster sampling design, the application of which in the field determines the following situations: (a) difficulty in locating secondary sampling units (SSUs) precisely as planned, so that a random pattern of SSUs can be identified; and (b) the possibility that some primary sampling units (PSUs) have fewer SSUs than planned, leading to PSUs of different sizes. In addition, when considering the estimated variance of the various potential estimators for two-stage cluster sampling, the part corresponding to the variation between SSUs tends to be small for large populations, so the estimator’s variance may depend only on the divergence between PSUs. Research on these aspects is incipient in grassland assessment, so this study generated an artificial population of 759 PSUs and examined the effect of six estimation methods, using 15 PSU sample sizes, on unbiased and relative sampling errors when estimating aboveground, belowground, and total biomass of halophytic grassland. The results indicated that methods 1, 2, 4, and 5 achieved unbiased biomass estimates regardless of sample size, while methods 3 and 6 led to slightly biased estimates. Methods 4 and 5 had relative sampling errors of less than 5% with a sample size of 140 when estimating total biomass.

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The Determination of Sample Size for Sensitive Issue Successive Survey with the Multiplication RRT Model under Two-Stage and Stratified Two-Stage Random Sampling and Its Application in Medical Survey

Mathematical Problems in Engineering ◽

10.1155/2019/1979616 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Bo Yu ◽

Xiaonan Liang ◽

Ying Wang ◽

Yun Liu ◽

Qiao Chang ◽

...

Keyword(s):

Sample Size ◽

Sampling Method ◽

Sampling Errors ◽

Two Stage ◽

Successive Sampling ◽

Optimal Sample ◽

Sensitive Issue ◽

Survey Accuracy ◽

The Cost

When designing the sample scheme, it is important to determine the sample size. The survey accuracy and cost of survey and sampling method should be considered comprehensively. In this article, we discuss the method of determining the sample size of complex successive sampling with rotation sample for sensitive issue and deduce the formulas for the optimal sample size under two-stage sampling and stratified two-stage sampling by using Cauchy-Schwartz inequality, respectively, so as to minimize the cost for given sampling errors and to minimize the sampling errors for given cost.

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Optimal sample size calculation for null hypothesis significance tests

10.1101/540468 ◽

2019 ◽

Author(s):

Joseph F. Mudge ◽

Jeffrey E. Houlahan

Keyword(s):

Sample Size ◽

Estimation Methods ◽

Sample Size Estimation ◽

Type I ◽

Type Ii ◽

Size Estimation ◽

Sample Sizes ◽

Optimal Sample Size ◽

Critical Effect ◽

Optimal Sample

AbstractTraditional study design tools for estimating appropriate sample sizes are not consistently used in ecology and can lead to low statistical power to detect biologically relevant effects. We have developed a new approach to estimating optimal sample sizes, requiring only three parameters; a maximum acceptable average of α and β, a critical effect size of minimum biological relevance, and an estimate of the relative costs of Type I vs. Type II errors.This approach can be used to show the general circumstances under which different combinations of critical effect sizes and maximum acceptable combinations of α and β are attainable for different statistical tests. The optimal α sample size estimation approach can require fewer samples than traditional sample size estimation methods when costs of Type I and II errors are assumed to be equal but recommends comparatively more samples for increasingly unequal Type I vs. Type II errors costs. When sampling costs and absolute costs of Type I and II errors are known, optimal sample size estimation can be used to determine the smallest sample size at which the cost of an additional sample outweighs its associated reduction in errors. Optimal sample size estimation constitutes a more flexible and intuitive tool than traditional sample size estimation approaches, given the constraints and unknowns commonly faced by ecologists during study.

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Characterizing Heterogeneity and Determining Sample Sizes for Accurately Estimating Wheat Fusarium Head Blight Index in Research Plots

Phytopathology ◽

10.1094/phyto-04-21-0157-r ◽

2021 ◽

Author(s):

Wanderson Bucker Moraes ◽

Laurence V Madden ◽

Pierce A. Paul

Keyword(s):

Sample Size ◽

Fusarium Head Blight ◽

Field Experiments ◽

Linear Models ◽

Spatial Scales ◽

Cluster Sampling ◽

Sample Sizes ◽

Head Blight ◽

Original Dataset ◽

Sampling Protocols

Since Fusarium head blight (FHB) intensity is usually highly variable within a plot, the number of spikes rated for FHB index (IND) quantification must be considered when designing experiments. In addition, quantification of sources of IND heterogeneity is crucial for defining sampling protocols. Field experiments were conducted to quantify the variability of IND (‘field severity’) at different spatial scales and to investigate the effects of sample size on estimated plot-level mean IND and its accuracy. A total of 216 7-row x 6-m-long plots of a moderately resistant and a susceptible cultivar were spray inoculated with different Fusarium graminearum spore concentrations at anthesis to generate a range of IND levels. A one-stage cluster sampling approach was used to estimate IND, with an average of 32 spikes rated at each of 10 equally spaced points per plot. Plot-level mean IND ranged from 0.9 to 37.9%. Heterogeneity of IND, quantified by fitting unconditional hierarchical linear models, was higher among spikes within clusters than among clusters within plots or among plots. The projected relative error of mean IND increased as mean IND decreased, and as sample size decreased below 100 spikes per plot. Simple random samples were drawn with replacement 50,000 times from the original dataset for each plot and used to estimate the effects of sample sizes on mean IND. Samples of 100 or more spikes resulted in more precise estimates of mean IND than smaller samples. Poor sampling may result in inaccurate estimates of IND and poor interpretation of results.

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A Comparative Study of Some Estimation Methods in Simple Linear Regression Model for Different Sample Sizes in Presence of Outliers

Turkish Journal of Agriculture - Food Science and Technology ◽

10.24925/turjaf.v3i6.380-386.304 ◽

2015 ◽

Vol 3 (6) ◽

pp. 380

Author(s):

Soner Çankaya ◽

Samet Hasan Abacı

Keyword(s):

Linear Regression ◽

Regression Model ◽

Sample Size ◽

Linear Regression Model ◽

Estimation Methods ◽

Simple Linear Regression ◽

Sample Sizes ◽

Simple Linear Regression Model ◽

Body Weights ◽

Chest Girth

The aim of this study was to compare some estimation methods (LS, M, S, LTS and MM) for estimating the parameters of simple linear regression model in the presence of outlier and different sample size (10, 20, 30, 50 and 100). To compare methods, the effect of chest girth on body weights of Karayaka lambs at weaning period was examined. Chest girth of lambs was used as independent variable and body weight at weaning period was used as dependent variable in the study. Also, it was taken consideration that there were 10-20% outliers of data set for different sample sizes. Mean square error (MSE) and coefficient of determination (R2) values were used as criteria to evaluate the estimator performance. Research findings showed that LTS estimator is the best models with minimum MSE and maximum R2 values for different size of sample in the presence of outliers. Thereby, LTS method can be proposed, to predict best-fitted model for relationship between chest girth and body weights of Karayaka lambs at weaning period, to the researches who are studying on small ruminants as an alternative way to estimate the regression parameters in the presence of outliers for different sample size.

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Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation

Mathematics ◽

10.3390/math8081258 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1258

Author(s):

M. Rosário Oliveira ◽

Ana Subtil ◽

Luzia Gonçalves

Keyword(s):

Sample Size ◽

Confidence Intervals ◽

Sensitivity And Specificity ◽

Sample Size Calculation ◽

Estimation Method ◽

Interval Estimation ◽

Sample Size Determination ◽

Estimation Methods ◽

Sample Sizes ◽

Expected Length

Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice.

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A Study of Sample Size for Two-Stage Cluster Sampling

Korean Journal of Applied Statistics ◽

10.5351/kjas.2011.24.2.393 ◽

2011 ◽

Vol 24 (2) ◽

pp. 393-400

Author(s):

Jong-Ho Song ◽

Hea-Sung Jea ◽

Min-Gue Park

Keyword(s):

Sample Size ◽

Cluster Sampling ◽

Two Stage

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Effects of Training Set Size on Supervised Machine-Learning Land-Cover Classification of Large-Area High-Resolution Remotely Sensed Data

Remote Sensing ◽

10.3390/rs13030368 ◽

2021 ◽

Vol 13 (3) ◽

pp. 368

Author(s):

Christopher A. Ramezan ◽

Timothy A. Warner ◽

Aaron E. Maxwell ◽

Bradley S. Price

Keyword(s):

Machine Learning ◽

Sample Size ◽

Remotely Sensed ◽

Training Data ◽

Supervised Machine Learning ◽

Sample Sizes ◽

Remotely Sensed Data ◽

Large Area ◽

Training Set ◽

Set Size

The size of the training data set is a major determinant of classification accuracy. Nevertheless, the collection of a large training data set for supervised classifiers can be a challenge, especially for studies covering a large area, which may be typical of many real-world applied projects. This work investigates how variations in training set size, ranging from a large sample size (n = 10,000) to a very small sample size (n = 40), affect the performance of six supervised machine-learning algorithms applied to classify large-area high-spatial-resolution (HR) (1–5 m) remotely sensed data within the context of a geographic object-based image analysis (GEOBIA) approach. GEOBIA, in which adjacent similar pixels are grouped into image-objects that form the unit of the classification, offers the potential benefit of allowing multiple additional variables, such as measures of object geometry and texture, thus increasing the dimensionality of the classification input data. The six supervised machine-learning algorithms are support vector machines (SVM), random forests (RF), k-nearest neighbors (k-NN), single-layer perceptron neural networks (NEU), learning vector quantization (LVQ), and gradient-boosted trees (GBM). RF, the algorithm with the highest overall accuracy, was notable for its negligible decrease in overall accuracy, 1.0%, when training sample size decreased from 10,000 to 315 samples. GBM provided similar overall accuracy to RF; however, the algorithm was very expensive in terms of training time and computational resources, especially with large training sets. In contrast to RF and GBM, NEU, and SVM were particularly sensitive to decreasing sample size, with NEU classifications generally producing overall accuracies that were on average slightly higher than SVM classifications for larger sample sizes, but lower than SVM for the smallest sample sizes. NEU however required a longer processing time. The k-NN classifier saw less of a drop in overall accuracy than NEU and SVM as training set size decreased; however, the overall accuracies of k-NN were typically less than RF, NEU, and SVM classifiers. LVQ generally had the lowest overall accuracy of all six methods, but was relatively insensitive to sample size, down to the smallest sample sizes. Overall, due to its relatively high accuracy with small training sample sets, and minimal variations in overall accuracy between very large and small sample sets, as well as relatively short processing time, RF was a good classifier for large-area land-cover classifications of HR remotely sensed data, especially when training data are scarce. However, as performance of different supervised classifiers varies in response to training set size, investigating multiple classification algorithms is recommended to achieve optimal accuracy for a project.

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