Confidence Intervals for the Weighted Sum of Two Independent Binomial Proportions

Decrouez, Geoffrey; Robinson, Andrew P.

doi:10.1111/j.1467-842x.2012.00680.x

Cited by 10 publications

(19 citation statements)

References 28 publications

(34 reference statements)

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“…Decrouez and Robinson [17] were interested in the weighted sum of two proportions, in the context of developing performance indicators in the operation of quarantine inspection, with a view to detecting mail items with high biosecurity risk material. The observed numbers of The function of interest is Decrouez and Robinson's [17] Table 3 shows inference for four data sets. Their statement that, due to the large sample sizes involved, "the normal approximation is very accurate" (p.292) is contentious: all four values for 2…”

Section: Functions Of Parametersmentioning

confidence: 99%

Bayesian Benefits for Binomial Applications in Practice

Tuyl

Howley

2019

JESBS

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Introduction: When it comes to the practice, and teaching, of statistics, the world has primarily focused on what is known as classical or frequentist methods, rather than Bayesian methods. Scope of the Study: This paper demonstrates some beneficial properties of Bayesian methods within the commonly practiced domain of inference by utilizing consultancy case studies, one concerning an unusual sample size question and one on the detection of mail items with high biosecurity risk material. Methods: We introduce through practical applications two more aspects of the Bayesian approach which we believe are invaluable to practitioners and instructors. Having in mind readers who may be less familiar with statistical software, we have added Excel instructions which are easy to translate for those who are familiar with any such software. Findings: These cases reflect two valuable aspects for both practitioners and instructors which are unique to the Bayesian paradigm. They are: 1. including prior information to improve inference and how to apply sensitivity analysis to this inclusion and 2. the effortless inference for functions of parameters, compared with frequentist approaches. These examples involving the binomial parameter have not been considered from this perspective before, are of significant practical value and thus benefit students and instructors of courses teaching Bayesian techniques and endeavoring to include authentic learning experiences.

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Section: Functions Of Parametersmentioning

confidence: 99%

Bayesian Benefits for Binomial Applications in Practice

Tuyl

Howley

2019

JESBS

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“…Decrouez and Robinson [48] documented the performance of various confidence interval methods for this case and recommend the Jeffrey Perks interval for a computationally simple method.…”

Section: The Wilson Score Interval For Class I User's Accuracy Is Givmentioning

confidence: 99%

“…And suppose α is a constant. Then as described by Decrouez and Robinson (2012), the Jeffrey Perks interval for q r α + is defined as follows ( Equation 15): …”

Section: The Wilson Score Interval For Class I User's Accuracy Is Givmentioning

confidence: 99%

Development of a Point-based Method for Map Validation and Confidence Interval Estimation: A Case Study of Burned Areas in Amazonia

Anderson¹,

Cheek²,

Aragão³

et al. 2017

J Remote Sensing & GIS

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Forest fires and their associated emissions are a key component for the efficient implementation of the Reducing Emissions from Deforestation and Forest Degradation (REDD+) policy. The most suitable method for quantifying large scale fire-associated impacts is by mapping burned areas using remote sensing data. However, to provide robust quantification of the impacts of fire and support coherent policy decisions, these thematic maps must have their accuracy quantitatively assessed. The aim of this research is to present a point-based validation method developed for quantifying the accuracy of burned area thematic maps and test this method in a study case in the Amazon. The method is general; it can be applied to any thematic map consisting of two land cover classes. A stratified random sampling scheme is used to ensure that each class is represented adequately. The confidence intervals for the user's accuracies and for both overall accuracy and area error are calculated using the Wilson Score method and Jeffrey Perks interval, respectively. Such interval methods are novel in the context of map accuracy assessment. Despite the complexity of calculation of the confidence intervals, their use is recommended. A spreadsheet to calculate point and interval estimates is provided for users.

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“…When subscores for two categories are available, confidence intervals for true composite scores can be computed by adopting interval estimation procedures for two binomial proportions (Agresti & Caffo, 2000;Beal, 1987;Decrouez & Robinson, 2012;Mee, 1984;Miettinen & Nurminen, 1985;Newcombe, 1998). However, it is often the case that tests consist of more than two categories, which makes the applications of these procedures very limited.…”

mentioning

confidence: 99%

Confidence Intervals for Weighted Composite Scores Under the Compound Binomial Error Model

Kim

Lee

2018

J Educational Measurement

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Reporting confidence intervals with test scores helps test users make important decisions about examinees by providing information about the precision of test scores. Although a variety of estimation procedures based on the binomial error model are available for computing intervals for test scores, these procedures assume that items are randomly drawn from a undifferentiated universe of items, and therefore might not be suitable for tests developed according to a table of specifications. To address this issue, four interval estimation procedures that use category subscores for the computation of confidence intervals are presented in this article. All four estimation procedures assume that subscores instead of test scores follow a binomial distribution (i.e., compound binomial error model). The relative performance of the four compound binomial–based interval estimation procedures is compared to each other and to the better known normal approximation and Wilson score procedures based on the binomial error model.

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Confidence Intervals for the Weighted Sum of Two Independent Binomial Proportions

Cited by 10 publications

References 28 publications

Bayesian Benefits for Binomial Applications in Practice

Bayesian Benefits for Binomial Applications in Practice

Development of a Point-based Method for Map Validation and Confidence Interval Estimation: A Case Study of Burned Areas in Amazonia

Confidence Intervals for Weighted Composite Scores Under the Compound Binomial Error Model

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