Confidence Intervals After Variance Stabilization May Go Head-to-Head with Exact Confidence Intervals: A New Class of Illustrations

2021 ◽  
pp. 000806832110511
Author(s):  
Nitis Mukhopadhyay
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Large Sample ◽  
New Class ◽  
Variance Stabilization ◽  
Subject Classifications ◽  
Coverage Probabilities ◽  
Exact Confidence Intervals ◽  
Exact Calculations ◽  
Better Than

We begin with an overview on variance stabilizing transformations (VST) along with three classical examples for completeness: the arcsine, square-root and Fisher's z-transformations (Examples 1–3). Then, we construct three new examples (Examples 4–6) of VST-based and central limit theorem (CLT)’based large-sample confidence interval methodologies. These are special examples in the sense that in each situation, we also have an exact confidence interval procedure for the parameter of interest. Tables 1–3 obtained exclusively under Examples 4–6 via exact calculations show that the VST-based (a) large-sample confidence interval methodology wins over the CLT-based large-sample confidence interval methodology, (b) confidence intervals’ exact coverage probabilities are better than or nearly same as those associated with the exact confidence intervals and (c) intervals are never wider (in the log-scale) than the CLT-based intervals across the board. A possibility of such a surprising behaviour of the VST-based confidence intervals over the exact intervals was not on our radar when we began this investigation. Indeed the VST-based inference methodologies may do extremely well, much more so than the existing literature reveals as evidenced by the new Examples 4–6. AMS subject classifications: 62E20; 62F25; 62F12

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

scholarly journals The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.

Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

2021 ◽  
Author(s):  
Theerapong Kaewprasert ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Bayesian Method ◽  
Simulation Studies ◽  
Jeffreys Prior ◽  
Inverse Gamma ◽  
Gamma Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
Percentile Bootstrap ◽  
Better Than

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

A new procedure to construct confidence intervals for genotypic variance and expected response to selection

Genome ◽  
1989 ◽  
Vol 32 (2) ◽  
pp. 307-308 ◽  
Author(s):  
G. C. C. Tai
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Progeny Test ◽  
Variance Ratio ◽  
Confidence Limits ◽  
Response To Selection ◽  
Genotypic Variance ◽  
Exact Confidence Intervals

This paper describes a procedure to construct confidence intervals for genotypic variance and expected response to selection estimated from progeny test experiments. It involves the introduction of parameters into the confidence limits of existing exact confidence intervals for variance and variance ratio. The parameters in the limits of the derived intervals are estimated by comparing the limits of different potential intervals covering the same parameter, i.e., genotypic variance or expected response to selection. This leads to the construction of a confidence interval for the concerned parameter.Key words: confidence intervals, genotypic variance, expected response to selection.

A-194 TOMM Cutoff Scores Using a Large Sample of Military Personnel

2021 ◽  
Vol 36 (6) ◽  
pp. 1249-1249
Author(s):  
Felicity R Doddato ◽  
Yishi Wang ◽  
Jessica Forde ◽  
Antonio Puente
Keyword(s):  
Probability Distribution ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Military Personnel ◽  
Neuropsychological Tests ◽  
Demographic Variables ◽  
Future Research ◽  
Neuropsychological Battery ◽  
Large Sample ◽  
Cutoff Scores

Abstract Objective The purpose of this study is to investigate the TOMM cutoff scores obtained in a large sample of military personnel. This study examines the traditional scores and proposes potential new ways to classify malingering using confidence intervals. Method The TOMM was administered as part of a neuropsychological battery a total of 1110 times, with the majority being one time. The battery contained 18 demographic variables and 15 neuropsychological tests. Participants were referred by military neurologists and medical officers for evaluation. Individuals had an initial clinical interview with a neuropsychologist prior to the battery being administered. Results TOMM scores from this sample ranged from 9 to 50. The majority of participants (N = 621, 79.60%) scored between 45 and 50. 26 participants (3.32%) received a 45, and 27 participants (3.46%) received a 44. Confidence intervals using means were calculated for each trial (95% CI [43.81, 44.74], [47.53, 48.28], 47.25, 48.10], respectively). The confidence interval for the average of all three trials was determined as well (95% CI [46.16, 46.95]). Conclusions These findings provide a description of the use of the TOMM with a large military sample. Further, the use of a confidence interval was added to provide a more robust assessment of effort. Future research should consider fitting scores to a probability distribution to determine the likelihood each participant is malingering based on the score they receive.

scholarly journals Confidence Intervals for the Ratio of Means of Two Independent Log-Normal Distributions

2021 ◽  
Vol 20 ◽  
pp. 45-52
Author(s):  
Lapasrada Singhasomboon ◽  
Wararit Panichkitkosolkul ◽  
Andrei Volodin
Keyword(s):  
Confidence Intervals ◽  
Coverage Probability ◽  
Real Life ◽  
Sample Sizes ◽  
Simple Method ◽  
Large Sample ◽  
Lognormal Distributions ◽  
Coverage Probabilities ◽  
Interval Width ◽  
Log Normal

In this paper, we investigate confidence intervals for the ratio of means of two independent lognormal distributions. The normal approximation (NA) approach was proposed. We compared the proposed with another approaches, the ML, GCI, and MOVER. The performance of these approaches were evaluated in terms of coverage probabilities and interval widths. The Simulation studies and results showed that the GCI and MOVER approaches performed similar in terms of the coverage probability and interval width for all sample sizes. The ML and NA approaches provided the coverage probability close to nominal level for large sample sizes. However, our proposed method provided the interval width shorter than other methods. Overall, our proposed is conceptually simple method. We recommend that our proposed approach is appropriate for large sample sizes because it is consistently performs well in terms of the coverage probability and the interval width is typically shorter than the other approaches. Finally, the proposed approaches are illustrated using a real-life example.

Concerning large sample tests and confidence intervals for mortality rates

1952 ◽  
Vol 11 (02) ◽  
pp. 104-114
Author(s):  
John E. Walsh
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Mortality Rates ◽  
Significance Tests ◽  
Mortality Study ◽  
Large Sample ◽  
Extra Effort ◽  
Initial Stage ◽  
Insurance Data ◽  
Study Application

In reference(1), some large sample significance tests and confidence intervals for mortality rates were presented. These results appear to be valid for the usual type of insurance data. Also, for an ordinary mortality study, application of a test or confidence interval does not require much additional work. This paper presents a review of reference (1) along with a discussion of the concepts involved. More extensive tables of significance tests and confidence intervals are included in this paper.To apply the results of (1), the data must be subdivided according to the first letter of the surname of the person insured. According to present practice, such information is not recorded for a mortality study. Since this recording requires little extra effort at the initial stage of an investigation, however, such information could easily be incorporated into future mortality studies.

Approximate Confidence Intervals for Standardized Effect Sizes in the Two-Independent and Two-Dependent Samples Design

2007 ◽  
Vol 32 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Wolfgang Viechtbauer
Keyword(s):  
Monte Carlo ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Effect Sizes ◽  
Iterative Estimation ◽  
Exact Confidence Intervals ◽  
Standardized Effect Sizes ◽  
Approximate Confidence Intervals ◽  
Exact Confidence Interval ◽  
Dependent Samples

Standardized effect sizes and confidence intervals thereof are extremely useful devices for comparing results across different studies using scales with incommensurable units. However, exact confidence intervals for standardized effect sizes can usually be obtained only via iterative estimation procedures. The present article summarizes several closed-form approximations to the exact confidence interval bounds in the two-independent and two-dependent samples design. Monte Carlo simulations were conducted to determine the accuracy of the various approximations under a wide variety of conditions. All methods except one provided accurate results for moderately large sample sizes and converged to the exact confidence interval bounds as sample size increased.

Estimating Nonorganic Hearing Thresholds Using Binaural Auditory Stimuli

2017 ◽  
Vol 26 (4) ◽  
pp. 486-495 ◽  
Author(s):  
Linda W. Norrix ◽  
Vivian Rubiano ◽  
Thomas Muller
Keyword(s):  
Hearing Loss ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Response Bias ◽  
Hearing Threshold ◽  
Auditory Stimuli ◽  
Unilateral Hearing Loss ◽  
Hearing Thresholds ◽  
True Threshold ◽  
Better Than

Purpose Minimum contralateral interference levels (MCILs) are used to estimate true hearing thresholds in individuals with unilateral nonorganic hearing loss. In this study, we determined MCILs and examined the correspondence of MCILs to true hearing thresholds to quantify the accuracy of this procedure. Method Sixteen adults with normal hearing participated. Subjects were asked to feign a unilateral hearing loss at 1.0, 2.0, and 4.0 kHz. MCILs were determined. Subjects also made lateralization judgments for simultaneously presented tones with varying interaural intensity differences. Results The 90% confidence intervals, calculated for the distributions, indicate that the MCIL in 90% of cases would be expected to be very close to threshold to approximately 17–19 dB poorer than the true hearing threshold. How close the MCIL is to true threshold appears to be based on the individual's response criterion. Conclusions Response bias influences the MCIL and how close an MCIL is to true hearing threshold. The clinician can never know a client's response bias and therefore should use a 90% confidence interval to predict the range for the expected true threshold. On the basis of this approach, a clinician may assume that true threshold is at or as much as 19 dB better than MCIL.

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