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Articles 1 - 27 of 27
Full-Text Articles in Physical Sciences and Mathematics
Making The Error Bar Overlap Myth A Reality: Comparative Confidence Intervals, Frank S. Corotto
Making The Error Bar Overlap Myth A Reality: Comparative Confidence Intervals, Frank S. Corotto
Georgia Journal of Science
Many interpret error bars to mean that if they do not overlap the difference is statistically “significant”. This overlap rule is really an overlap myth; the rule does not hold true for any conventional type of error bar. There are rules of thumb for estimating P values, but it would be better to show error bars for which the overlap rule holds true. Here I explain how to calculate comparative confidence intervals which, when plotted as error bars, let us judge significance based on overlap or separation. Others have published on these intervals (the mathematical basis goes back to John …
Confidence Intervals Of Covid-19 Vaccine Efficacy Rates, Frank Wang
Confidence Intervals Of Covid-19 Vaccine Efficacy Rates, Frank Wang
Numeracy
This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be misconstrued by inexperienced students. With Bayesian statistics, one can find the posterior probability distribution of an unknown parameter, and state the probability of vaccine efficacy rate, which makes the communication of uncertainty more flexible. We use a hypothetical example and a real baseball example to guide readers to …
Credibility Evaluation Of Hardware-In-The-Loop Simulation Test For Guided Weapons, Jianbin Dou, Xiaobing Wang, Bin Shan, Zhang Yan
Credibility Evaluation Of Hardware-In-The-Loop Simulation Test For Guided Weapons, Jianbin Dou, Xiaobing Wang, Bin Shan, Zhang Yan
Journal of System Simulation
Abstract: The thesis explained the concept of credibility evaluation of hardware-in-the-loop simulation. The models and the processes were introduced in three parts: credibility evaluation of simulation system, monitoring of simulation test process, and credibility evaluation of simulation results. The credibility evaluation model of hardware-in-the-loop simulation system was built based on TOPSIS and the credibility evaluation model of simulation results was built based on simulation and firing practace. This way could answer the credibility of hardware-in-the-loop simulation, and provide strong support for hardware-in-the-loop simulation in guided weapons test and evaluation.
Sequential Estimation By Intervals Of A Fixed Width Of The Asymptotic Variance Of Rank Estimates Of The Shift Parameter, Gulnoza Rakhimova
Sequential Estimation By Intervals Of A Fixed Width Of The Asymptotic Variance Of Rank Estimates Of The Shift Parameter, Gulnoza Rakhimova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, we consider a sequential interval estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter. Reviewed the asymptotical properties of estimates of functionals of an unknown probability density and the conditions of the asymptotical consistency of a confidence interval of a fixed width and the asymptotical efficiency of the stopping time. The convergence rate of consistency of the fixed width interval for the asymptotic variance of rank estimates of the shift parameter is obtained.
Robust Confidence Intervals For The Population Mean Alternatives To The Student-T Confidence Interval, Moustafa Omar Ahmed Abu-Shawiesh, Aamir Saghir
Robust Confidence Intervals For The Population Mean Alternatives To The Student-T Confidence Interval, Moustafa Omar Ahmed Abu-Shawiesh, Aamir Saghir
Journal of Modern Applied Statistical Methods
In this paper, three robust confidence intervals are proposed as alternatives to the Student‑t confidence interval. The performance of these intervals was compared through a simulation study shows that Qn-t confidence interval performs the best and it is as good as Student’s‑t confidence interval. Real-life data was used for illustration and performing a comparison that support the findings obtained from the simulation study.
Assessing The Accuracy Of Approximate Confidence Intervals Proposed For The Mean Of Poisson Distribution, Alireza Shirvani, Malek Fathizadeh
Assessing The Accuracy Of Approximate Confidence Intervals Proposed For The Mean Of Poisson Distribution, Alireza Shirvani, Malek Fathizadeh
Journal of Modern Applied Statistical Methods
The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.
Performance Evaluation Of Confidence Intervals For Ordinal Coefficient Alpha, Heather J. Turner, Prathiba Natesan, Robin K. Henson
Performance Evaluation Of Confidence Intervals For Ordinal Coefficient Alpha, Heather J. Turner, Prathiba Natesan, Robin K. Henson
Journal of Modern Applied Statistical Methods
The aim of this study was to investigate the performance of the Fisher, Feldt, Bonner, and Hakstian and Whalen (HW) confidence intervals methods for the non-parametric reliability estimate, ordinal alpha. All methods yielded unacceptably low coverage rates and potentially increased Type-I error rates.
Confidence Intervals For The Scaled Half-Logistic Distribution Under Progressive Type-Ii Censoring, Kiran Ganpati Potdar, D. T. Shirke
Confidence Intervals For The Scaled Half-Logistic Distribution Under Progressive Type-Ii Censoring, Kiran Ganpati Potdar, D. T. Shirke
Journal of Modern Applied Statistical Methods
Confidence interval construction for the scale parameter of the half-logistic distribution is considered using four different methods. The first two are based on the asymptotic distribution of the maximum likelihood estimator (MLE) and log-transformed MLE. The last two are based on pivotal quantity and generalized pivotal quantity, respectively. The MLE for the scale parameter is obtained using the expectation-maximization (EM) algorithm. Performances are compared with the confidence intervals proposed by Balakrishnan and Asgharzadeh via coverage probabilities, length, and coverage-to-length ratio. Simulation results support the efficacy of the proposed approach.
A Comparison Of Usual T-Test Statistic And Modified T-Test Statistics On Skewed Distribution Functions, Wooi K. Lim, Alice W. Lim
A Comparison Of Usual T-Test Statistic And Modified T-Test Statistics On Skewed Distribution Functions, Wooi K. Lim, Alice W. Lim
Journal of Modern Applied Statistical Methods
When the sample size n is small, the random variable T= √n(\overline{X} – μ)/S is said to follow a central t distribution with degrees of freedom (n – 1), where \overline{X} is the sample mean and S is the sample standard deviation, provided that the data X ~ N (μ, σ2). The random variable T can be used as a test statistic to hypothesize the population mean μ. Some argue that the t-test statistic is robust against the normality of the distribution and claim that the normality assumption is not necessary. In this …
Bayesian Inference For Median Of The Lognormal Distribution, K. Aruna Rao, Juliet Gratia D'Cunha
Bayesian Inference For Median Of The Lognormal Distribution, K. Aruna Rao, Juliet Gratia D'Cunha
Journal of Modern Applied Statistical Methods
Lognormal distribution has many applications. The past research papers concentrated on the estimation of the mean of this distribution. This paper develops credible interval for the median of the lognormal distribution. The estimated coverage probability and average length of the credible interval is compared with the confidence interval using Monte Carlo simulation.
Modern Approach For Designing And Solving Interval Estimated Linear Fractional Programming Models, S. Ananthalakshmi, C. Vijayalakshmi, V. Ganesan
Modern Approach For Designing And Solving Interval Estimated Linear Fractional Programming Models, S. Ananthalakshmi, C. Vijayalakshmi, V. Ganesan
Applications and Applied Mathematics: An International Journal (AAM)
Optimization methods have been widely applied in statistics. In mathematical programming, the coefficients of the models are always categorized as deterministic values. However uncertainty always exists in realistic problems. Therefore, interval-estimated optimization models may provide an alternative choice for considering the uncertainty into the optimization models. In this aspect, this paper concentrates, the lower and upper values of interval estimated linear fractional programming model (IELFPM) are obtained by using generalized confidence interval estimation method. An IELFPM is a LFP with interval form of the coefficients in the objective function and all requirements. The solution of the IELFPM is also analyzed.
Evaluation Of Area Under The Constant Shape Bi-Weibull Roc Curve, Sudesh Pundir, R Amala
Evaluation Of Area Under The Constant Shape Bi-Weibull Roc Curve, Sudesh Pundir, R Amala
Journal of Modern Applied Statistical Methods
The Receiver Operating Characteristic (ROC) curve generated based on assuming a constant shape Bi-Weibull distribution is studied. In the context of ROC curve analysis, it is assumed that biomarker values from controls and cases follow some specific distribution and the accuracy is evaluated by using the ROC model developed from that specified distribution. This article assumes that the biomarker values from the two groups follow Weibull distributions with equal shape parameter and different scale parameters. The ROC model, area under the ROC curve (AUC), asymptotic and bootstrap confidence intervals for the AUC are derived. Theoretical results are validated by simulation …
Constructing Confidence Intervals For Effect Sizes In Anova Designs, Li-Ting Chen, Chao-Ying Joanne Peng
Constructing Confidence Intervals For Effect Sizes In Anova Designs, Li-Ting Chen, Chao-Ying Joanne Peng
Journal of Modern Applied Statistical Methods
A confidence interval for effect sizes provides a range of plausible population effect sizes (ES) that are consistent with data. This article defines an ES as a standardized linear contrast of means. The noncentral method, Bonett’s method, and the bias-corrected and accelerated bootstrap method are illustrated for constructing the confidence interval for such an effect size. Results obtained from the three methods are discussed and interpretations of results are offered.
Bootstrap Interval Estimation Of Reliability Via Coefficient Omega, Miguel A. Padilla, Jasmin Divers
Bootstrap Interval Estimation Of Reliability Via Coefficient Omega, Miguel A. Padilla, Jasmin Divers
Journal of Modern Applied Statistical Methods
Three different bootstrap confidence intervals (CIs) for coefficient omega were investigated. The CIs were assessed through a simulation study with conditions not previously investigated. All methods performed well; however, the normal theory bootstrap (NTB) CI had the best performance because it had more consistent acceptable coverage under the simulation conditions investigated.
A Robust Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
A Robust Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
Journal of Modern Applied Statistical Methods
A robust Root Mean Square Standardized Effect Size (RMSSER) was developed to address the unsatisfactory performance of the Root Mean Square Standardized Effect Size. The coverage performances of the confidence intervals (CI) for RMSSER were investigated. The coverage probabilities of the non-central F distribution-based CI for RMSSER were adequate.
Estimating Internal Consistency Using Bayesian Methods, Miguel A. Padilla, Guili Zhang
Estimating Internal Consistency Using Bayesian Methods, Miguel A. Padilla, Guili Zhang
Journal of Modern Applied Statistical Methods
Bayesian internal consistency and its Bayesian credible interval (BCI) are developed and Bayesian internal consistency and its percentile and normal theory based BCIs were investigated in a simulation study. Results indicate that the Bayesian internal consistency is relatively unbiased under all investigated conditions and the percentile based BCIs yielded better coverage performance.
Adjusted Confidence Interval For The Population Median Of The Exponential Distribution, Moustafa Omar Ahmed Abu-Shawiesh
Adjusted Confidence Interval For The Population Median Of The Exponential Distribution, Moustafa Omar Ahmed Abu-Shawiesh
Journal of Modern Applied Statistical Methods
The median confidence interval is useful for one parameter families, such as the exponential distribution, and it may not need to be adjusted if censored observations are present. In this article, two estimators for the median of the exponential distribution, MD, are considered and compared based on the sample median and the maximum likelihood method. The first estimator is the sample median, MD1, and the second estimator is the maximum likelihood estimator of the median, MDMLE. Both estimators are used to propose a modified confidence interval for the population median of the exponential distribution, MD …
On Exact 100(1-Α)% Confidence Interval Of Autocorrelation Coefficient In Multivariate Data When The Errors Are Autocorrelated, Madhusudan Bhandary
On Exact 100(1-Α)% Confidence Interval Of Autocorrelation Coefficient In Multivariate Data When The Errors Are Autocorrelated, Madhusudan Bhandary
Journal of Modern Applied Statistical Methods
An exact 100(1−α)% confidence interval for the autocorrelation coefficient ρ is derived based on a single multinormal sample. The confidence interval is the interval between the two roots of a quadratic equation in ρ . A real life example is also presented.
Confidence Interval Estimation For Intraclass Correlation Coefficient Under Unequal Family Sizes, Madhusudan Bhandary, Koji Fujiwara
Confidence Interval Estimation For Intraclass Correlation Coefficient Under Unequal Family Sizes, Madhusudan Bhandary, Koji Fujiwara
Journal of Modern Applied Statistical Methods
Confidence intervals (based on the χ2 -distribution and (Z) standard normal distribution) for the intraclass correlation coefficient under unequal family sizes based on a single multinormal sample have been proposed. It has been found that the confidence interval based on the χ2 -distribution consistently and reliably produces better results in terms of shorter average interval length than the confidence interval based on the standard normal distribution: especially for larger sample sizes for various intraclass correlation coefficient values. The coverage probability of the interval based on the χ2 -distribution is competitive with the coverage probability of the interval …
Bayesian Inference On The Variance Of Normal Distribution Using Moving Extremes Ranked Set Sampling, Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari
Bayesian Inference On The Variance Of Normal Distribution Using Moving Extremes Ranked Set Sampling, Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari
Journal of Modern Applied Statistical Methods
Bayesian inference of the variance of the normal distribution is considered using moving extremes ranked set sampling (MERSS) and is compared with the simple random sampling (SRS) method. Generalized maximum likelihood estimators (GMLE), confidence intervals (CI), and different testing hypotheses are considered using simple hypothesis versus simple hypothesis, simple hypothesis versus composite alternative, and composite hypothesis versus composite alternative based on MERSS and compared with SRS. It is shown that modified inferences using MERSS are more efficient than their counterparts based on SRS.
Probability Of Coverage And Interval Length For Two-Group Techniques Assessing The Median And Trimmed Mean, S. Jonathan Mends-Cole
Probability Of Coverage And Interval Length For Two-Group Techniques Assessing The Median And Trimmed Mean, S. Jonathan Mends-Cole
Journal of Modern Applied Statistical Methods
The purpose of the present study was to assess the probability of coverage and interval length of selected statistical techniques that have a higher finite sample breakdown point than the mean and appropriate levels of probability of coverage when using Bradley’s (1978) criterion. The techniques were examined using real education and psychology datasets (Sawilowsky & Fahoome, 2003, Sawilowsky & Blair, 1992). Welch’s test exhibited appropriate coverage for the smooth symmetric, mass at zero, digit preference, and extreme bimodal distributions. Yuen’s technique performed well under an extreme bimodal distribution. Results concerning the Maritz-Jarrett and the McKean-Schrader techniques are also presented.
Coverage Performance Of The Non-Central F-Based And Percentile Bootstrap Confidence Intervals For Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
Coverage Performance Of The Non-Central F-Based And Percentile Bootstrap Confidence Intervals For Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
Journal of Modern Applied Statistical Methods
The coverage performance of the confidence intervals (CIs) for the Root Mean Square Standardized Effect Size (RMSSE) was investigated in a balanced, one-way, fixed-effects, between-subjects ANOVA design. The noncentral F distribution-based and the percentile bootstrap CI construction methods were compared. The results indicated that the coverage probabilities of the CIs for RMSSE were not adequate.
Probability Coverage And Interval Length For Welch’S And Yuen’S Techniques: Shift In Location, Change In Scale, And (Un)Equal Sizes, S. Jonathan Mends-Cole
Probability Coverage And Interval Length For Welch’S And Yuen’S Techniques: Shift In Location, Change In Scale, And (Un)Equal Sizes, S. Jonathan Mends-Cole
Journal of Modern Applied Statistical Methods
Coverage for Welch’s technique was less than the confidence-level when size was inversely proportional to variance and skewness was extreme. Under negative kurtosis, coverage for Yuen’s technique was attenuated. Under skewness and heteroscedasticity, coverage for Yuen’s technique was more accurate than Welch’s technique.
Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield
Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield
Journal of Modern Applied Statistical Methods
Confidence intervals must be robust in having nominal and actual probability coverage in close agreement. This article examined two ways of computing an effect size in a two-group problem: (a) the classic approach which divides the mean difference by a single standard deviation and (b) a variant of a method which replaces least squares values with robust trimmed means and a Winsorized variance. Confidence intervals were determined with theoretical and bootstrap critical values. Only the method that used robust estimators and a bootstrap critical value provided generally accurate probability coverage under conditions of nonnormality and variance heterogeneity in balanced as …
Variance Stabilizing Power Transformation For Time Series, Victor M. Guerrero, Rafael Perera
Variance Stabilizing Power Transformation For Time Series, Victor M. Guerrero, Rafael Perera
Journal of Modern Applied Statistical Methods
A confidence interval was derived for the index of a power transformation that stabilizes the variance of a time-series. The process starts from a model-independent procedure that minimizes a coefficient of variation to yield a point estimate of the transformation index. The confidence coefficient of the interval is calibrated through a simulation.
A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky
A Different Future For Social And Behavioral Science Research, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
The dissemination of intervention and treatment outcomes as effect sizes bounded by conf idence intervals in order to think meta-analytically was promoted in a recent article in Educational Researcher. I raise concerns with unfettered reporting of effect sizes, point out the con in confidence interval, and caution against thinking meta-analytically. Instead, cataloging effect sizes is recommended for sample size estimation and power analysis to improve social and behavioral science research.
Accounting For Non-Independent Observations In 2×2 Tables, With Application To Correcting For Family Clustering In Exposure-Risk Relationship Studies, Leslie A. Kalsih, Katherine A. Riester, Stuart J. Pocock
Accounting For Non-Independent Observations In 2×2 Tables, With Application To Correcting For Family Clustering In Exposure-Risk Relationship Studies, Leslie A. Kalsih, Katherine A. Riester, Stuart J. Pocock
Journal of Modern Applied Statistical Methods
Participants in epidemiologic studies may not represent statistically independent observations. We consider modifications to conventional analyses of 2×2 tables, including Fisher’s exact test and confidence intervals, to account for correlated observations in this setting. An example is provided, assessing the robustness of conclusions from a published analysis.