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- Journal of Modern Applied Statistical Methods (22)
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Articles 1 - 30 of 39
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 …
Sample Size Formulas For Estimating Areas Under The Receiver Operating Characteristic Curves With Precision And Assurance, Grace Lu
Electronic Thesis and Dissertation Repository
The area under the receiver operating characteristic curve (AUC) is commonly used to quantify the discriminative ability of tests with ordinal or continuous test data. When planning a study to evaluate a new test, it is important to determine a minimum sample size required to achieve a prespecified precision of estimating AUC. However, conventional sample size formulas do not consider the probability of achieving a prespecified precision, resulting in underestimation of sample sizes. To incorporate the assurance probability, asymptotic sample size formulas were derived using different variance estimators for AUC in this thesis. The precision of AUC estimations was quantified …
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 …
Accurate Confidence Intervals For Risk Difference In Meta-Analysis With Rare Events, Tao Jiang, Baixin Cao, Guogen Shan
Accurate Confidence Intervals For Risk Difference In Meta-Analysis With Rare Events, Tao Jiang, Baixin Cao, Guogen Shan
Environmental & Occupational Health Faculty Publications
Background: Meta-analysis provides a useful statistical tool to effectively estimate treatment effect from multiple studies. When the outcome is binary and it is rare (e.g., safety data in clinical trials), the traditionally used methods may have unsatisfactory performance. Methods: We propose using importance sampling to compute confidence intervals for risk difference in meta-analysis with rare events. The proposed intervals are not exact, but they often have the coverage probabilities close to the nominal level. We compare the proposed accurate intervals with the existing intervals from the fixed- or random-effects models and the interval by Tian et al. (2009). Results: We …
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.
Randomization-Based Confidence Intervals For Cluster Randomized Trials, Dustin J. Rabideau, Rui Wang
Randomization-Based Confidence Intervals For Cluster Randomized Trials, Dustin J. Rabideau, Rui Wang
Harvard University Biostatistics Working Paper Series
In a cluster randomized trial (CRT), groups of people are randomly assigned to different interventions. Existing parametric and semiparametric methods for CRTs rely on distributional assumptions or a large number of clusters to maintain nominal confidence interval (CI) coverage. Randomization-based inference is an alternative approach that is distribution-free and does not require a large number of clusters to be valid. Although it is well-known that a CI can be obtained by inverting a randomization test, this requires randomization testing a non-zero null hypothesis, which is challenging with non-continuous and survival outcomes. In this paper, we propose a general method for …
Towards Using Model Averaging To Construct Confidence Intervals In Logistic Regression Models, Artem Uvarov
Towards Using Model Averaging To Construct Confidence Intervals In Logistic Regression Models, Artem Uvarov
Electronic Thesis and Dissertation Repository
Regression analyses in epidemiological and medical research typically begin with a model selection process, followed by inference assuming the selected model has generated the data at hand. It is well-known that this two-step procedure can yield biased estimates and invalid confidence intervals for model coefficients due to the uncertainty associated with the model selection. To account for this uncertainty, multiple models may be selected as a basis for inference. This method, commonly referred to as model-averaging, is increasingly becoming a viable approach in practice.
Previous research has demonstrated the advantage of model-averaging in reducing bias of parameter estimates. However, there …
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.
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 Computational Method For Estimating And Finding The Hconfidence Interval Of The Ratio Scale Parameters In The Two-Sample Problem, Mona Abdullah Alduailij
A Computational Method For Estimating And Finding The Hconfidence Interval Of The Ratio Scale Parameters In The Two-Sample Problem, Mona Abdullah Alduailij
Dissertations
Testing equality of variances between two samples is applied in various fields. However, in the absence of non-normal assumptions, equality of variance tests would not yield robust results. In real life situation, the absence of such assumptions is even evident, which calls for more reliable tests to accommodate for the lack of these assumptions. There are abundant parametric and nonparametric methods for estimating the scale parameter; yet a distribution-free method for estimating and finding the confident interval ratio of scale parameters in the two-sample problem would be a reliable alternative. A comparison between existing parametric and non-parametric rank tests for …
Risk, Odds, And Their Ratios, Joseph Hilbe
Risk, Odds, And Their Ratios, Joseph Hilbe
Joseph M Hilbe
A brief monograph explaining the meaning of the terms, risk, risk ratio, odds, and odds ratio and how to calculate each, together with standard errors and confidence intervals. Stata code is provided showing how all of the terms can be calculated by hand, as well as by using logistic and Poisson models.
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.
Accurately Sized Test Statistics With Misspecified Conditional Homoskedasticity, Douglas Steigerwald, Jack Erb
Accurately Sized Test Statistics With Misspecified Conditional Homoskedasticity, Douglas Steigerwald, Jack Erb
Douglas G. Steigerwald
We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. …
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 …
Correction Methods, Approximate Biases, And Inference For Misclassified Data, Meng-Shiou Shieh
Correction Methods, Approximate Biases, And Inference For Misclassified Data, Meng-Shiou Shieh
Open Access Dissertations
When categorical data are misplaced into the wrong category, we say the data is affected by misclassification. This is common for data collection. It is well-known that naive estimators of category probabilities and coefficients for regression that ignore misclassification can be biased. In this dissertation, we develop methods to provide improved estimators and confidence intervals for a proportion when only a misclassified proxy is observed, and provide improved estimators and confidence intervals for regression coefficients when only misclassified covariates are observed. Following the introduction and literature review, we develop two estimators for a proportion , one which reduces the bias, …
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.
Estimating The Difference Of Percentiles From Two Independent Populations., Romual Eloge Tchouta
Estimating The Difference Of Percentiles From Two Independent Populations., Romual Eloge Tchouta
Electronic Theses and Dissertations
We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.
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.
How Do You Interpret A Confidence Interval?, Paul Savory
How Do You Interpret A Confidence Interval?, Paul Savory
Industrial and Management Systems Engineering: Instructional Materials
A confidence interval (CI) is an interval estimate of a population parameter. Instead of estimating the parameter by a single value, a point estimate, an interval likely to cover the parameter is developed. Many student incorrectly interpret the meaning of a confidence interval. This paper offers a quick overview of how to correctly interpret a confidence interval.