Read Book Understanding the New Statistics : Effect Sizes, Confidence
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Minimum Sample Sizes for On-Road Measurements of Car
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by International Institute for Applied Systems Analysis (IIASA) Manuscript – Final and authoritative paper published in Environmental Science & Technology, 18 Oct 2019. https://pubs.acs.org/doi/abs/10.1021/acs.est.9b04123 1 When is enough? Minimum sample sizes for on-road 2 measurements of car emissions 3 Yuche Chen‡ *, Yunteng Zhang‡, Jens Borken-Kleefeld† * 4 ‡Department of Civil and Environmental Engineering, University of South Carolina, USA 5 †International Institute for Applied System Analysis, Laxenburg, Austria 6 * Corresponding author: Yuche Chen, [email protected]; Jens Borken-Kleefeld, 7 [email protected] 8 9 Key words: Monte Carlo simulation, bootstrap, in-use surveillance, diesel car, Europe, Euro 6, 10 mean, variance, remote emission sensing. 11 Manuscript – Final and authoritative paper published in Environmental Science & Technology, 18 Oct 2019. https://pubs.acs.org/doi/abs/10.1021/acs.est.9b04123 12 ABSTRACT 13 The power of remote vehicle emission sensing stems from the big sample size obtained and its 14 related statistical representativeness for the measured emission rates. But how many records are 15 needed for a representative measurement and when does the information gain per record become 16 insignificant? We use Monte Carlo simulations to determine the relationship between the sample 17 size and the accuracy of the sample mean and variance. We take the example of NO emissions 18 from diesel cars measured by remote emission monitors between 2011 and 2018 at various 19 locations in Europe. We find that no more than 200 remote sensing records are sufficient to 20 approximate the mean emission rate for Euro 4, 5 and 6a,b diesel cars with 80% certainty within 21 a ±1 g NO per kg fuel tolerance margin (~±50 mg NO per km). -
Likelihood-Based Random-Effects Meta-Analysis with Few Studies
Seide et al. RESEARCH Likelihood-based random-effects meta-analysis with few studies: Empirical and simulation studies Svenja E Seide1,2†, Christian R¨over1* and Tim Friede1ˆ Abstract Background: Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved by more sophisticated modeling. Methods: We consider likelihood-based methods, the DerSimonian-Laird approach, Empirical Bayes, several adjustment methods and a fully Bayesian approach. Confidence intervals are based on a normal approximation, or on adjustments based on the Student-t-distribution. In addition, a linear mixed model and two generalized linear mixed models (GLMMs) assuming binomial or Poisson distributed numbers of events per study arm are considered for pairwise binary meta-analyses. We extract an empirical data set of 40 meta-analyses from recent reviews published by the German Institute for Quality and Efficiency in Health Care (IQWiG). Methods are then compared empirically and as well as in a simulation study, based on few studies, imbalanced study sizes, and considering odds-ratio (OR) and risk ratio (RR) effect sizes. Coverage probabilities and interval widths for the combined effect estimate are evaluated to compare the different approaches. Results: Empirically, a majority of the identified meta-analyses include only 2 studies. Variation of methods or effect measures affects the estimation results. In the simulation study, coverage probability is, in the presence of heterogeneity and few studies, mostly below the nominal level for all frequentist methods based on normal approximation, in particular when sizes in meta-analyses are not balanced, but improve when confidence intervals are adjusted. -
Targeted Maximum Likelihood Estimation of Treatment Effects In
Targeted maximum likelihood estimation of treatment e®ects in randomized controlled trials and drug safety analysis by Kelly L. Moore A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Biostatistics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Mark J. van der Laan, Chair Professor Ira B. Tager Professor Alan E. Hubbard Fall 2009 The dissertation of Kelly L. Moore, titled Targeted maximum likelihood estimation of treatment e®ects in randomized controlled trials and drug safety analysis, is approved: Chair Date Date Date University of California, Berkeley Fall 2009 Targeted maximum likelihood estimation of treatment e®ects in randomized controlled trials and drug safety analysis Copyright 2009 by Kelly L. Moore 1 Abstract Targeted maximum likelihood estimation of treatment e®ects in randomized controlled trials and drug safety analysis by Kelly L. Moore Doctor of Philosophy in Biostatistics University of California, Berkeley Professor Mark J. van der Laan, Chair In most randomized controlled trials (RCTs), investigators typically rely on estimators of causal e®ects that do not exploit the information in the many baseline covariates that are routinely collected in addition to treatment and the outcome. Ignoring these covariates can lead to a signi¯cant loss is estimation e±ciency and thus power. Statisticians have underscored the gain in e±ciency that can be achieved from covariate adjustment in RCTs with a focus on problems involving linear models. Despite recent theoretical advances, there has been a reluctance to adjust for covariates based on two primary reasons; 1) covariate-adjusted estimates based on non-linear regression models have been shown to be less precise than unadjusted methods, and, 2) concern over the opportunity to manipulate the model selection process for covariate adjustment in order to obtain favorable results. -
Tolerance-Package
Package ‘tolerance’ February 5, 2020 Type Package Title Statistical Tolerance Intervals and Regions Version 2.0.0 Date 2020-02-04 Depends R (>= 3.5.0) Imports MASS, rgl, stats4 Description Statistical tolerance limits provide the limits between which we can expect to find a speci- fied proportion of a sampled population with a given level of confidence. This package pro- vides functions for estimating tolerance limits (intervals) for various univariate distributions (bi- nomial, Cauchy, discrete Pareto, exponential, two-parameter exponential, extreme value, hyper- geometric, Laplace, logistic, negative binomial, negative hypergeometric, normal, Pareto, Pois- son-Lindley, Poisson, uniform, and Zipf-Mandelbrot), Bayesian normal tolerance limits, multi- variate normal tolerance regions, nonparametric tolerance intervals, tolerance bands for regres- sion settings (linear regression, nonlinear regression, nonparametric regression, and multivari- ate regression), and analysis of variance tolerance intervals. Visualizations are also avail- able for most of these settings. License GPL (>= 2) NeedsCompilation no Author Derek S. Young [aut, cre] Maintainer Derek S. Young <[email protected]> Repository CRAN Date/Publication 2020-02-05 13:10:05 UTC R topics documented: tolerance-package . .3 acc.samp . .4 anovatol.int . .5 bayesnormtol.int . .7 bintol.int . .9 bonftol.int . 12 cautol.int . 13 1 2 R topics documented: diffnormtol.int . 14 DiffProp . 16 DiscretePareto . 18 distfree.est . 19 dpareto.ll . 20 dparetotol.int . 21 exp2tol.int . 23 exptol.int . 25 exttol.int . 26 F1.............................................. 28 fidbintol.int . 29 fidnegbintol.int . 31 fidpoistol.int . 33 gamtol.int . 35 hypertol.int . 37 K.factor . 38 K.factor.sim . 40 K.table . 42 laptol.int . 44 logistol.int . -
Comparing Interval Estimates What Is a Tolerance Interval? Other Interval
Evaluating Tolerance Interval Estimates Michelle Quinlan, University of Nebraska-Lincoln James Schwenke, Boehringer Ingelheim Pharmaceuticals, Inc. University of Nebraska Walt Stroup, University of Nebraska-Lincoln Department of Statistics PQRI Stability Shelf Life Working Group Comparing Interval Estimates 22 . Computed using be / (ratio of between to within batch variance) and The mean of each interval estimate across iterations is computed Statistical interval estimates are constructed to central t-distribution Comparisons are made among the interval estimates . Estimate parameters . Variance is a linear combination of independent mean squares, df calculated . Quantify characteristics of population using Satterthwaite approximation To correctly interpret estimates, it must be clearly defined what each interval β-content tolerance interval: is estimating Prμ,σˆˆ {Pr X [μˆ - kσ ˆ x < X < μ ˆ + kσ ˆ x |μ,σ ˆ ˆ x ] β} = γ . Confidence/prediction intervals are well understood x γ = confidence coefficient . Definition of a tolerance interval varies among literature sources . Interval that contains at least 100β% of population with given confidence What is a Tolerance Interval? level γ (Mee) Tolerance intervals are being used with more frequency, thus a consistent o Computed using factors from Normal and Chi-squared distributions definition needs to be established o β-content interval in models with only 1 source of variation are computed using noncentral t-distribution Definitions found in literature: . Wald and Wolfowitz use same definition to define tolerance intervals but instead use the formula: . A bound that covers at least (100-α)% of the measurements with (100- γ)% n confidence (Walpole and Myers) X 2 rs χ n,β o Focuses on where individual observations fall o Equivalent to a (100-γ)% CI on middle (100-α)% of Normal distribution SAS® Proc Capabilities Method 3 computes an approximate statistical . -
1 Introduction: Statistical Intervals
Avd. Matematisk statistik Sf2955 COMPUTER INTENSIVE METHODS TOLERANCE INTERVALS with A COMPUTER ASSIGNMENT 2011 Timo Koski 1 Introduction: Statistical Intervals Many practical problems are phrased in terms of individual measurements rather than parameters of distributions. We take two such examples. The first one will require, what is to be called a prediction interval, instead of a confidence interval. A consumer is considering buying a car. Then this person should be far more interested in knowing whether a full tank on a particu- lar automobile will suffice to carry her/him the 500 kms to her/his destination than in learning that there is a 95% confidence inter- val for the mean mileage of the model, which is possible to use to project the average or total gasoline consumption for the ma- nufactured fleet of such cars over their first 5000 kilometers of use. A different situation appears in the following. This will require, what is to be called a tolerance interval, instead of a confidence interval. A design engineer is charged with the problem of determining how large a tank the car model really needs to guarantee that 99% of the cars produced will have a cruising range of 500 kilometers. 1 What the engineer really needs is a tolerance interval for a fraction of 100 β = 99% mileages of such automobiles. × Prediction and tolerance intervals address problems of inference for (future) measurements. 2 Definitions of Other Intervals than Confi- dence Intervals We must distinguish between two different questions (I - II) concerning in- ference for future values. Let X1,...,Xn be I.I.D. -
Meta-Analysis of Standardised Mean Differences from Randomised Trials with Treatment-Related Clustering Associated with Care Providers
This is a repository copy of Meta-analysis of standardised mean differences from randomised trials with treatment-related clustering associated with care providers. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/109207/ Version: Accepted Version Article: Walwyn, R and Roberts, C (2017) Meta-analysis of standardised mean differences from randomised trials with treatment-related clustering associated with care providers. Statistics in Medicine, 36 (7). pp. 1043-1067. ISSN 0277-6715 https://doi.org/10.1002/sim.7186 © 2016 John Wiley & Sons, Ltd. This is the peer reviewed version of the following article: "Walwyn, R., and Roberts, C. (2017) Meta-analysis of standardised mean differences from randomised trials with treatment-related clustering associated with care providers. Statist. Med., 36 (7): 1043–1067. doi: 10.1002/sim.7186." which has been published in final form at https://doi.org/10.1002/sim.7186. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. -
Model-Based Estimation Official Statistics
Model-Basedd Estimationmatio for Offi cial SStatistics08007atistics Jan van den Brakel and Jelke Bethlehem The views expressed in this paper are those of the author(s) and do not necessarily refl ect the policies of Statistics Netherlands Discussionpaper (08002) Statistics Netherlands Voorburg/Heerlen, 2008 Explanation of symbols . = data not available * = provisional fi gure x = publication prohibited (confi dential fi gure) – = nil or less than half of unit concerned – = (between two fi gures) inclusive 0 (0,0) = less than half of unit concerned blank = not applicable 2005-2006 = 2005 to 2006 inclusive 2005/2006 = average of 2005 up to and including 2006 2005/’06 = crop year, fi nancial year, school year etc. beginning in 2005 and ending in 2006 2003/’04–2005/’06 = crop year, fi nancial year, etc. 2003/’04 to 2005/’06 inclusive Due to rounding, some totals may not correspond with the sum of the separate fi gures. Publisher Statistics Netherlands second half of 2008: Prinses Beatrixlaan 428 Henri Faasdreef 312 2273 XZ Voorburg 2492 JP The Hague Prepress Statistics Netherlands - Facility Services Cover TelDesign, Rotterdam Information Telephone .. +31 88 570 70 70 Telefax .. +31 70 337 59 94 Via contact form: www.cbs.nl/information Where to order E-mail: [email protected] Telefax .. +31 45 570 62 68 Internet http://www.cbs.nl ISSN: 1572-0314 © Statistics Netherlands, Voorburg/Heerlen, 2008. 6008308002 X-10 Reproduction is permitted. ‘Statistics Netherlands’ must be quoted as source. Summary: This paper summarizes the advantages and disadvantages of design-based and model-assisted estimation procedures that are widely applied by most of the European national statistical institutes. -
Invasive Plant Researchers Should Calculate Effect Sizes, Not P-Values Author(S): Matthew J
Invasive Plant Researchers Should Calculate Effect Sizes, Not P-Values Author(s): Matthew J. Rinella and Jeremy J. James Source: Invasive Plant Science and Management, 3(2):106-112. 2010. Published By: Weed Science Society of America DOI: 10.1614/IPSM-09-038.1 URL: http://www.bioone.org/doi/full/10.1614/IPSM-09-038.1 BioOne (www.bioone.org) is an electronic aggregator of bioscience research content, and the online home to over 160 journals and books published by not-for-profit societies, associations, museums, institutions, and presses. Your use of this PDF, the BioOne Web site, and all posted and associated content indicates your acceptance of BioOne’s Terms of Use, available at www.bioone.org/page/terms_of_use. Usage of BioOne content is strictly limited to personal, educational, and non-commercial use. Commercial inquiries or rights and permissions requests should be directed to the individual publisher as copyright holder. BioOne sees sustainable scholarly publishing as an inherently collaborative enterprise connecting authors, nonprofit publishers, academic institutions, research libraries, and research funders in the common goal of maximizing access to critical research. Invasive Plant Science and Management 2010 3:106–112 Review Invasive Plant Researchers Should Calculate Effect Sizes, Not P-Values Matthew J. Rinella and Jeremy J. James* Null hypothesis significance testing (NHST) forms the backbone of statistical inference in invasive plant science. Over 95% of research articles in Invasive Plant Science and Management report NHST results such as P-values or statistics closely related to P-values such as least significant differences. Unfortunately, NHST results are less informative than their ubiquity implies. -
Background Material
Appendix A Background Material All who debate on matters of uncertainity, should be free from prejudice, partiality, anger, or compassion. —Caius Sallustius Crispus A.1 Some Classical Likelihood Theory Most of the VGLM/VGAM framework is infrastructure directed towards maxi- mizing a full-likelihood model, therefore it is useful to summarize some supporting results from classical likelihood theory. The following is a short summary of a few selected topics serving the purposes of this book. The focus is on aspects of di- rect relevance to the practitioners and users of the software. The presentation is informal and nonrigorous; rigorous treatments, including justification and proofs, can be found in the texts listed in the bibliographic notes. The foundation of this subject was developed by Fisher a century ago (around the decade of WW1), and he is regarded today as the father of modern statistics. A.1.1 Likelihood Functions The usual starting point is to let Y be a random variable with density func- T tion f(y; θ) depending on θ =(θ1,...,θp) , a multidimensional unknown param- eter. Values that Y can take are denoted in lower-case, i.e., y. By ‘density function’, here is meant a probability (mass) function for a discrete-valued Y , and probabil- ity density function for continuous Y . We shall refer to f as simply the density function, and use integration rather than summation to denote quantities such as expected values, e.g., E(Y )= f(y) dy where the range of integration is over the support of the distribution, i.e., those values of y where f(y) > 0 (called Y). -
A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models
mathematics Article A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models Maryam Al-Kandari 1,*, Kingsley Adjenughwure 2 and Kyriakos Papadopoulos 1 1 Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Khaldiyah City, Kuwait; [email protected] 2 Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece; [email protected] * Correspondence: [email protected] Received: 10 August 2020; Accepted: 21 August 2020; Published: 25 August 2020 Abstract: Linear regression is a simple but powerful tool for prediction. However, it still suffers from some deficiencies, which are related to the assumptions made when using a model like normality of residuals, uncorrelated errors, where the mean of residuals should be zero. Sometimes these assumptions are violated or partially violated, thereby leading to uncertainties or unreliability in the predictions. This paper introduces a new method to account for uncertainty in the residuals of a linear regression model. First, the error in the estimation of the dependent variable is calculated and transformed to a fuzzy number, and this fuzzy error is then added to the original crisp prediction, thereby resulting in a fuzzy prediction. The results are compared to a fuzzy linear regression with crisp input and fuzzy output, in terms of their ability to represent uncertainty in prediction. Keywords: tolerance interval; fuzzy linear regression; crisp linear regression; fuzzy-statistics 1. Introduction In classical linear regression models, assumptions like linearity, fixed independent variables, normality of residuals, uncorrelated errors are made to simplify model estimation procedures. Despite these assumptions, the results are often taken at face value with very little effort, to adequately represent the uncertainty in predictions made by the model. -
Precise Unbiased Estimation in Randomized Experiments Using Auxiliary Observational Data
Precise Unbiased Estimation in Randomized Experiments using Auxiliary Observational Data Johann A. Gagnon-Bartsch∗1, Adam C. Sales∗2, Edward Wu1, Anthony F. Botelho3, Luke W. Miratrix4, and Neil T. Heffernan3 1University of Michigan, Department of Statistics 2University of Texas, Austin, College of Education 3Worcester Polytechnic Institute, Learning Sciences and Technologies 4Harvard University, School of Education February 2, 2020 Abstract Randomized controlled trials (RCTs) are increasingly prevalent in education re- search, and are often regarded as a gold standard of causal inference. Two main virtues of randomized experiments are that they (1) do not suffer from confounding, thereby allowing for an unbiased estimate of an intervention's causal impact, and (2) allow for design-based inference, meaning that the physical act of randomization largely justifies the statistical assumptions made. However, RCT sample sizes are often small, leading to low precision; in many cases RCT estimates may be too imprecise to guide policy or inform science. Observational studies, by contrast, have strengths and weaknesses complementary to those of RCTs. Observational studies typically offer much larger sample sizes, but may sufferDRAFT confounding. In many contexts, experimental and obser- vational data exist side by side, allowing the possibility of integrating \big observational data" with \small but high-quality experimental data" to get the best of both. Such approaches hold particular promise in the field of education, where RCT sample sizes are often small due to cost constraints, but automatic collection of observational data, such as in computerized educational technology applications, or in state longitudinal data systems (SLDS) with administrative data on hundreds of thousand of students, has made rich, high-dimensional observational data widely available.