DOCSLIB.ORG

Modern Engineering Statistics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modern Engineering Statistics P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics THOMAS P. RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION iii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 xx P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics i P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 ii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Modern Engineering Statistics THOMAS P. RYAN Acworth, Georgia A JOHN WILEY & SONS, INC., PUBLICATION iii P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come September 27, 2007 19:31 Copyright C 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008 or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com Wiley Bicentennial Logo: Richard J. Pacifico Library of Congress Cataloging-in-Publication Data: Ryan, Thomas P., 1945– Modern engineering statistics / Thomas P. Ryan. p. cm. Includes bibliographical references and index. ISBN 978-0-470-08187-7 1. Engineering–Statistical methods. I. Title. TA340.R93 2007 620.0072–dc22 20060521558 Printed in the United States of America 10987654321 iv P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 Contents Preface xvii 1. Methods of Collecting and Presenting Data 1 1.1 Observational Data and Data from Designed Experiments, 3 1.2 Populations and Samples, 5 1.3 Variables, 6 1.4 Methods of Displaying Small Data Sets, 7 1.4.1 Stem-and-Leaf Display, 8 1.4.2 Time Sequence Plot and Control Chart, 9 1.4.3 Lag Plot, 11 1.4.4 Scatter Plot, 12 1.4.5 Digidot Plot, 14 1.4.6 Dotplot, 14 1.5 Methods of Displaying Large Data Sets, 16 1.5.1 Histogram, 16 1.5.2 Boxplot, 20 1.6 Outliers, 22 1.7 Other Methods, 22 1.8 Extremely Large Data Sets: Data Mining, 23 1.9 Graphical Methods: Recommendations, 23 1.10 Summary, 24 References, 24 Exercises, 25 2. Measures of Location and Dispersion 45 2.1 Estimating Location Parameters, 46 2.2 Estimating Dispersion Parameters, 50 2.3 Estimating Parameters from Grouped Data, 55 v P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 vi contents 2.4 Estimates from a Boxplot, 57 2.5 Computing Sample Statistics with MINITAB, 58 2.6 Summary, 58 Reference, 58 Exercises, 58 3. Probability and Common Probability Distributions 68 3.1 Probability: From the Ethereal to the Concrete, 68 3.1.1 Manufacturing Applications, 70 3.2 Probability Concepts and Rules, 70 3.2.1 Extension to Multiple Events, 73 3.2.1.1 Law of Total Probability and Bayes’ Theorem, 74 3.3 Common Discrete Distributions, 76 3.3.1 Expected Value and Variance, 78 3.3.2 Binomial Distribution, 80 3.3.2.1 Testing for the Appropriateness of the Binomial Model, 86 3.3.3 Hypergeometric Distribution, 87 3.3.4 Poisson Distribution, 88 3.3.4.1 Testing for the Appropriateness of the Poisson Model, 90 3.3.5 Geometric Distribution, 91 3.4 Common Continuous Distributions, 92 3.4.1 Expected Value and Variance, 92 3.4.2 Determining Probabilities for Continuous Random Variables, 92 3.4.3 Normal Distribution, 93 3.4.3.1 Software-Aided Normal Probability Computations, 97 3.4.3.2 Testing the Normality Assumption, 97 3.4.4 t-Distribution, 97 3.4.5 Gamma Distribution, 100 3.4.5.1 Chi-Square Distribution, 100 3.4.5.2 Exponential Distribution, 101 3.4.6 Weibull Distribution, 102 3.4.7 Smallest Extreme Value Distribution, 103 3.4.8 Lognormal Distribution, 104 3.4.9 F Distribution, 104 3.5 General Distribution Fitting, 106 3.6 How to Select a Distribution, 107 3.7 Summary, 108 References, 109 Exercises, 109 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 contents vii 4. Point Estimation 121 4.1 Point Estimators and Point Estimates, 121 4.2 Desirable Properties of Point Estimators, 121 4.2.1 Unbiasedness and Consistency, 121 4.2.2 Minimum Variance, 122 4.2.3 Estimators Whose Properties Depend on the Assumed Distribution, 124 4.2.4 Comparing Biased and Unbiased Estimators, 124 4.3 Distributions of Sampling Statistics, 125 4.3.1 Central Limit Theorem, 126 4.3.1.1 Illustration of Central Limit Theorem, 126 4.3.2 Statistics with Nonnormal Sampling Distributions, 128 4.4 Methods of Obtaining Estimators, 128 4.4.1 Method of Maximum Likelihood, 128 4.4.2 Method of Moments, 130 4.4.3 Method of Least Squares, 131 4.5 Estimating σθˆ, 132 4.6 Estimating Parameters Without Data, 133 4.7 Summary, 133 References, 134 Exercises, 134 5. Confidence Intervals and Hypothesis Tests—One Sample 140 5.1 Confidence Interval for µ: Normal Distribution, σ Not Estimated from Sample Data, 140 5.1.1 Sample Size Determination, 142 5.1.2 Interpretation and Use, 143 5.1.3 General Form of Confidence Intervals, 145 5.2 Confidence Interval for µ: Normal Distribution, σ Estimated from Sample Data, 146 5.2.1 Sample Size Determination, 146 5.3 Hypothesis Tests for µ: Using Z and t, 147 5.3.1 Null Hypotheses Always False?, 147 5.3.2 Basic Hypothesis Testing Concepts, 148 5.3.3 Two-Sided Hypothesis Tests Vis-`a-Vis Confidence Intervals, 152 5.3.4 One-Sided Hypothesis Tests Vis-`a-Vis One-Sided Confidence Intervals, 153 5.3.5 Relationships When the t-Distribution is Used, 155 5.3.6 When to Use t or Z (or Neither)?, 155 5.3.7 Additional Example, 156 5.4 Confidence Intervals and Hypothesis Tests for a Proportion, 157 5.4.1 Approximate Versus Exact Confidence Interval for a Proportion, 158 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 viii contents 5.5 Confidence Intervals and Hypothesis Tests for σ 2 and σ , 161 5.5.1 Hypothesis Tests for σ 2 and σ , 163 5.6 Confidence Intervals and Hypothesis Tests for the Poisson Mean, 164 5.7 Confidence Intervals and Hypothesis Tests When Standard Error Expressions are Not Available, 166 5.8 Type I and Type II Errors, 168 5.8.1 p-Values, 170 5.8.2 Trade-off Between Error Risks, 172 5.9 Practical Significance and Narrow Intervals: The Role of n, 172 5.10 Other Types of Confidence Intervals, 173 5.11 Abstract of Main Procedures, 174 5.12 Summary, 175 Appendix: Derivation, 176 References, 176 Exercises, 177 6. Confidence Intervals and Hypothesis Tests—Two Samples 189 6.1 Confidence Intervals and Hypothesis Tests for Means: Independent Samples, 189 6.1.1 Using Z, 190 6.1.2 Using t, 192 6.1.3 Using Neither t nor Z, 197 6.2 Confidence Intervals and Hypothesis Tests for Means: Dependent Samples, 197 6.3 Confidence Intervals and Hypothesis Tests for Two Proportions, 200 6.3.1 Confidence Interval, 202 6.4 Confidence Intervals and Hypothesis Tests for Two Variances, 202 6.5 Abstract of Procedures, 204 6.6 Summary, 205 References, 205 Exercises, 205 7. Tolerance Intervals and Prediction Intervals 214 7.1 Tolerance Intervals: Normality Assumed, 215 7.1.1 Two-Sided Interval, 216 7.1.1.1 Approximations, 217 7.1.2 Two-Sided Interval, Possibly Unequal Tails, 218 7.1.3 One-Sided Bound, 218 7.2 Tolerance Intervals and Six Sigma, 219 P1: OTE/OTE/SPH P2: OTE JWDD066-RYAN-FM JWDD066-Ryan PRINTER: To Come July 24, 2007 16:43 contents ix 7.3 Distribution-Free Tolerance Intervals, 219 7.3.1 Determining Sample Size, 221 7.4 Prediction Intervals, 221 7.4.1 Known Parameters, 222 7.4.2 Unknown Parameters with Normality Assumed (Single Observation), 223 7.4.2.1 Sensitivity to Nonnormality, 223 7.4.2.2 Width of the Interval, 224 7.4.3 Nonnormal Distributions: Single Observation, 224 7.4.4 Nonnormal Distributions: Number of Failures, 225 7.4.5 Prediction Intervals for Multiple Future Observations, 225 7.4.6 One-Sided Prediction Bounds, 225 7.4.6.1 One-Sided Prediction Bounds for Certain Discrete Distributions, 226 7.4.7 Distribution-Free Prediction Intervals, 226 7.5 Choice Between Intervals, 227 7.6 Summary, 227 References, 228 Exercises, 229 8.
Load more

Recommended publications
  • Introduction to Statistically Designed Experiments, NREL
    Introduction to Statistically Designed Experiments Mike Heaney ([email protected]) ASQ Denver Section 1300 Monthly Membership Meeting September 13, 2016 Englewood, Colorado NREL/PR-5500-66898 Objectives Give some basic background information on statistically designed experiments Demonstrate the advantages of using statistically designed experiments1 1 Often referred to as design of experiments (DOE or DOX), or experimental design. 2 A Few Thoughts Many companies/organizations do experiments for Process improvement Product development Marketing strategies We need to plan our experiments as efficiently and effectively as possible Statistically designed experiments have a proven track record (Mullin 2013 in Chemical & Engineering News) Conclusions supported by statistical tests Substantial reduction in total experiments Why are we still planning experiments like it’s the 19th century? 3 Outline • Research Problems • The Linear Model • Key Types of Designs o Full Factorial o Fractional Factorial o Response Surface • Sequential Approach • Summary 4 Research Problems Research Problems Is a dependent variable (Y) affected by multiple independent variables (Xs)? Objective: Increase bearing lifetime (Hellstrand 1989) Y Bearing lifetime (hours) X1 Inner ring heat treatment Outer ring osculation (ratio Outer Ring X2 between ball diameter and outer ring raceway radius) Ball X3 Cage design Cage Inner Ring 6 Research Problems Objective: Hydrogen cyanide (HCN) removal in diesel exhaust gas (Zhao et al. 2006) Y HCN conversion X1 Propene
    [Show full text]
  • Appendix A: Mathematical Formulas
    Appendix A: Mathematical Formulas Logarithms Inab = \na -\-\nb', \na/b = \na— \nb; \na^=b\na Geometric Series If Irl < 1, we find that oo oo E ar^ = ; y^akr^ = r; ^=0 A:=o y^ n Z-^ 1 -r ^^ 1 -r ^=1 k=0 Limits UHospitaVs rule. Suppose that \\vOix->XQ fix) = lim;c-^A:o sM = 0* or that liirix-^xo Z^-^) = l™x^jco SM — =t^^- Then, under some conditions, we can write that y fix) ^. fix) um = hm . x-^XQ g{x) x^xo g^{x) If the functions f\x) and g\x) satisfy the same conditions as f(x) and g(x), we can repeat the process. Moreover, the constant XQ may be equal to ±oo. Derivatives Derivative of a quotient: d fix) gix)fix) - fix)g\x) = 7^ 11 gix) ^0. dx gix) g^ix) 340 Appendix A: Mathematical Formulas Remark. This formula can also be obtained by differentiating the product f(x)h(x), where/Z(A:) := l/g(x). Chain rule. If w = ^(jc), then we have: d d du , , ^fiu) = —f(u) . — = f\u)g\x) = AgixWix). dx du dx For example, if w = jc^, we calculate — exp(M^) = exp(w^)2w • 2x = 4x^ expU"*). dx Integrals Integration by parts: j udv = uv — I vdu. Integration by substitution. If the inverse function g~^ exists, then we can write that rh rd j f(x)dx = j f[g(y)]g{y)dy, where a = g(c) ^ c = g ^(a) and b = g(d) <^ d = g ^(b). For example, / e''^'dx-^=^' f 2yeydy=2yey\l-2 f e^ dy = 2e^-\-2.
    [Show full text]
  • STATISTICAL SCIENCE Volume 31, Number 4 November 2016
    STATISTICAL SCIENCE Volume 31, Number 4 November 2016 ApproximateModelsandRobustDecisions..................James Watson and Chris Holmes 465 ModelUncertaintyFirst,NotAfterwards....................Ingrid Glad and Nils Lid Hjort 490 ContextualityofMisspecificationandData-DependentLosses..............Peter Grünwald 495 SelectionofKLNeighbourhoodinRobustBayesianInference..........Natalia A. Bochkina 499 IssuesinRobustnessAnalysis.............................................Michael Goldstein 503 Nonparametric Bayesian Clay for Robust Decision Bricks ..................................................Christian P. Robert and Judith Rousseau 506 Ambiguity Aversion and Model Misspecification: An Economic Perspective ................................................Lars Peter Hansen and Massimo Marinacci 511 Rejoinder: Approximate Models and Robust Decisions. .James Watson and Chris Holmes 516 Filtering and Tracking Survival Propensity (Reconsidering the Foundations of Reliability) .......................................................................Nozer D. Singpurwalla 521 On Software and System Reliability Growth and Testing. ..............FrankP.A.Coolen 541 HowAboutWearingTwoHats,FirstPopper’sandthendeFinetti’s?..............Elja Arjas 545 WhatDoes“Propensity”Add?...................................................Jane Hutton 549 Reconciling the Subjective and Objective Aspects of Probability ...............Glenn Shafer 552 Rejoinder:ConcertUnlikely,“Jugalbandi”Perhaps..................Nozer D. Singpurwalla 555 ChaosCommunication:ACaseofStatisticalEngineering...............Anthony
    [Show full text]
  • Statistics: Challenges and Opportunities for the Twenty-First Century
    This is page i Printer: Opaque this Statistics: Challenges and Opportunities for the Twenty-First Century Edited by: Jon Kettenring, Bruce Lindsay, & David Siegmund Draft: 6 April 2003 ii This is page iii Printer: Opaque this Contents 1 Introduction 1 1.1 The workshop . 1 1.2 What is statistics? . 2 1.3 The statistical community . 3 1.4 Resources . 5 2 Historical Overview 7 3 Current Status 9 3.1 General overview . 9 3.1.1 The quality of the profession . 9 3.1.2 The size of the profession . 10 3.1.3 The Odom Report: Issues in mathematics and statistics 11 4 The Core of Statistics 15 4.1 Understanding core interactivity . 15 4.2 A detailed example of interplay . 18 4.3 A set of research challenges . 20 4.3.1 Scales of data . 20 4.3.2 Data reduction and compression. 21 4.3.3 Machine learning and neural networks . 21 4.3.4 Multivariate analysis for large p, small n. 21 4.3.5 Bayes and biased estimation . 22 4.3.6 Middle ground between proof and computational ex- periment. 22 4.4 Opportunities and needs for the core . 23 4.4.1 Adapting to data analysis outside the core . 23 4.4.2 Fragmentation of core research . 23 4.4.3 Growth in the professional needs. 24 4.4.4 Research funding . 24 4.4.5 A Possible Program . 24 5 Statistics in Science and Industry 27 5.1 Biological Sciences . 27 5.2 Engineering and Industry . 33 5.3 Geophysical and Environmental Sciences .
    [Show full text]
  • Why Distinguish Between Statistics and Mathematical Statistics – the Case of Swedish Academia
    Why distinguish between statistics and mathematical statistics { the case of Swedish academia Peter Guttorp1 and Georg Lindgren2 1Department of Statistics, University of Washington, Seattle 2Mathematical Statistics, Lund University, Lund 2017/10/11 Abstract A separation between the academic subjects statistics and mathematical statistics has existed in Sweden almost as long as there have been statistics professors. The same distinction has not been maintained in other countries. Why has it been kept so for long in Sweden, and what consequences may it have had? In May 2015 it was 100 years since Mathematical Statistics was formally estab- lished as an academic discipline at a Swedish university where Statistics had existed since the turn of the century. We give an account of the debate in Lund and elsewhere about this division dur- ing the first decades after 1900 and present two of its leading personalities. The Lund University astronomer (and mathematical statistician) C.V.L. Charlier was a lead- ing proponent for a position in mathematical statistics at the university. Charlier's adversary in the debate was Pontus Fahlbeck, professor in political science and statis- tics, who reserved the word statistics for \statistics as a social science". Charlier not only secured the first academic position in Sweden in mathematical statistics for his former Ph.D. student Sven Wicksell, but he also demonstrated that a mathematical statistician can be influential in matters of state, finance, as well as in different nat- ural sciences. Fahlbeck saw mathematical statistics as a set of tools that sometimes could be useful in his brand of statistics. After a summary of the organisational, educational, and scientific growth of the statistical sciences in Sweden that has taken place during the last 50 years, we discuss what effects the Charlier-Fahlbeck divergence might have had on this development.
    [Show full text]
  • Science and Engineering Labor Force
    National Science Board | Science & Engineering Indicators 2018 3 | 1 CHAPTER 3 Science and Engineering Labor Force Table of Contents Highlights................................................................................................................................................................................. 3-6 U.S. S&E Workforce: Definition, Size, and Growth ............................................................................................................ 3-6 S&E Workers in the Economy .............................................................................................................................................. 3-6 S&E Labor Market Conditions ............................................................................................................................................. 3-7 Demographics of the S&E Workforce ................................................................................................................................. 3-7 Global S&E Labor Force........................................................................................................................................................ 3-8 Introduction............................................................................................................................................................................. 3-9 Chapter Overview ................................................................................................................................................................. 3-9 Chapter
    [Show full text]
  • Probability Distributions Used in Reliability Engineering
    Probability Distributions Used in Reliability Engineering Probability Distributions Used in Reliability Engineering Andrew N. O’Connor Mohammad Modarres Ali Mosleh Center for Risk and Reliability 0151 Glenn L Martin Hall University of Maryland College Park, Maryland Published by the Center for Risk and Reliability International Standard Book Number (ISBN): 978-0-9966468-1-9 Copyright © 2016 by the Center for Reliability Engineering University of Maryland, College Park, Maryland, USA All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from The Center for Reliability Engineering, Reliability Engineering Program. The Center for Risk and Reliability University of Maryland College Park, Maryland 20742-7531 In memory of Willie Mae Webb This book is dedicated to the memory of Miss Willie Webb who passed away on April 10 2007 while working at the Center for Risk and Reliability at the University of Maryland (UMD). She initiated the concept of this book, as an aid for students conducting studies in Reliability Engineering at the University of Maryland. Upon passing, Willie bequeathed her belongings to fund a scholarship providing financial support to Reliability Engineering students at UMD. Preface Reliability Engineers are required to combine a practical understanding of science and engineering with statistics. The reliability engineer’s understanding of statistics is focused on the practical application of a wide variety of accepted statistical methods. Most reliability texts provide only a basic introduction to probability distributions or only provide a detailed reference to few distributions.
    [Show full text]
  • A Project Based Approach to Doe in Materials Lawrence Genalo Iowa State University, [email protected]
    Materials Science and Engineering Conference Materials Science and Engineering Papers, Posters and Presentations 1999 A Project Based Approach To Doe In Materials Lawrence Genalo Iowa State University, [email protected] Follow this and additional works at: http://lib.dr.iastate.edu/mse_conf Part of the Curriculum and Instruction Commons, Engineering Education Commons, Other Materials Science and Engineering Commons, and the Science and Mathematics Education Commons Recommended Citation Genalo, Lawrence, "A Project Based Approach To Doe In Materials" (1999). Materials Science and Engineering Conference Papers, Posters and Presentations. 20. http://lib.dr.iastate.edu/mse_conf/20 This Conference Proceeding is brought to you for free and open access by the Materials Science and Engineering at Iowa State University Digital Repository. It has been accepted for inclusion in Materials Science and Engineering Conference Papers, Posters and Presentations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. A Project Based Approach To Doe In Materials Abstract At Iowa State University, the Materials Science and Engineering Department teaches a course in the statistics of materials. Approximately one third of this two credit course is devoted to the design of experiments (DOE). A relatively brief introduction to the theory of DOE sets the stage for the inclusion of a software package used to assist materials engineers to design and analyze the results of experiments. Texts for engineering statistics (1-3) contain chapters dealing with the design of experiments. Literature in materials journals routinely contains references to DOE (4-8). Coupling these texts and recent articles with some practical exposure to design of experiments and the software used to do this, allows students some exposure to industrial practice.
    [Show full text]
  • A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education
    RERXXX10.3102/0034654317723009Belland et al.Bayesian Network Meta-Analysis of Scaffolding 723009research-article2017 Review of Educational Research December 2017, Vol. 87, No. 6, pp. 1042 –1081 DOI: 10.3102/0034654317723009 © 2017 AERA. http://rer.aera.net A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education Brian R. Belland, Andrew E. Walker, and Nam Ju Kim Utah State University Computer-based scaffolding provides temporary support that enables stu- dents to participate in and become more proficient at complex skills like problem solving, argumentation, and evaluation. While meta-analyses have addressed between-subject differences on cognitive outcomes resulting from scaffolding, none has addressed within-subject gains. This leaves much quantitative scaffolding literature not covered by existing meta-analyses. To address this gap, this study used Bayesian network meta-analysis to synthe- size within-subjects (pre–post) differences resulting from scaffolding in 56 studies. We generated the posterior distribution using 20,000 Markov Chain Monte Carlo samples. Scaffolding has a consistently strong effect across stu- dent populations, STEM (science, technology, engineering, and mathemat- ics) disciplines, and assessment levels, and a strong effect when used with most problem-centered instructional models (exception: inquiry-based learn- ing and modeling visualization) and educational levels (exception: second- ary education). Results also indicate some promising
    [Show full text]
  • A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education
    RERXXX10.3102/0034654317723009Belland et al.Bayesian Network Meta-Analysis of Scaffolding 723009research-article2017 View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DigitalCommons@USU Review of Educational Research December 2017, Vol. 87, No. 6, pp. 1042 –1081 DOI: 10.3102/0034654317723009 © 2017 AERA. http://rer.aera.net A Bayesian Network Meta-Analysis to Synthesize the Influence of Contexts of Scaffolding Use on Cognitive Outcomes in STEM Education Brian R. Belland, Andrew E. Walker, and Nam Ju Kim Utah State University Computer-based scaffolding provides temporary support that enables stu- dents to participate in and become more proficient at complex skills like problem solving, argumentation, and evaluation. While meta-analyses have addressed between-subject differences on cognitive outcomes resulting from scaffolding, none has addressed within-subject gains. This leaves much quantitative scaffolding literature not covered by existing meta-analyses. To address this gap, this study used Bayesian network meta-analysis to synthe- size within-subjects (pre–post) differences resulting from scaffolding in 56 studies. We generated the posterior distribution using 20,000 Markov Chain Monte Carlo samples. Scaffolding has a consistently strong effect across stu- dent populations, STEM (science, technology, engineering, and mathemat- ics) disciplines, and assessment levels, and a strong effect when used with most problem-centered instructional models (exception: inquiry-based learn- ing and modeling visualization) and educational levels (exception: second- ary education). Results also indicate some promising areas for future scaffolding research, including scaffolding among students with learning disabilities, for whom the effect size was particularly large (ḡ = 3.13).
    [Show full text]
  • Application of Statistics in Engineering Technology Programs
    American Journal of Engineering Education –2010 Volume 1, Number 1 Application Of Statistics In Engineering Technology Programs Wei Zhan, Texas A&M University, USA Rainer Fink, Texas A&M University, USA Alex Fang, Texas A&M University, USA ABSTRACT Statistics is a critical tool for robustness analysis, measurement system error analysis, test data analysis, probabilistic risk assessment, and many other fields in the engineering world. Traditionally, however, statistics is not extensively used in undergraduate engineering technology (ET) programs, resulting in a major disconnect from industry expectations. The research question: How to effectively integrate statistics into the curricula of ET programs, is in the foundation of this paper. Based on the best practices identified in the literature, a unique “learning-by-using” approach was deployed for the Electronics Engineering Technology Program at Texas A&M University. Simple statistical concepts such as standard deviation of measurements, signal to noise ratio, and Six Sigma were introduced to students in different courses. Design of experiments (DOE), regression, and the Monte Carlo method were illustrated with practical examples before the students applied the newly understood tools to specific problems faced in their engineering projects. Industry standard software was used to conduct statistical analysis on real results from lab exercises. The result from a pilot project at Texas A&M University indicates a significant increase in using statistics tools in course projects by students. Data from student surveys in selected classes indicate that students gained more confidence in statistics. These preliminary results show that the new approach is very effective in applying statistics to engineering technology programs.
    [Show full text]
  • Bayesian Methods for Robustness in Process
    The Pennsylvania State University The Graduate School Department of Industrial and Manufacturing Engineering BAYESIAN METHODS FOR ROBUSTNESS IN PROCESS OPTIMIZATION A Thesis in Industrial Engineering and Operations Research by Ramkumar Rajagopal °c 2004 Ramkumar Rajagopal Submitted in Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy August 2004 We approve the thesis of Ramkumar Rajagopal. Date of Signature Enrique del Castillo Associate Professor of Industrial Engineering Thesis Advisor Chair of Committee Tom M. Cavalier Professor of Industrial Engineering M. Jeya Chandra Professor of Industrial Engineering Steven F. Arnold Professor of Statistics Richard J. Koubek Professor of Industrial Engineering Head of the Department of Industrial and Manufacturing Engineering iii ABSTRACT The core objective of the research presented in this dissertation is to develop new methodologies based on Bayesian inference procedures for some problems occurring in manufacturing processes. The use of Bayesian methods of inference provides a natural framework to obtain solutions that are robust to various uncertainties in such processes as well as to assumptions made during the analysis. Speci¯cally, the methods presented here aim to provide robust solutions to problems in process optimization, tolerance control and multiple criteria decision making. Traditional approaches for process optimization start by ¯tting a model and then op- timizing the model to obtain optimal operating settings. These methods do not account for any uncertainty in the parameters of the model or in the form of the model. Bayesian approaches have been proposed recently to account for the uncertainty on the parameters of the model, assuming the model form is known.
    [Show full text]