Measuring test measurement error : a general approach

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Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (789 download)

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Book Synopsis Measuring test measurement error : a general approach by : Donald Boyd

Download or read book Measuring test measurement error : a general approach written by Donald Boyd and published by . This book was released on 2012 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Test-based accountability including value-added assessments and experimental and quasi-experimental research in education rely on achievement tests to measure student skills and knowledge. Yet we know little regarding important properties of these tests, an important example being the extent of test measurement error and its implications for educational policy and practice. While test vendors provide estimates of split-test reliability, these measures do not account for potentially important day-to-day differences in student performance. We show there is a credible, low-cost approach for estimating the total test measurement error that can be applied when one or more cohorts of students take three or more tests in the subject of interest (e.g., state assessments in three consecutive grades). Our method generalizes the test-retest framework allowing for either growth or decay in knowledge and skills between tests as well as variation in the degree of measurement error across tests. The approach maintains relatively unrestrictive, testable assumptions regarding the structure of student achievement growth. Estimation only requires descriptive statistics (e.g., correlations) for the tests. When student-level test-score data are available, the extent and pattern of measurement error heteroskedasticity also can be estimated. Utilizing math and ELA test data from New York City, we estimate the overall extent of test measurement error is more than twice as large as that reported by the test vendor and demonstrate how using estimates of the total measurement error and the degree of heteroskedasticity along with observed scores can yield meaningful improvements in the precision of student achievement and achievement-gain estimates.

Measurement Error and Research Design

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Publisher : SAGE
ISBN 13 : 9781412906425
Total Pages : 460 pages
Book Rating : 4.9/5 (64 download)

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Book Synopsis Measurement Error and Research Design by : Madhu Viswanathan

Download or read book Measurement Error and Research Design written by Madhu Viswanathan and published by SAGE. This book was released on 2005-02-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Measurement Error and Research Design is an ideal text for research methods courses across the social sciences, especially those in which a primer on measurement is needed. For the novice researcher, this book facilitates understanding of the basic principles required to design measures and methods for empirical research. For the experienced researcher, this book provides an in-depth analysis and discussion of the essence of measurement error and the procedures to minimize it. Most important, the book's unique approach bridges measurement and methodology through clear illustrations of the intangibles of scientific research."--BOOK JACKET.

New Developments in Statistical Information Theory Based on Entropy and Divergence Measures

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Publisher : MDPI
ISBN 13 : 3038979368
Total Pages : 344 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis New Developments in Statistical Information Theory Based on Entropy and Divergence Measures by : Leandro Pardo

Download or read book New Developments in Statistical Information Theory Based on Entropy and Divergence Measures written by Leandro Pardo and published by MDPI. This book was released on 2019-05-20 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly non-robust in cases of model misspecification under the presence of outlying observations. It is well-known that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.

Evaluating Measurement Accuracy

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Publisher : Springer Science & Business Media
ISBN 13 : 1441914560
Total Pages : 278 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Evaluating Measurement Accuracy by : Semyon G. Rabinovich

Download or read book Evaluating Measurement Accuracy written by Semyon G. Rabinovich and published by Springer Science & Business Media. This book was released on 2009-12-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Evaluating Measurement Accuracy" is intended for anyone who is concerned with measurements in any field of science or technology. It reflects the latest developments in metrology and offers new results, but is designed to be accessible to readers at different levels: meteorologists, engineers and experimental scientists who use measurements as tools in their professions, graduate and undergraduate students in the natural sciences and engineering, and technicians performing complex measurements in industry, quality control, and trade. The material of the book is presented from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements. This inclusion is a notable and unique aspect of this title as complex measurements done in industry and trade are often neglected in metrological literature, leaving the practitioners of these measurements to devise their own ad-hoc techniques.

Evaluating Measurement Accuracy

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Publisher : Springer Science & Business Media
ISBN 13 : 1461467179
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Evaluating Measurement Accuracy by : Semyon G Rabinovich

Download or read book Evaluating Measurement Accuracy written by Semyon G Rabinovich and published by Springer Science & Business Media. This book was released on 2013-07-03 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Evaluating Measurement Accuracy, 2nd Edition” is intended for those who are concerned with measurements in any field of science or technology. It reflects the latest developments in metrology and offers new results, but is designed to be accessible to readers at different levels: scientists who advance the field of metrology, engineers and experimental scientists who use measurements as tool in their professions, students and graduate students in natural sciences and engineering, and, in parts describing practical recommendations, technicians performing mass measurements in industry, quality control, and trade. This book presents material from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements. This new edition adds a method for estimating accuracy of indirect measurements with independent arguments, whose development Dr. Rabinovich was able to complete very recently. This method, which is called the Method of Enumeration, produces estimates that are no longer approximate, similar to the way the method of reduction described in the first edition removed approximation in estimating uncertainty of indirect measurements with dependent arguments. The method of enumeration completes addressing the range of problems whose solutions signify the emergence of the new theory of accuracy of measurements. A new method is added for building a composition of histograms, and this method forms a theoretical basis for the method of enumeration.Additionally, as a companion to this book, a concise practical guide that assembles simple step-by-step procedures for typical tasks the practitioners are likely to encounter in measurement accuracy estimation is available at SpringerLink.

Value Added Modeling and Growth Modeling with Particular Application to Teacher and School Effectiveness

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Publisher : IAP
ISBN 13 : 1623967767
Total Pages : 327 pages
Book Rating : 4.6/5 (239 download)

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Book Synopsis Value Added Modeling and Growth Modeling with Particular Application to Teacher and School Effectiveness by : Robert W. Lissitz

Download or read book Value Added Modeling and Growth Modeling with Particular Application to Teacher and School Effectiveness written by Robert W. Lissitz and published by IAP. This book was released on 2014-12-01 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling student growth has been a federal policy requirement under No Child Left Behind (NCLB). In addition to tracking student growth, the latest Race To The Top (RTTP) federal education policy stipulates the evaluation of teacher effectiveness from the perspective of added value that teachers contribute to student learning and growth. Student growth modeling and teacher value-added modeling are complex. The complexity stems, in part, from issues due to non-random assignment of students into classes and schools, measurement error in students’ achievement scores that are utilized to evaluate the added value of teachers, multidimensionality of the measured construct across multiple grades, and the inclusion of covariates. National experts at the Twelfth Annual Maryland Assessment Research Center’s Conference on “Value Added Modeling and Growth Modeling with Particular Application to Teacher and School Effectiveness” present the latest developments and methods to tackle these issues. This book includes chapters based on these conference presentations. Further, the book provides some answers to questions such as what makes a good growth model? What criteria should be used in evaluating growth models? How should outputs from growth models be utilized? How auxiliary teacher information could be utilized to improve value added? How multiple sources of student information could be accumulated to estimate teacher effectiveness? Whether student-level and school-level covariates should be included? And what are the impacts of the potential heterogeneity of teacher effects across students of different aptitudes or other differing characteristics on growth modeling and teacher evaluation? Overall, this book addresses reliability and validity issues in growth modeling and value added modeling and presents the latest development in this area. In addition, some persistent issues have been approached from a new perspective. This edited volume provides a very good source of information related to the current explorations in student growth and teacher effectiveness evaluation.

Measurement Errors and Uncertainties

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387253589
Total Pages : 326 pages
Book Rating : 4.2/5 (535 download)

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Book Synopsis Measurement Errors and Uncertainties by : S. G. Rabinovich

Download or read book Measurement Errors and Uncertainties written by S. G. Rabinovich and published by Springer Science & Business Media. This book was released on 2005-08-15 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical reference on theory and methods of estimating measurement errors and uncertainty for both scientists and engineers in industry and experimental research. Building on the fundamentals of measurement theory, this book offers a wealth of practial recommendations and procedures. It differs from the majority of books in that it balances coverage of probabilistic methods with detailed information on the characterization, calibration, standardization and limitations of measuring instruments, with specific examples from both electrical and mechanical systems. In addition to a general updating to reflect current research, new material in this edition includes increased coverage of indirect measurements, with a new, simpler, more efficient method for this class of measurements.

Measurement Error

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Publisher : CRC Press
ISBN 13 : 1420066587
Total Pages : 465 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Measurement Error by : John P. Buonaccorsi

Download or read book Measurement Error written by John P. Buonaccorsi and published by CRC Press. This book was released on 2010-03-02 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 20 years, comprehensive strategies for treating measurement error in complex models and accounting for the use of extra data to estimate measurement error parameters have emerged. Focusing on both established and novel approaches, Measurement Error: Models, Methods, and Applications provides an overview of the main techniques and illu

Design and Analysis of Reliability Studies

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Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Design and Analysis of Reliability Studies by : Graham Dunn

Download or read book Design and Analysis of Reliability Studies written by Graham Dunn and published by Oxford University Press, USA. This book was released on 1989 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide to a wide variety of statistical methods is designed for use in reliability studies. It provides a general and practically oriented text on the dependability of behavioral measurements. These range from formal diagnoses, through simple ordinal rating scales, to psychometric test scores assumed to be measured on an interval scale.

Psychological Testing in the Service of Disability Determination

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Publisher : National Academies Press
ISBN 13 : 0309370930
Total Pages : 233 pages
Book Rating : 4.3/5 (93 download)

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Book Synopsis Psychological Testing in the Service of Disability Determination by : Institute of Medicine

Download or read book Psychological Testing in the Service of Disability Determination written by Institute of Medicine and published by National Academies Press. This book was released on 2015-06-29 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The United States Social Security Administration (SSA) administers two disability programs: Social Security Disability Insurance (SSDI), for disabled individuals, and their dependent family members, who have worked and contributed to the Social Security trust funds, and Supplemental Security Income (SSSI), which is a means-tested program based on income and financial assets for adults aged 65 years or older and disabled adults and children. Both programs require that claimants have a disability and meet specific medical criteria in order to qualify for benefits. SSA establishes the presence of a medically-determined impairment in individuals with mental disorders other than intellectual disability through the use of standard diagnostic criteria, which include symptoms and signs. These impairments are established largely on reports of signs and symptoms of impairment and functional limitation. Psychological Testing in the Service of Disability Determination considers the use of psychological tests in evaluating disability claims submitted to the SSA. This report critically reviews selected psychological tests, including symptom validity tests, that could contribute to SSA disability determinations. The report discusses the possible uses of such tests and their contribution to disability determinations. Psychological Testing in the Service of Disability Determination discusses testing norms, qualifications for administration of tests, administration of tests, and reporting results. The recommendations of this report will help SSA improve the consistency and accuracy of disability determination in certain cases.

Handbook of the Economics of Education

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Publisher : Elsevier
ISBN 13 : 0323992412
Total Pages : 614 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Handbook of the Economics of Education by :

Download or read book Handbook of the Economics of Education written by and published by Elsevier. This book was released on 2023-01-18 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of the Economics of Education describes the research frontier in key topical areas and sets the agenda for further work. Modern analysis in the economics of education has made tremendous strides in understanding fundamental issues related to the production of human capital and the impact of varying institutional features of education systems. By bringing together some of the world’s leading scholars, this volume provides a unique view of scholarship in the area. The international perspectives of the editors – Hanushek at Stanford, Machin at LSE, and Woessmann at Munich – leads to a volume with something for all researchers. Topics range from the economics of early childhood education to inequality in society to cash transfers in developing countries. Identification and evaluation of the state of the art. Clear descriptions of the meaning of existing research and the most likely avenues for the future Insights into how policy interventions in education can help or hurt human capital outcomes

Research Methods in Psychology For Dummies

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Publisher : John Wiley & Sons
ISBN 13 : 1119035104
Total Pages : 365 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Research Methods in Psychology For Dummies by : Martin Dempster

Download or read book Research Methods in Psychology For Dummies written by Martin Dempster and published by John Wiley & Sons. This book was released on 2015-10-13 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your hands-on introduction to research methods in psychology Looking for an easily accessible overview of research methods in psychology? This is the book for you! Whether you need to get ahead in class, you're pressed for time, or you just want a take on a topic that's not covered in your textbook, Research Methods in Psychology For Dummies has you covered. Written in plain English and packed with easy-to-follow instruction, this friendly guide takes the intimidation out of the subject and tackles the fundamentals of psychology research in a way that makes it approachable and comprehensible, no matter your background. Inside, you'll find expert coverage of qualitative and quantitative research methods, including surveys, case studies, laboratory observations, tests and experiments—and much more. Serves as an excellent supplement to course textbooks Provides a clear introduction to the scientific method Presents the methodologies and techniques used in psychology research Written by the authors of Psychology Statistics For Dummies If you're a first or second year psychology student and want to supplement your doorstop-sized psychology textbook—and boost your chances of scoring higher at exam time—this hands-on guide breaks down the subject into easily digestible bits and propels you towards success.

Handbook of Test Methods and Practices [on the Fundamentals of Testing Electronic Equipment]

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Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Handbook of Test Methods and Practices [on the Fundamentals of Testing Electronic Equipment] by : Philco Corporation

Download or read book Handbook of Test Methods and Practices [on the Fundamentals of Testing Electronic Equipment] written by Philco Corporation and published by . This book was released on 1956 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles of Psychological Assessment

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Publisher : CRC Press
ISBN 13 : 1003861172
Total Pages : 785 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Principles of Psychological Assessment by : Isaac T. Petersen

Download or read book Principles of Psychological Assessment written by Isaac T. Petersen and published by CRC Press. This book was released on 2024-05-02 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the principles of psychological assessment to help researchers and clinicians better develop, evaluate, administer, score, integrate, and interpret psychological assessments. It discusses psychometrics (reliability and validity), the assessment of various psychological domains (behavior, personality, intellectual functioning), various measurement methods (e.g., questionnaires, observations, interviews, biopsychological assessments, performance-based assessments), and emerging analytical frameworks to evaluate and improve assessment including: generalizability theory, structural equation modeling, item response theory, and signal detection theory. The text also discusses ethics, test bias, and cultural and individual diversity. Key Features Gives analysis examples using free software Helps readers apply principles to research and practice Provides text, analysis code/syntax, R output, figures, and interpretations integrated to guide readers Uses the freely available petersenlab package for R Principles of Psychological Assessment: With Applied Examples in R is intended for use by graduate students, faculty, researchers, and practicing psychologists.

Military Standard

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Publisher :
ISBN 13 :
Total Pages : 920 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Military Standard by : United States. Dept. of Defense

Download or read book Military Standard written by United States. Dept. of Defense and published by . This book was released on with total page 920 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Getting Value Out of Value-Added

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Publisher : National Academies Press
ISBN 13 : 030915099X
Total Pages : 97 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Getting Value Out of Value-Added by : National Academy of Education

Download or read book Getting Value Out of Value-Added written by National Academy of Education and published by National Academies Press. This book was released on 2010-01-25 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Value-added methods refer to efforts to estimate the relative contributions of specific teachers, schools, or programs to student test performance. In recent years, these methods have attracted considerable attention because of their potential applicability for educational accountability, teacher pay-for-performance systems, school and teacher improvement, program evaluation, and research. Value-added methods involve complex statistical models applied to test data of varying quality. Accordingly, there are many technical challenges to ascertaining the degree to which the output of these models provides the desired estimates. Despite a substantial amount of research over the last decade and a half, overcoming these challenges has proven to be very difficult, and many questions remain unanswered-at a time when there is strong interest in implementing value-added models in a variety of settings. The National Research Council and the National Academy of Education held a workshop, summarized in this volume, to help identify areas of emerging consensus and areas of disagreement regarding appropriate uses of value-added methods, in an effort to provide research-based guidance to policy makers who are facing decisions about whether to proceed in this direction.

Lean Math: Figuring to Improve

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Publisher : SME
ISBN 13 : 0872638812
Total Pages : 466 pages
Book Rating : 4.8/5 (726 download)

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Book Synopsis Lean Math: Figuring to Improve by : Mark R. Hamel

Download or read book Lean Math: Figuring to Improve written by Mark R. Hamel and published by SME. This book was released on 2017-01-25 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lean transformations are decidedly more challenging when the math is inconsistent with lean principles, misapplied, or just plain wrong. Math should never get in the way of a lean transformation, but instead should facilitate it. Lean Math is the indispensable reference for this very purpose. A single, comprehensive source, the book presents standard and specialized approaches to tackling the math required of lean and six sigma practitioners across all industries—seasoned and newly minted practitioners alike. Lean Math features more than 160 thoughtfully organized entries. Ten chapters cover system-oriented math, time, the “-ilities” (availability, repeatability, stability, etc.), work, inventory, performance metrics, basic math and hypothesis testing, measurement, experimentation, and more. Two appendices cover standard work for analyzing data and understanding and dealing with variation. Practitioners will quickly locate the precise entry(ies) that is relevant to the problem or continuous improvement opportunity at hand. Each entry not only provides background on the related lean principles, formulas, examples, figures, and tables, but also tips, cautions, cross-references to other associated entries, and the occasional “Gemba Tale” that shares real-world experiences. The book consistently encourages the practitioner to engage in math-assisted plan-do-check-act (PDCA) cycles, employing approaches that include simulation and “trystorming.” Lean Math truly transcends the “numbers” by reinforcing and refreshing lean thinking for the very purpose of Figuring to Improve. REVIEWER COMMENTS “Hamel and O’Connor provide both the novice and experienced lean practitioner a comprehensive, common-sense reference for lean math. For example, I know that our Lean Support Office team would have gladly used dozens of Lean Math entries during a recent lean management system pilot. The concepts, context, and examples would have certainly helped our execution and provided greater clarity during our training activities. Lean Math is a must have book for Lean Support Office people!” —Dave Pienta, Director, Lean Support Office, Moog, Inc. Aircraft Group “A practical math book may sound like an oxymoron, but Lean Math is both pragmatic and accessible. Hamel and O’Connor do an excellent job keeping the math as simple as possible, while bringing lean principles to the forefront of the discussion. The use of insurance and healthcare industry examples especially helps simplify the translation for lean practitioners in non-manufacturing industries. Readers will be able to use the numerous tables and figures to clearly illustrate and teach lean concepts to others. Lean Math is a reference book that every lean practitioner or Black Belt should have in their library!” —Peter Barnett, MBB, Liberty Management System Architect, Liberty Mutual Insurance “Lean Math is a comprehensive reference book within which the lean practitioner can quickly find straightforward examples illustrating how to perform almost any lean calculation. Equally useful, it imparts the importance of the relevant lean principal(s). While coaching some recent transformation efforts, I put Lean Math to the test by asking several novice practitioners to reference it during their work. They were promptly rewarded with deeper insight and effectiveness—a reflection of this book’s utility and value to the lean practitioner.” —Greg Lane, international lean transformation coach, speaker, and author of three books including, “Made-to-Order Lean: Excelling in a High-Mix, Low-Volume Environment” “While the technical, social, and management sciences behind lean must be learned by doing, their conceptual bases are absolutely validated by the math. This validation is particularly crucial to overcoming common blind spots ingrained by traditional practice. Hamel and O’Connor’s text is a comprehensive and readable resource for lean implementers at all levels who are seeking a deeper understanding of lean tools and systems. Clear diagrams and real-world examples create a bridge for readers between theory and practice—theory proven by practice. If math is the language of science, then Lean Math is indeed the language of lean science.” —Bruce Hamilton, President, Greater Boston Manufacturing Partnership, Director Emeritus for the Shingo Institute “Mark and Michael have done a tremendous service for the lean community by tackling this daunting subject. There are so many ways to quantify value, display improvement, and define complex problems that choosing the right methods and measures becomes an obstacle to progress. Lean Math helps remove that obstacle. Almost daily, operations leaders in every industry need the practical math and lean guidance in these pages. Now, finally, we have it in one place. Thank you.” —Zane Ferry, Executive Director, National Operations, QMS Continuous Improvement, Quest Diagnostics “Too many lean books dwell on principles, but offer little to address critical how-to questions, such as, ‘How do I use these concepts to solve my specific problem?’ With plain English explanations, simple illustrations, and examples across industries, Lean Math bridges a long-standing gap. Hamel and O’Connor’s Lean Math is sure to become a must-have reference for every lean practitioner working to improve performance in any modern workplace.” —Jeff Fuchs, Executive Director, Maryland World Class Consortia, Past Chairman, Lean Certification Oversight Committee “Lean Math fills a huge gap in the continuous improvement library, helping practitioners to translate data, activities, and ideas into meaningful information for effective experimentation and intelligent decisions. This reference comes at a critical time for the healthcare industry as we struggle to improve quality, while controlling costs. Though we don’t make widgets, our people, processes, and patients will benefit from the tools provided in this reference. The numerous examples, as well as the Gemba Tales scattered throughout the book, bring life to the principles and formulas. Lean Math is impressive in both scope and presentation of content.” —Tim Pettry, Senior Process Improvement Specialist, Cleveland Clinic “Lean Math is a great book for those times when only the correct answer will do. The math, along with the Gemba Tales, are helpful for those in the midst of the technical aspects of a transformation, as well as those of us who once knew much of this but haven’t used it in a while.” —Beau Keyte, organization transformation and performance improvement coach, author of two Shingo-Award winning books: “The Complete Lean Enterprise” and “Perfecting Patient Journeys” “Math and numbers aren’t exclusively the domain of six sigma! Toyota leaders describe lean as an organizational culture, a managerial approach, and a philosophy. They also maintain that the last piece of lean is technical methods, which includes the math we need for properly sizing inventory levels, validating hypotheses, gauging improvement, and more. Lean Math is a useful book that compiles important mathematical and quantitative methods that complement the people side of lean. Hamel and O’Connor are extremely qualified to deftly explain these methods. Lest you think it’s a dry math text, there are Gemba Tales and examples from multiple industries, including healthcare, which illustrate these approaches in very relatable ways.” —Mark Graban, Shingo-Award winning author, speaker, consultant, and blogger “When you begin a lean journey, it’s like starting an exercise regimen—the most important thing is to start. But as you mature, and as you achieve higher levels of excellence, rigor becomes increasingly important. Lean Math provides easy, elegant access to the necessary rigor required for effective measurement and analysis and does so in practical terms with excellent examples.” —Misael Cabrera, PE, Director, Arizona Department Environmental Quality