Encyclopedia of Measurement and Statistics

Encyclopedia of Measurement and Statistics


Edited by: Neil J. Salkind


The Encyclopedia of Measurement and Statistics presents state-of-the-art information and ready-to-use facts from the fields of measurement and statistics in an unintimidating style. The ideas and tools contained in these pages are approachable and can be invaluable for understanding our very technical world and the increasing flow of information. Although there are references that cover statistics and assessment in depth, none provides as comprehensive a resource in as focused and accessible a manner as the three volumes of this Encyclopedia. Through approximately 500 contributions, experts provide an overview and an explanation of the major topics in these two areas.

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  • Subject Index
  • Front Matter
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    • Biographies
    • Charts, Graphs, and Visual Displays
    • Computer Topics and Tools
    • Concepts and Issues in Measurement
    • Concepts and Issues in Statistics
    • Data and Data Reduction Techniques
    • Descriptive Statistics
    • Evaluation
    • Experimental Methods
    • Inferential Statistics
    • Organizations and Publications
    • Prediction and Estimation
    • Probability
    • Qualitative Methods
    • Samples, Sampling, and Distributions
    • Statistical Techniques
    • Statistical Tests
    • Tests by Name
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      Editorial Board


      Neil J. Salkind

      University of Kansas

      Managing Editor

      Kristin Rasmussen

      University of Kansas

      Advisory Board

      Jeffrey Banfield

      Department of Mathematical Sciences Montana State University

      Bruce Frey

      Department of Psychology and Research in Education University of Kansas

      Wenxin Jiang

      Department of Statistics Northwestern University

      Galin L. Jones

      School of Statistics University of Minnesota

      Jianan Peng

      Department of Mathematics and Statistics Acadia University

      Jerome P. Reiter

      Practice of Statistics and Decision Sciences Institute of Statistics and Decision Sciences Duke University

      List of Entries

      Reader's Guide

      The purpose of the Reader's Guide is to provide you with a tool you can use to locate specific entries in the encyclopedia, as well as to find out what other related entries might be of interest to you. For example, if you are interested in the visual display of information and want to learn how to create a bar chart (under the general heading of Charts, Graphs, and Visual Displays in the Reader's Guide), you can also find reference to such entries as Histogram, Line Chart, and Mosaic Plots, all related to the same general topic.

      The Reader's Guide is also a very direct and simple way to get an overview of which items are contained in the encyclopedia. Although each of the categories lists items in alphabetic order (as the encyclopedia is organized), you can glance through the main headings of the guide and then focus more on a particular area of interest. Then, just turn to any particular entry you want to locate. These are easily found because they appear in alphabetical order.

      About the Editor

      Neil J. Salkind (PhD, University of Maryland, 1973) is a Professor of Psychology and Research in Education at the University of Kansas in Lawrence, Kansas. He completed postdoctoral training as a member of the Bush Child and Family Policy Institute at the University of North Carolina and has authored and coauthored more than 125 scholarly papers and books. Most recently, he is the author of Statistics for People Who (Think They) Hate Statistics: The Excel Edition (2007), Tests & Measurement for People Who (Think They) Hate Tests & Measurement (2006), the Encyclopedia of Human Development (2006), Theories of Human Development (2004), and Statistics for People Who (Think They) Hate Statistics (2004), all published by Sage. He was the editor of Child Development Abstracts and Bibliography, published by the Society for Research in Child Development (SRCD), from 1988 through 2001, and he is the treasurer-elect of Division 7 of the American Psychological Association.


      Francisco J. Abad

      Universidad Autonoma de Madrid

      Inmaculada Aban

      University of Alabama at Birmingham

      Hervé Abdi

      University of Texas at Dallas

      Phillip L. Ackerman

      Georgia Institute of Technology

      Demetrios S. Alexopoulos

      University of Patras, Greece

      Audrey Amrein-Beardsley

      Arizona State University

      Lauren E. Auld

      DePauw University

      Carrie R. Ball

      University of Wisconsin–Madison

      Kimberly A. Barchard

      University of Nevada, Las Vegas

      Jonathan Barzilai

      Dalhousie University

      Edward J. Bedrick

      University of New Mexico

      Mark L. Berenson

      Montclair State University

      Dongsheng Bi

      University of Nebraska Lincoln

      Damian P. Birney

      University of Sydney

      David M. Boynton

      Saint Michael's College

      Bruce A. Bracken

      College of William & Mary

      Jennifer Bragger

      Montclair State University

      Gary G. Brannigan

      State University of New York–Plattsburgh

      Ernest W. Brewer

      University of Tennessee

      Carolyn Brodbeck

      Chapman University

      Sarah Brookhart

      American Psychological Society

      Duane Brown

      University of North Carolina, Chapel Hill

      Jennifer Ann Brown

      University of Canterbury

      Shawn T. Bubany

      University of Minnesota

      Michael J. Burke

      Tulane University

      Mary Margaret Capraro

      Texas A&M University

      Robert M. Capraro

      Texas A&M University

      Joseph E. Cavanaugh

      University of Iowa

      Hua-Hua Chang

      University of Illinois

      Elaine Chapman

      University of Western Australia

      Bernard C. K. Choi

      Public Health Agency of Canada

      Siu L. Chow

      University of Regina

      Michelle D. Chudleigh

      Alberta Hospital Edmonton

      Moo K. Chung

      University of Wisconsin

      M. H. Clark

      Southern Illinois University

      Murray Clayton

      University of Wisconsin–Madison

      A. Jill Clemence

      Austen Riggs Center

      Roberto Colom

      Universidad Autonoma de Madrid

      John Colombo

      University of Kansas

      Andrew L. Comrey

      University of California, Los Angeles

      Dianne Cook

      Iowa State University

      R. Kelly Crace

      College of William & Mary

      Bonnie Cramond

      University of Georgia

      William L. Curlette

      Georgia State University

      Larry Daniel

      University of North Florida

      Craig Darch

      University of Auburn

      Duncan Day

      Queen's University

      E. Jacquelin Dietz

      Meredith College

      Bryan J. Dik

      Colorado State University

      Heather Doescher

      University of Wisconsin–Madison

      Romilia Domínguez de Ramírez

      University of Houston

      Joseph A. Doster

      University of North Texas

      Donald M. Dougherty

      Wake Forest University Baptist Medical Center

      Ronald C. Eaves

      Auburn University

      Anna Ebel-Lam

      Queen's University

      Maeghan N. Edwards

      Pennsylvania State University

      Stephen N. Elliott

      Vanderbilt University

      Susan Embretson

      Georgia Institute of Technology

      Craig K. Enders

      Arizona State University

      Marie Joelle Estrada

      University of North Carolina, Chapel Hill

      Martin G. Evans

      University of Toronto

      Leandre R. Fabrigar

      Queen's University

      Gail F. Fahoome

      Wayne State University

      Andy P. Field

      University of Sussex

      Barry Forer

      University of British Columbia

      Robert A. Forsyth

      University of Iowa

      Brian F. French

      Purdue University

      Kathryn H. Ganske

      Georgia State University

      Travis L. Gee

      University of Queensland, Australia

      Carole E. Gelfer

      William Paterson University

      James E. Gentle

      George Mason University

      Morton A. Gernsbacher

      University of Wisconsin–Madison

      Maribeth Gettinger

      University of Wisconsin–Madison

      Marjan Ghahramanlou-Holloway

      Uniformed Services University of the Health Sciences

      Lisa M. Given

      University of Alberta

      Kevin W. Glavin

      Kent State University

      Charles Golden

      Nova Southeastern University

      Adele Eskeles Gottfried

      California State University, Northridge

      Naomi Grant

      Queen's University

      James W. Grice

      Oklahoma State University

      Erik J. Groessl

      VA San Diego / University of California, San Diego

      Lyndsi M. Grover

      University of North Texas

      Suzanne M. Grundy

      California State University, San Bernardino

      Anthony J. Guarino

      University of Auburn

      Mads Haahr

      Trinity College Dublin

      John W. Hagen

      Society of Research in Child Development

      Brian Haig

      University of Canterbury

      Thomas Haladyna

      Arizona State University

      Young-Hoon Ham

      University of Tennessee

      Ronald K. Hambleton

      University of Massachusetts

      Chirok Han

      Victoria University of Wellington

      David Hann

      University of Kansas

      Jo-Ida C. Hansen

      University of Minnesota

      James W. Hardin

      University of South Carolina

      Clay Helberg

      SPSS Inc.

      Susanne Hempel

      University of York

      Ryan G. Henry

      Brigham Young University

      Kristin Heron

      Syracuse University

      Matthew J. Hertenstein

      DePauw University

      Christine L. Himes

      Syracuse University

      Nathaniel R. Hirtz

      Murray State University

      David B. Hitchcock

      University of South Carolina

      James S. Ho

      Alberta Hospital Edmonton

      Heike Hofmann

      Iowa State University

      Cody S. Hollist

      University of Nebraska–Lincoln

      Johnny Holloway

      American University

      Robert Hopkins

      Queens University

      Jennifer R. Hsu

      William Paterson University

      Louis M. Hsu

      Fairleigh Dickinson University

      Allison Huck

      University of Kentucky

      Schuyler W. Huck

      University of Tennessee

      Bradley E. Huitema

      Western Michigan University

      Russell T. Hurlburt

      University of Nevada, Las Vegas

      Jennifer Ivie

      University of Kansas

      Robert A. Jacobs

      University of Rochester

      John Jamieson

      Lakehead University

      Galin L. Jones

      University of Minnesota

      Samuel Juni

      New York University

      Sema A. Kalaian

      Eastern Michigan University

      Matthew E. Kaler

      University of Minnesota

      Kristen M. Kalymon

      University of Wisconsin–Madison

      Robert M. Kaplan

      University of California, Los Angeles

      Michael A. Karchmer

      Gallaudet Research Institute

      Michael Karson

      University of Denver

      Rafa M. Kasim

      Kent State University

      Allison B. Kaufman

      University of California, Riverside

      James C. Kaufman

      California State University, San Bernardino

      Lisa Keller

      University of Massachusetts, Amherst

      Lindy Kilik

      Queen's University

      Kyung Hee Kim

      Eastern Michigan University

      Roger E. Kirk

      Baylor University

      Steve Kirkland

      University of Regina

      Theresa Kline

      University of Calgary

      James Randolph Knaub, Jr.

      U.S. Government, Energy Information Administration

      John C. Kolar

      Medical City Children's Hospital, Dallas

      Nicole B. Koppel

      Montclair State University

      Richard M. Kreminski

      Texas A&M University–Commerce

      Joachim I. Krueger

      Brown University

      Thomas Kubiszyn

      University of Houston

      Jouni Kuha

      London School of Economics

      Jonna M. Kulikowich

      Pennsylvania State University

      Wilda Laija-Rodriguez

      California State University, Northridge

      David M. Lane

      Rice University

      Sean Laraway

      San Jose State University

      Michael D. Larsen

      Iowa State University

      Nicole Lazar

      University of Georgia

      Howard B. Lee

      University of California, Riverside

      W. Vanessa Lee

      University of Minnesota

      Nancy L. Leech

      Colorado University, Denver

      Lawrence Leemis

      College of William & Mary

      Pui-Wa Lei

      Pennsylvania State University

      Russell V. Lenth

      University of Iowa

      Ming-Ying Leung

      University of Texas at El Paso

      Melanie Leuty

      University of Minnesota

      Ronald F. Levant

      University of Akron

      Robert W. Levenson

      University of California, Berkeley

      Jacob J. Levy

      University of Tennessee

      Bruce Lindsay

      Pennsylvania State University

      Brian R. Little

      Carleton University and Harvard University

      David F. Lohman

      University of Iowa

      Jeffrey D. Long

      University of Minnesota

      Sarah A. Lopienski

      Kent State University

      Kathryn Lou

      University of Pennsylvania

      Gerard H. Maassen

      Utrecht University

      Karen MacGregor

      Queens University

      Effie Maclellan

      University of Strathclyde

      W. Todd Maddox

      University of Texas at Austin

      Silvia A. Madrid

      University of Arizona

      Susan J. Maller

      Purdue University

      Dawn M. Marsh

      Wake Forest University Baptist Medical Center

      Luci A. Martin

      University of North Texas

      Kenneth B. Matheny

      Georgia State University

      Charles W. Mathias

      Wake Forest University Health Sciences

      Sonia Matwin

      University of Utah

      Mary Ann McCabe

      American Psychological Association

      Geoffrey McLachlan

      University of Queensland

      Adam W. Meade

      North Carolina State University

      Christopher J. Mecklin

      Murray State University

      Franklin Mendivil

      Acadia University

      Jorge L. Mendoza

      University of Oklahoma

      George Michailidis

      University of Michigan

      Jeremy Miles

      University of York

      Richard B. Miller

      Brigham Young University

      Ross E. Mitchell

      Gallaudet University

      Amitava Mitra

      Auburn University

      Geert Molenberghs

      University Hasselt

      Paul Molin

      University of Bourgogne

      Dirk F. Moore

      University of Medicine and Dentistry of New Jersey

      Kevin E. Moore

      DePaul University

      Bernice S. Moos

      Stanford University

      Rudolf H. Moos

      Stanford University

      Mark Mostert

      Regent University

      Ronald Neath

      University of Minnesota

      Liqiang Ni

      University of Central Florida

      Adelheid A. M. Nicol

      Royal Military College

      Meghan E. Norris

      Queen's University

      Anthony J. Onwuegbuzie

      University of South Florida

      J. Shelly Paik

      Queen's University

      Anita W. P. Pak

      University of Ottawa

      Paul E. Panek

      Ohio State University–Newark

      Hans Anand Pant

      Humboldt University of Berlin

      Dong-Ho Park

      University of Tennessee

      Scott Parker

      American University

      Sandrine Pavoine

      Muséum National d'Histoire Naturelle, Paris

      Manohar Pawar

      Charles Sturt University

      Edsel Pena

      University of South Carolina

      Sarah Peterson

      University of Kansas

      Andrew M. Pomerantz

      Southern Illinois University Edwardsville

      Jennifer L. Porter

      DePauw University

      Ronald D. Porter

      Queen's University

      Patricia Ramsey

      Fordham University

      Philip H. Ramsey

      Queens College of City University of New York

      John Randal

      Victoria University of Wellington

      Kristin Rasmussen

      University of Kansas

      Marco Reale

      University of Canterbury

      John R. Reddon

      Alberta Hospital Edmonton

      Malcolm James Ree

      Our Lady of the Lake University

      Jerome Reiter

      Duke University

      Bixiang Ren

      University of Tennessee

      Alberto Restori

      California State University, Northridge

      James C. Rhoads

      Westminster College

      Andrew T. Roach

      Vanderbilt University

      Beth Rodgers

      University of Wisconsin–Milwaukee

      Michael C. Rodriguez

      University of Minnesota

      Ward Rodriguez

      California State University, East Bay

      Javier Rojo

      Rice University

      Patrick J. Rosopa

      University of Central Florida

      Thomas E. Rudy

      University of Pittsburgh

      André A. Rupp

      Humboldt University

      Charles J. Russo

      University of Dayton

      Thomas Rutledge

      UC San Diego

      Steve Saladin

      University of Idaho

      Neil J. Salkind

      University of Kansas

      Elizabeth M. Salter

      University of Texas at Dallas

      Mark L. Savickas

      Northeast Ohio Universities College of Medicine

      Shlomo S. Sawilowsky

      Wayne State University

      Khalid Sayood

      University of Nebraska–Lincoln

      Carl J. Scarrott

      University of Canterbury

      Stanley L. Sclove

      University of Illinois at Chicago

      Kyoungah See

      Miami University

      William R. Shadish

      University of California, Merced

      Ramalingam Shanmugam

      Texas State University

      Boris Shulkin

      Wayne State University

      Dean Keith Simonton

      University of California, Davis

      Gary N. Siperstein

      University of Massachusetts, Boston

      Stephen G. Sireci

      University of Massachusetts, Amherst

      William P. Skorupski

      University of Kansas

      Joshua Smyth

      Syracuse University

      Robert A. Spies

      University of Nebraska–Lincoln

      Christopher J. Sroka

      Ohio State University

      Douglas Steinley

      University of Missouri–Columbia

      Steven E. Stemler

      Wesleyan University

      Michael Stewart

      University of Sydney

      David W. Stockburger

      United States Air Force Academy

      Eugene F. Stone-Romero

      University of Texas, San Antonio

      Bryce F. Sullivan

      Southern Illinois University Edwardsville

      Jun Sun

      Texas A&M University

      Martin A. Tanner

      Northwestern University

      Christopher P. Terry

      Syracuse University

      Robert M. Thorndike

      Western Washington University

      Davood Tofighi

      Arizona State University

      Larry Toothaker

      University of Oklahoma

      Marietta J. Tretter

      Texas A&M University

      George C. Tseng

      University of Pittsburgh

      Ping-Lun Tu

      University of Tennessee

      Jung-Ying Tzeng

      North Carolina State University

      Graham Upton

      University of Essex

      Dominique Valentin

      University of Bourgogne

      Nicholas G. Velissaris

      Society for Research in Child Development

      Geert Verbeke

      Katholieke Universiteit Leuven

      Fran Vertue

      Child and Family Psychology Centre

      Abdus S. Wahed

      University of Pittsburgh

      Harald Walach

      University College Northampton

      Russell F. Waugh

      Edith Cowan University

      Ann M. Weber

      University of Wisconsin–Madison

      Gail Weems

      University of Arkansas Little Rock

      Kimberly Weems

      North Carolina State University

      Kirsten Wells

      Kansas University

      Shane M. Whippler

      Alberta Hospital Edmonton

      Rand R. Wilcox

      University of Southern California

      Todd J. Wilkinson

      University of Minnesota

      Siân E. Williams

      Canterbury Christ Church University

      Thomas O. Williams, Jr.

      Virginia Polytechnic Institute

      Jay K. Wood

      Queens University

      Suzanne Woods-Groves

      Auburn University

      Daniel B. Wright

      University of Sussex

      Karl L. Wuensch

      East Carolina University

      Hongwei Yang

      University of Tennessee–Knoxville

      Keming Yang

      University of Reading

      Zhiliang Ying

      Columbia University

      Vincent R. Zalcik

      Alberta Hospital Edmonton

      April L. Zenisky

      University of Massachusetts, Amherst

      Jin Zhang

      University of Manitoba

      Zhigang Zhang

      Oklahoma State University

      Shuangmei (Christine) Zhou

      University of Minnesota

      Marvin Zuckerman

      University of Delaware

      Bruno D. Zumbo

      University of British Columbia


      It's an interesting paradox when an important subject, which can help us make sense of our busy, everyday world, is considered very difficult to approach. Such is the case with measurement and statistics. However, this does not necessarily have to be the case, and we believe that the Encyclopedia of Measurement and Statistics will show you why.

      These two areas of study encompass a very wide range of topics, and a knowledge of even the basic concepts and ideas allows us to be much better prepared as intelligent consumers of information.

      Whether we are interested in knowing if there is a difference between two groups in their preference for a particular brand of cereal or how the Americans with Disabilities Act works, we need to know how to analyze and interpret information. And often, when that information is in the form of numbers, that's where statistics and measurement come into play. That basic stat course in college might have been a nightmare, but the material is no more difficult to grasp and apply than is any other discipline in the social and behavioral sciences.

      Although hundreds of books have been written about the different topics that are contained in the Encyclopedia of Measurement and Statistics, and there are thousands upon thousands of studies that have been conducted in this area, what we offer here is something quite different—a comprehensive overview of important topics. What we hope we have accomplished are entries that comprise a comprehensive overview of the most important topics in the areas of measurement and statistics—entries that share this important information in a way that is informative; not too technical; and even, in some cases, entertaining.

      Through almost 500 contributions and some special elements that will be described later in this preface, experts in each of the entries contained in these pages contribute an overview and an explanation of the major topics in these two fields.

      The underlying rationale for the selection of particular topics and their presentation in this encyclopedia comes from the need to share with the educated reader topics that are rich, diverse, and deserving of closer inspection. Within these pages, we provide the overview and the detail that we feel is necessary to become well acquainted with these topics.

      As in many other encyclopedias, the Encyclopedia of Measurement and Statistics is organized in alphabetical order, from A through Z. However, particular themes were identified early on that could be used to organize conceptually the information and the entries. These themes or major topic areas constitute the Reader's Guide, which appears on page xiii. Categories such as Experimental Methods, Qualitative Methods, and Organizations and Publications are only a few of the many that help organize the entire set of contributions.

      The Process

      The first task in the creation of a multivolume encyclopedia such as this is the development of a complete and thorough listing of the important topics in the disciplines of measurement and statistics. This process started with the identification of entries that the editor and advisory board thought were important to include. We tried to make sure that these entries included topics that would be of interest to a general readership, but we wanted to exclude terms and ideas that were too highly technical or too far removed from the interests of the everyday reader. This list was reviewed several times until we felt that it was a comprehensive set of topics that best fit the vision for the encyclopedia.

      Like many other disciplines, there is a great deal of overlap between different important concepts and ideas in measurement and statistics. For example, although there is an entry titled Descriptive Statistics (which is a general overview), there is much greater detail in the entries titled Mean and Median. That overlap is fine because it provides two different, and compatible, views of the same topic and can only help reinforce one's knowledge. We hope that the crossreferences we provide will help the user understand this and get the most out of learning about any one idea, term, or procedure.

      As expected, this list was edited and revised as we worked and as authors were recruited to write particular entries. Enthusiastic authors suggested new topics that might have been overlooked as well as removing topics that might have no appeal. All of these changes were taken into consideration as the final list was assembled.

      The next step was to assign a length to a particular entry, which ranged from 500 words for simple definitions or biographies (such as the one for the Arithmetic Mean or Charles Babbage, respectively) to almost 4,000 words for longer, more in-depth exploration for topics (such as the entry on Aptitude Tests). In between were articles that were 1,500 and 2,000 words in length. (At times, authors asked that the length be extended because they had so much information they wanted to share and they felt that the limitation on space was unwarranted. In most cases, it was not a problem to allow such an extension.)

      The final step was the identification of authors. This took place through a variety of mechanisms, including the identification of individuals based on the advisory board recommendations and/or the editor's professional and personal experiences, authors of journal articles and books who focused on a particular area directly related to the entry, and referrals from other individuals who were well known in the field.

      Once authors were identified and invited, and once they confirmed that they could participate, they were sent detailed instructions and given a deadline for the submission of their entry. The results, as you well know by now, after editing, layout, and other production steps, are in your hands.

      How to use this Reference

      We know the study of measurement and statistics can be less than inviting. But, as we mentioned at the beginning of this preface, and want to emphasize once again here, the ideas and tools contained in these pages are approachable and can be invaluable for understanding our very technical world and an increasing flow of information.

      Although many of the ideas you read about in these pages are relatively recent, some are centuries old. Yet both kinds hold promise for your being able to better navigate the increasingly complex world of information we each face every day.

      So, although many of us believe that this encyclopedia should only be consulted when a term or idea needs some clarification, why not take some time and just browse through the material and see what types of entries are offered and how useful you might find them?

      As we wrote earlier, a primary goal of creating this set of volumes was to open up the broad discipline of measurement and statistics to a wider and more general audience than usual.

      Take these books and find a comfortable seat in the library, browse through the topics, and read the ones that catch your eye. We're confident that you'll continue reading and looking for additional related entries, such as “Applying Ideas on Statistics and Measurement,” where you can find examples of how these ideas are applied and, in doing so, learn more about whatever interests you.

      Should you want to find a topic within a particular area, consult the Reader's Guide, which organizes entries within this two-volume set into one general category. Using this tool, you can quickly move to an area or a specific topic that you find valuable and of interest.

      Finally, there other elements that should be of interest.

      Appendix A is a guide to basic statistics for those readers who might like a more instructional, step-by-step presentation of basic concepts in statistics and measurement. It also includes a table of critical values used in hypothesis testing and an important part of any reference in this area. These materials are taken from Statistics for People Who (Think They) Hate Statistics, written by the editor and also published by Sage.

      Appendix B represents a collection of some important and useful sites on the Internet that have additional information about measurement and statistics. Although such sites tend to remain stable, there may be some changes in the Internet address. If you cannot find the Web page using the address that is provided, then search for the name of the Web site using Google or another search engine.

      Finally, Appendix C is a glossary of terms and concepts you will frequently come across in these volumes.


      This has been a challenging and rewarding project. It was ambitious in scope because it tried to corral a wide and diverse set of topics within measurement and statistics into a coherent set of volumes.

      First, thanks to the Advisory Board, a group of scholars in many different areas that took the time to review the list of entries and make invaluable suggestions as to what the reader might find valuable and how that topic should be approached. The Advisory Board members are very busy people who took the time to help the editor develop a list that is broad in scope and represents the most important topics in human development. You can see a complete list of who these fine people are on page vi.

      My editor and my publisher at Sage Publications, Lisa Cuevas Shaw and Rolf Janke, respectively, deserve a great deal of thanks for bringing this project to me and providing the chance to make it work. They are terrific people who provide support and ideas and are always there to listen. And perhaps best of all, they get things done.

      Other people also helped make this task enjoyable and helped create the useful, informative, and approachable set of volumes you hold in your hands. Among these people are Tracy Alpern, Sage senior project editor, and Bonnie Freeman, Liann Lech, and Carla Freeman, copy editors.

      I'll save one of the biggest thank-yous for Kristin Rasmussen, the managing editor, who managed this project in every sense of the word, including the formidable tasks of tracking entries, submissions, reviews, and resubmissions. All of this was easily accomplished with enthusiasm, initiative, and perseverance when answering endless questions through thousands of e-mails to hundreds of authors. She is currently a doctoral student at the University of Kansas and has an exceptionally bright future. Thank you sincerely.

      And, of course, how could anything of this magnitude ever have been done without the timely execution and accurate scholarship of the contributing authors? They understood that the task at hand was to introduce educated readers (such as you) to new areas of interest in a very broad field, and without exception, they did a wonderful job. You will see throughout that their writing is clear and informative—just what material like this should be for the intelligent reader. To them, a sincere thank you and a job well done.

      Finally, as always, none of this would have happened or been worth undertaking without my comrade in (almost all) ups and down and ins and outs, and my truest and best friend, Leni. Sara and Micah, versions 1.1 and 1.2, didn't hurt either.

      Neil J.Salkind University of Kansas
    • Appendix A

      Ten Commandments of Data Collection

      The following text is taken from Neil J. Salkind's best-selling introduction to statistics text, Statistics for People Who (Think They) Hate Statistics, 2nd edition (2004).

      Now that you know how to analyze data, you would be well served to hear something about collecting them. The data collection process can be a long and rigorous one, even if it involves only a simple, one-page questionnaire given to a group of students, parents, patients, or voters. The data collection process may very well be the most time-consuming part of your project. But as many researchers do, this period of time is also used to think about the upcoming analysis and what it will entail.

      Here they are: the ten commandments for making sure your data get collected in a way that they are usable. Unlike the original Ten Commandments, these should not be carved in stone (because they can certainly change), but if you follow them, you can avoid lots of aggravation.

      Commandment 1. As you begin thinking about a research question, also begin thinking about the type of data you will have to collect to answer that question. Interview? Questionnaire? Paper and pencil? Find out how other people have done it in the past by reading the relevant journals in your area of interest and consider doing what they did.

      Commandment 2. As you think about the type of data you will be collecting, think about where you will be getting the data. If you are using the library for historical data or accessing files of data that have already been collected, such as census data (available through the U.S. Census Bureau and some online), you will have few logistical problems. But what if you want to assess the interaction between newborns and their parents? The attitude of teachers toward unionizing? The age at which people over 50 think they are old? All of these questions involve needing people to provide the answers, and finding people can be tough. Start now.

      Commandment 3. Make sure that the data collection forms you use are clear and easy to use. Practice on a set of pilot data so you can make sure it is easy to go from the original scoring sheets to the data collection form.

      Commandment 4. Always make a duplicate copy of the data file, and keep it in a separate location. Keep in mind that there are two types of people: those who have lost their data and those who will. Keep a copy of data collection sheets in a separate location. If you are recording your data as a computer file, such as a spreadsheet, be sure to make a backup!

      Commandment 5. Do not rely on other people to collect or transfer your data unless you have personally trained them and are confident that they understand the data collection process as well as you do. It is great to have people help you, and it helps keep the morale up during those long data collection sessions. But unless your helpers are competent beyond question, you could easily sabotage all your hard work and planning.

      Commandment 6. Plan a detailed schedule of when and where you will be collecting your data. If you need to visit three schools and each of 50 children needs to be tested for a total of 10 minutes at each school, that is 25 hours of testing. That does not mean you can allot 25 hours from your schedule for this activity. What about travel from one school to another? What about the child who is in the bathroom when it is his turn, and you have to wait 10 minutes until he comes back to the classroom? What about the day you show up and Cowboy Bob is the featured guest… and on and on. Be prepared for anything, and allocate 25% to 50% more time in your schedule for unforeseen happenings.

      Commandment 7. As soon as possible, cultivate possible sources for your subject pool. Because you already have some knowledge in your own discipline, you probably also know of people who work with the type of population you want or who might be able to help you gain access to these samples. If you are in a university community, it is likely that there are hundreds of other people competing for the same subject sample that you need. Instead of competing, why not try a more out-of-the-way (maybe 30 minutes away) school district or social group or civic organization or hospital, where you might be able to obtain a sample with less competition?

      Commandment 8. Try to follow up on subjects who missed their testing session or interview. Call them back and try to reschedule. Once you get in the habit of skipping possible participants, it becomes too easy to cut the sample down to too small a size. And you can never tell—the people who drop out might be dropping out for reasons related to what you are studying. This can mean that your final sample of people is qualitatively different from the sample you started with.

      Commandment 9. Never discard the original data, such as the test booklets, interview notes, and so forth. Other researchers might want to use the same database, or you may have to return to the original materials for further information.

      And Number 10? Follow the previous 9. No kidding!

      Tables of Critical Values

      The following tables are taken from Neil J. Salkind's best-selling introduction to statistics text, Statistics for People Who (Think They) Hate Statistics, 2nd edition (2004).

      Table 1 Areas Beneath the Normal Curve
      Area Between the Mean and theArea Between the Mean and theArea Between the Mean and theArea Between the Mean and theArea Between the Mean and theArea Between the Mean and theArea Between the Mean and theArea Between the Mean and the
      Table 2 t Values Needed for Rejection of the Null Hypothesis
      How to use this table:
      • Compute the t value test statistic.
      • Compare the obtained t value to the critical value listed in this table. Be sure you have calculated the number of degrees of freedom correctly and you have selected an appropriate level of significance.
      • If the obtained value is greater than the critical or tabled value, the null hypothesis (that the means are equal) is not the most attractive explanation for any observed differences.
      • If the obtained value is less than the critical or table value, the null hypothesis is the most attractive explanation for any observed differences.
      One-Tailed TestTwo-Tailed Test
      Table 3 Critical Values for Analysis of Variance or F Test
      How to use this table:
      • Compute the F value.
      • Determine the number of degrees of freedom for the numerator (k–1) and the number of degrees of freedom for the denominator (nk).
      • Locate the critical value by reading across to locate the degrees of freedom in the numerator and down to locate the degrees of freedom in the denominator. The critical value is at the intersection of this column and row.
      • If the obtained value is greater than the critical or tabled value, the null hypothesis (that the means are equal to one another) is not the most attractive explanation for any observed differences.
      • If the obtained value is less than the critical or tabled value, the null hypothesis is the most attractive explanation for any observed differences.
      df for the Numerator
      df for the DenominatorType I Error Rate123456
      Table 4 Values of the Correlation Coefficient Needed for Rejection of the Null Hypothesis
      How to use this table:
      • Compute the value of the correlation coefficient.
      • Compare the value of the correlation coefficient with the critical value listed in this table.
      • If the obtained value is greater than the critical or tabled value, the null hypothesis (that the correlation coefficient is equal to 0) is not the most attractive explanation for any observed differences.
      • If the obtained value is less than the critical or tabled value, the null hypothesis is the most attractive explanation for any observed differences.
      One-Tailed TestTwo-Tailed Test
      Table 5 Critical Values for the Chi-Square Test
      How to use this table:
      • Compute the χ2 value.
      • Determine the number of degrees of freedom for the rows (R–1) and the number of degrees of freedom for the columns (C–1). If it's a one-dimensional table, then you have only columns.
      • Locate the critical value by locating the degrees of freedom in the titled (df) column, and under the appropriate column for level of significance, read across.
      • If the obtained value is greater than the critical or tabled value, the null hypothesis (that the frequencies are equal to one another) is not the most attractive explanation for any observed differences.
      • If the obtained value is less than the critical or tabled value, the null hypothesis is the most attractive explanation for any observed differences.
      Level of Significance

      Appendix B

      Internet Sites about Statistics

      What follows is a listing of Internet sites and a brief description of each that focus on the general areas of statistics and measurement. Also included are sites where data (on many different topics) have been collected and can be accessed.

      As you use these, keep in mind the following:

      • Internet addresses (known as URLs) often change, as does the content. If one of these Internet addresses does not work, search for the name of the site using any search engine.
      • Any Internet site is only as good as its content. For example, N or N − 1 might be given as the correct denominator for a formula, and although that might be true, you should double check any information with another Internet resource or a book on the subject.
      • If you find something that is inaccurate on a site, contact the Webmaster or the author of the site and let him or her know that a correction needs to be made.

      Name: http://statistics.com

      Where to find it: http://www.statistics.com/

      If there is a queen of statistics sites, then http://statistics.com is it. It offers not only links to hundreds of other sites and an online introductory statistics course, but also online professional development courses. You can try statistics software, look at the free stuff available on the Web, get help if you're a teacher with quizzes and other teaching materials, and even participate in online discussions. This is the place to start your travels.

      Name: U.S. Department of Labor, Bureau of Labor Statistics

      Where to find it: http://www.bls.gov/

      Local, state, and federal government agencies are data warehouses, full of information about everything from employment to demographics to consumer spending. This particular site (which is relatively old at 10 years on the Web) is for the Bureau of Labor Statistics, the principal fact-finding agency for the federal government in the areas of labor economics and statistics. It is full of numbers and ideas. Some of the data can be downloaded as HTML or Excel files, and you can also get historical data going back 10 years in some instances.

      Name: Probability and Quintile Applets Where to find it: http://www.stat.stanford.edu/~naras/jsm/FindProbability.html

      Applets are small programs that can visually represent an idea or a process very effectively. These two, by Balasubramanian Narasimhan from Stanford University, do such things as compute the probability of a score under the normal curve (see Figure 1 on the following page) and calculate the quintiles (fifths) of a distribution. They are easy to use, fun to play with, and very instructional. You can find another similar applet by Gary McClelland at http://psych.colorado.edu/~mcclella/java/normal/handleNormal.html

      Figure 1 Probability Applet

      Name: FedStats

      Where to find it: http://www.fedstats.gov/

      Here's another huge storehouse of data that is the entry point for many different federal agencies. You can easily access data from individual states or from agencies by subjects (such as health), access published collections of statistics, and even get the kids involved in child-oriented agency Web sites both entertaining and educational.

      Name: Random Birthday Applet

      Where to find it: http://www-stat.stanford.edu/~susan/surprise/Birthday.html

      This is an incredible illustration of how probability works. You enter the number of birthdays you want generated at random, and the laws of probability should operate so that in a group of 30 such random selections, the odds are very high that there will be at least two matches for the same birthday. Try it—it works.

      Name: The Statistics Homepage

      Where to find it: http://www.statsoftinc.com/textbook/stathome.html

      Here you'll find a self-contained course in basic statistics, brought to you by the people who developed and sell StatSoft, one of many statistical programs. On this site, you will find tutorials that take you from the elementary concepts of statistics through the more advanced topics, such as factor and discriminant analysis.

      Name: National Center for Health Statistics

      Where to find it: http://www.cdc.gov/nchs/

      The National Center for Health Statistics compiles information that helps guide actions and policies to improve health in the United States. Among other things, these data are used to help identify health problems, evaluate the effectiveness of programs, and provide data for policymakers.

      Name: The World Wide Web Virtual Library: Statistics

      Where to find it: http://www.stat.ufl.edu/vlib/statistics.html

      The good people at the University of Florida's Department of Statistics bring you this page, which contains links to statistics departments all over the world. It provides a great deal of information about graduate study in these areas as well as other resources.

      Name: Social Statistics Briefing Room

      Where to find it: http://www.whitehouse.gov/fsbr/ssbr.html

      This service, which calls the White House home, provides access to current federal social statistics and links to information from a wide range of federal agencies. This is a very good, and broad, starting point to access data made available through different agencies.

      Name: Statistics on the Web

      Where to find it: http://my.execpc.com/~helberg/statistics.html

      More groupings of URLs and Internet addresses from Clay Helberg. A bit like http://statistics.com, but full of listings of professional organizations, publications, and software packages (many of which you can download for a trial).

      Name: Food and Agriculture Organization for the United Nations

      Where to find it: http://faostat.fao.org/

      If you want to go international, this is a site containing online information (in multilingual formats) and databases for more than 3 million time series records covering international statistics in areas such as production, population, and exports.

      Name: Web Pages That Perform Statistical Calculations!

      Where to find it: http://members.aol.com/johnp71/javastat.html

      At the time of this writing, this site contains more than 600 links to books, tutorials, free software, and interactive tools, such as a guide to what statistical test to use to answer what questions, all assembled by John Pezzullo.

      Name: Free Statistical Software

      Where to find it: http://freestatistics.altervista.org/stat.php

      An extensive collection of statistical analysis software packages that range from simple programs for students to advanced programs that do everything from statistical visualization to time series analysis. Many of these programs are freeware, and many are open source, available to be modified by users.

      Name: Java Applets

      Where to find it: http://www.stat.duke.edu/sites/java.html

      The Institute of Statistics and Decision Sciences at Duke University and NWP Associates put together a collection of Java applets (Java is the language in which these small programs are written, and applets are small applications) that allows the user to demonstrate interactively various statistical techniques and tools, such as constructing histograms and illustrating how the central limit theorem works.

      Name: HyperStat Online Textbook

      Where to find it: http://davidmlane.com/hyperstat/

      This site contains an entire online course in basic statistics from David Lane that covers every topic from simple descriptive statistics to effect size. The “Hyper” nature of the site allows the user to easily move from one topic to another through the extensive use of live links. And, as a bonus, each new screen has additional links to sites that focus on learning statistics.

      Name: Rice Virtual Lab in Statistics

      Where to find it: http://www.ruf.rice.edu/~lane/rvls.html

      This is where the HyperStat Online Textbook has its home and is the main page (also done by David Lane) of Rice University's statistics program. In addition to the HyperStat link, it has links to simulations, case studies, and a terrific set of applets that are very useful for teaching and demonstration purposes.

      Name: Reliability, Validity, and Fairness of Classroom Assessments

      Where to find it: http://www.ncrel.org/sdrs/areas/issues/methods/assment/as5relia.htm

      A discussion of the reliability, validity, and fairness of classroom testing from the North Central Educational Laboratory.

      Name: The Multitrait Multimethod Matrix

      Where to find it: http://www.socialresearchmethods.net/kb/mtmmmat.htm

      A very good site for a discussion of validity issues in measurement in general and specific discussion about the multitrait multimethod brought to you by William M. K. Trochim.

      Name: Content Validity, Face Validity, and Quantitative Face Validity

      Where to find it: http://www.burns.com/wcbcontval.htm

      Although a bit dated (around 1996), this Web site offers a detailed discussion by William C. Burns on content, face, quantitative, and other types of validity.

      Name: The National Education Association

      Where to find it: http://www.nea.org/parents/testingguide.html. also

      This national organization of teaching professionals provides assistance to parents, teachers, and others in understanding test scores.

      Name: The Learning Center

      Where to find it: http://webster.commnet.edu/faculty/~simonds/tests.htm

      It's a reality that other than through studying, test scores can be improved if test takers understand the different demands of different types of tests. This item contains information on using different strategies to increase test scores.

      Name: The Advanced Placement

      Where to find it: http://apbio.biosci.uga.edu/exam/Essays/

      This is an old site, but people at the University of Georgia have posted items from a variety of different topic areas covered in the Advanced Placement (AP) exams that high school students can take in a step to qualify for college credit.

      Name: Essay Question

      Where to find it: http://www.salon.com/tech/feature/1999/05/25/computer_grading/

      http://Salon.com offers a discussion of automated grading in general and specially, as well as essay question grading using computers.

      Name: Matching Questions on Minerals and Rocks

      Where to find it: http://www.usd.edu/esci/exams/matching.html

      A good example of how easy it is to adapt matching questions to an interactive electronic format.

      An increasingly large part of doing research, as well as other intensive, more qualitative projects, involves specially designed software. At http://www.scolari.com/, you can find a listing of several different types and explore which might be right for you if you intend to pursue this method (interviewing) and this methodology (qualitative).

      FairTest—The National Center for Fair and Open Testing at http://www.fairtest.org/index.htm has as its mission to “end the misuses and flaws of standardized testing and to ensure that evaluation of students, teachers and schools is fair, open, valid and educationally beneficial.” A really interesting site to visit.

      Preparing Students to Take Standardized Achievement Tests (at http://pareonline.net/getvn.asp?v=1&n=11) was written by William A. Mehrens (and first appeared in Practical Assessment, Research & Evaluation) for school administrators and teachers and discusses what test scores mean and how they can be most useful in understanding children's performance.

      The Clifton StrengthsFinder™ at http://education.gallup.com/content/default.asp?ci=886 is a Webbased assessment tool published by the Gallup Organization (yep, the poll people) to help people better understand their talents and strengths by measuring the presence of 34 themes of talent. You might want to take it and explore these themes.

      Find out just about everything you ever wanted to know (and more) about human intelligence at Human Intelligence: Historical Influences, Current Controversies and Teaching Resources at http://www.indiana.edu/~intell/

      The following text is taken from Neil J. Salkind's best-selling introduction to statistics text, Statistics for People Who (Think They) Hate Statistics, 2nd edition (2004).

      Pages and pages of every type of statistical resource you can want has been creatively assembled by Professor David W. Stockburger at http://www.psychstat.smsu.edu/scripts/dws148f/statisticsresourcesmain.asp. This site receives the gold medal of statistics sites. Don't miss it.

      For example, take a look at Berrie's page (at http://www.huizen.dds.n~berrie/) and see some QuickTime (short movies) of the effects of changing certain data points on the value of the mean and standard deviation. Or, look at the different home pages that have been created by instructors for courses offered around the country. Or, look at all of the different software packages that can do statistical analysis.

      Want to draw a histogram? How about a table of random numbers? A sample-size calculator? The Statistical Calculators page at http://www.stat.ucla.edu/calculators/ has just about every type (more than 15) of calculator and table you could need. Enough to carry you through any statistics course that you might take and even more.

      For example, you can click on the Random Permutations link and complete the two boxes (as you see in Figure 2 for 2 random permutations of 100 integers), and you get the number of permutations you want. This is very handy when you need a table of random numbers for a specific number of participants so you can assign them to groups.

      Figure 1 Generating a Set of Random Numbers

      The History of Statistics page located at http://www.Anselm.edu/homepage/jpitocch/biostatshist.html contains portraits and bibliographies of famous statisticians and a time line of important contributions to the field of statistics. So, do names like Bernoulli, Galton, Fisher, and Spearman pique your curiosity? How about the development of the first test between two averages during the early 20th century? It might seem a bit boring until you have a chance to read about the people who make up this field and their ideas—in sum, pretty cool ideas and pretty cool people.

      SurfStat Australia (at http://www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html) is the online component of a basic stat course taught at the University of Newcastle, Australia, but has grown far beyond just the notes originally written by Annette Dobson in 1987, and updated over several years' use by Anne Young, Bob Gibberd, and others. Among other things, SurfStat contains a complete interactive statistics text. Besides the text, there are exercises, a list of other statistics sites on the Internet, and a collection of Java applets (cool little programs you can use to work with different statistical procedures).

      This online tutorial with 18 lessons, at http://www.davidmlane.com/hyperstat/index.html, offers nicely designed and userfriendly coverage of the important basic topics. What we really liked about the site was the glossary, which uses hypertext to connect different concepts to one another. For example, in Figure 3, you can see the definition of descriptive statistics also linked to other glossary terms, such as mean, standard deviation, and box plot. Click on any of those and zap! you're there.

      Figure 1 Sample HyperStat Screen

      There are data all over the place, ripe for the picking. Here are just a few. What to do with these? Download them to be used as examples in your work or as examples of analysis that you might want to do, and you can use these as a model.

      Then there are all the data sets that are available through the federal government (besides the census). Your tax money supports it, so why not use it? For example, there's FEDSTATS (at http://www.fedstats.gov/), where more than 70 agencies in the U.S. federal government produce statistics of interest to the public. The Federal Interagency Council on Statistical Policy maintains this site to provide easy access to the full range of statistics and information produced by these agencies for public use. Here you can find country profiles contributed by the (boo!) CIA; public school student, staff, and faculty data (from the National Center for Education Statistics); and the Atlas of the United States Mortality (from the National Center for Health Statistics). What a ton of data!

      The University of Michigan's Statistical Resources on the Web (at http://www.lib.umich.edu/govdocs/stats.html) has hundreds and hundreds of resource links, including those to banking, book publishing, the elderly, and, for those of you with allergies, pollen count. Browse, search for what exactly it is that you need—no matter, you are guaranteed to find something interesting.

      At http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html, you can find a data set including the 1994 National League Baseball Salaries or the data on TV, Physicians, and Life Expectancy. Nothing earth-shaking, just fun to download and play with.

      The World Wide Web Virtual Library: Statistics is the name of the page, but the one-word title is misleading because the site (from the good people at the University of Florida at http://www.stat.ufl.edu/vlib/statistics.html) includes information on just about every facet of the topic, including data sources, job announcements, departments, divisions and schools of statistics (a huge description of programs all over the world), statistical research groups, institutes and associations, statistical services, statistical archives and resources, statistical software vendors and software, statistical journals, mailing list archives, and related fields. Tons of great information is available here. Make it a stop along the way.

      Statistics on the Web at http://www.maths.uq.edu.au/~gks/webguide/datasets.html is another location that's just full of information and references that you can easily access. Here, you'll find information on professional organizations, institutes and consulting groups, educational resources, Web courses, online textbooks, publications and publishers, statistics book lists, software-oriented pages, mailing lists and discussion groups, and even information on statisticians and other statistical people.

      Figure 1 Selecting the Correct Stat Technique to Use—Just a Few Clicks Away

      If you do ever have to teach statistics, or even tutor fellow students, this is one place you'll want to visit: http://noppa5.pc.helsinki.fi/links.html. It contains hundreds of resources on every topic that was covered in Statistics for People Who (Think They) Hate Statistics and more. You name it and it's here: regression, demos, history, Sila (a demonstration of inference), an interactive online tutorial, statistical graphics, handouts to courses, teaching materials, journal articles, and even quizzes! Whew, what a deal. There tends to be a lot of material that may not be suited to what you are doing in this class, but this wide net has certainly captured some goodies.

      http://Statistics.com (http://www.statistics.com) has it all—a wealth of information on courses, software, statistical methods, jobs, books, and even a homework helper. For example, if you want to know about free Webbased stat packages, click on that link on the left-hand side of the page. Here's one (see Figure 4) from Dr. Bill Trochim…. You just click your way through answering questions to get the answer to what type of analysis should be used.

      Appendix C


      The following text is taken from Neil J. Salkind's best-selling introduction to statistics text, Statistics for People Who (Think They) Hate Statistics, 2nd edition (2004).

        Analysis of variance
      • A test for the difference between two or more means. A simple analysis of variance (or ANOVA) has only one independent variable, whereas a factorial analysis of variance tests the means of more than one independent variable. One-way analysis of variance looks for differences between the means of more than two groups.
        Arithmetic mean
      • A measure of central tendency that sums all the scores in the data sets and divides by the number of scores.
      • The quality of the normal curve such that the tails never touch.
      • The most representative score in a set of scores.
        Bell-shaped curve
      • A distribution of scores that is symmetrical about the mean, median, and mode and has asymptotic tails.
        Class interval
      • The upper and lower boundaries of a set of scores used in the creation of a frequency distribution.
        Coefficient of alienation
      • The amount of variance unaccounted for in the relationship between two variables.
        Coefficient of determination
      • The amount of variance accounted for in the relationship between two variables.
        Coefficient of nondetermination
      • See coefficient of alienation
        Concurrent validity
      • A type of validity that examines how well a test outcome is consistent with a criterion that occurs in the present.
        Construct validity
      • A type of validity that examines how well a test reflects an underlying construct.
        Content validity
      • A type of validity that examines how well a test samples a universe of items.
        Correlation coefficient
      • A numerical index that reflects the relationship between two variables.
        Correlation matrix
      • A set of correlation coefficients.
      • Another term for the outcome variable.
        Criterion validity
      • A type of validity that examines how well a test reflects some criterion that occurs either in the present (concurrent) or in the future (predictive).
        Critical value
      • The value necessary for rejection (or nonacceptance) of the null hypothesis.
        Cumulative frequency distribution
      • A frequency distribution that shows frequencies for class intervals along with the cumulative frequency for each.
      • A record of an observation or an event such as a test score, a grade in math class, or a response time.
        Data point
      • An observation.
        Data set
      • A set of data points.
        Degrees of freedom
      • A value that is different for different statistical tests and approximates the sample size of number of individual cells in an experimental design.
        Dependent variable
      • The outcome variable or the predicted variable in a regression equation.
        Descriptive statistics
      • Values that describe the characteristics of a sample or population.
        Direct correlation
      • A positive correlation where the values of both variables change in the same direction.
        Directional research hypothesis
      • A research hypothesis that includes a statement of inequality.
        Effect size
      • A measure of the magnitude of a particular outcome.
        Error in prediction
      • The difference between the actual score (Y) and the predicted score (Y¯).
        Error of estimate
      • See error in prediction
        Error score
      • The part of a test score that is random and contributes to the unreliability of a test.
        Factorial analysis of variance
      • An analysis of variance with more than one factor or independent variable.
        Factorial design
      • A research design where there is more than one treatment variable.
        Frequency distribution
      • A method for illustrating the distribution of scores within class intervals.
        Frequency polygon
      • A graphical representation of a frequency distribution.
      • A graphical representation of a frequency distribution.
      • An if-then statement of conjecture that relates variables to one another.
        Independent variable
      • The treatment variable that is manipulated or the predictor variable in a regression equation.
        Indirect correlation
      • A negative correlation where the values of variables move in opposite directions.
        Inferential statistics
      • Tools that are used to infer the results based on a sample to a population.
        Interaction effect
      • The outcome where the effect of one factor is differentiated across another factor.
        Internal consistency reliability
      • A type of reliability that examines the one-dimensional nature of an assessment tool.
        Interrater reliability
      • A type of reliability that examines the consistency of raters.
        Interval level of measurement
      • A scale of measurement that is characterized by equal distances between points on some underlying continuum.
      • The quality of a distribution such that it is flat or peaked.
      • The quality of a normal curve that defines its peakedness.
        Line of best fit
      • The regression line that best fits the actual scores and minimizes the error in prediction.
        Linear correlation
      • A correlation that is best expressed as a straight line.
        Main effect
      • In analysis of variance, when a factor or an independent variable has a significant effect upon the outcome variable.
      • A type of average where scores are summed and divided by the number of observations.
        Mean deviation
      • The average deviation for all scores from the mean of a distribution.
        Measures of central tendency
      • The mean, median, and mode.
      • The point at which 50% of the cases in a distribution fall below and 50% fall above.
      • The central point in a class interval.
      • The most frequently occurring score in a distribution.
        Multiple regression
      • A statistical technique where several variables are used to predict one.
        Nominal level of measurement
      • A scale of measurement that is characterized by categories with no order or difference in magnitude.
        Nondirectional research hypothesis
      • A hypothesis that posits no direction, but a difference.
        Nonparametric statistics
      • Distribution-free statistics.
        Normal curve
      • See bell-shaped curve
        Null hypothesis
      • A statement of equality between a set of variables.
        Observed score
      • The score that is recorded or observed.
        Obtained value
      • The value that results from the application of a statistical test.
      • A visual representation of a cumulative frequency distribution.
        One-tailed test
      • A directional test.
        One-way analysis of variance
      • See analysis of variance
        Ordinal level of measurement
      • A scale of measurement that is characterized by an underlying continuum that is ordered.
      • Those scores in a distribution that are noticeably much more extreme than the majority of scores. Exactly what score is an outlier is usually an arbitrary decision made by the researcher.
        Parallel forms reliability
      • A type of reliability that examines the consistency across different forms of the same test.
        Parametric statistics
      • Statistics used for the inference from a sample to a population.
        Pearson product-moment correlation
      • See correlation coefficient
        Percentile point
      • The point at or below where a score appears.
      • The quality of a normal curve that defines its flatness.
      • All the possible subjects or cases of interest.
        Post hoc
      • After the fact, referring to tests done to determine the true source of a difference between three or more groups.
        Predictive validity
      • A type of validity that examines how well a test outcome is consistent with a criterion that occurs in the future.
      • The variable that predicts an outcome.
      • The highest minus the lowest score, and a gross measure of variability. Exclusive range is the highest score minus the lowest score. Inclusive range is the highest score minus the lowest score plus 1.
        Ratio level of measurement
      • A scale of measurement that is characterized by an absolute zero.
        Regression equation
      • The equation that defines the points and the line that are closest to the actual scores.
        Regression line
      • The line drawn based on the values in the regression equation.
      • The quality of a test such that it is consistent.
        Research hypothesis
      • A statement of inequality between two variables.
      • A subset of a population.
        Sampling error
      • The difference between sample and population values.
        Scales of measurement
      • Different ways of categorizing measurement outcomes.
        Scattergram, or scatterplot
      • A plot of paired data points.
        Significance level
      • The risk set by the researcher for rejecting a null hypothesis when it is true.
        Simple analysis of variance
      • See analysis of variance
        Skew, or skewness
      • The quality of a distribution that defines the disproportionate frequency of certain scores. A longer right tail than left corresponds to a smaller number of occurrences at the high end of the distribution; this is a positively skewed distribution. A shorter right tail than left corresponds to a larger number of occurrences at the high end of the distribution; this is a negatively skewed distribution.
        Source table
      • A listing of sources of variance in an analysis of variance summary table.
        Standard deviation
      • The average deviation from the mean.
        Standard error of estimate
      • A measure of accuracy in prediction.
        Standard score
      • See z score
        Statistical significance
      • See significance level
      • A set of tools and techniques used to organize and interpret information.
        Test-retest reliability
      • A type of reliability that examines consistency over time.
        Test statistic value
      • See obtained value
        True score
      • The unobservable part of an observed score that reflects the actual ability or behavior.
        Two-tailed test
      • A test of a nondirectional hypothesis where the direction of the difference is of little importance.
        Type I error
      • The probability of rejecting a null hypothesis when it is true.
        Type II error
      • The probability of accepting a null hypothesis when it is false.
        Unbiased estimate
      • A conservative estimate of a population parameter.
      • The quality of a test such that it measures what it says it does.
      • The amount of spread or dispersion in a set of scores.
      • The square of the standard deviation, and another measure of a distribution's spread or dispersion.
        Y′ or Y prime
      • The predicted Y value.
        z score
      • A raw score that is adjusted for the mean and standard deviation of the distribution from which the raw score comes.

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