Encyclopedia of Measurement and Statistics
Encyclopedias
Edited by: Neil J. Salkind
Abstract
The Encyclopedia of Measurement and Statistics presents stateoftheart information and readytouse 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.
 Entries AZ
 Subject Index

 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

 A
 B
 C
 D
 E
 F
 G
 H
 I
 J
 K
 L
 M
 N
 O
 P
 Q
 R
 S
 T
 U
 V
 W
 X
 Y
 Z

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Copyright
Editorial Board
Editor
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
 Ability Tests
 Abstracts
 Acceptance Sampling
 Achievement Tests
 Active Life Expectancy
 Adaptive Sampling Design
 Adjective Checklist
 Age Norms
 Akaike Information Criterion
 Alcohol Use Inventory
 Alternate Assessment
 Alternative Hypothesis
 American Doctoral Dissertations
 American Psychological Association
 American Psychological Society. See
 American Statistical Association
 Americans with Disabilities Act
 Analysis of Covariance (ANCOVA)
 Analysis of Variance (ANOVA)
 Anthropometry
 Applied Research
 Aptitude Tests
 Area Chart
 Arithmetic Mean
 Armed Forces Qualification Test
 Armed Services Vocational Aptitude Battery
 Artificial Neural Network
 Assessment of Interactions in Multiple Regression
 Association for Psychological Science
 Asymmetry of G
 Attenuation, Correction for
 Attitude Tests
 Attributable Risk
 Attrition Bias
 Audit Trail
 Authenticity
 Autocorrelation
 Average
 Average Deviation
 Babbage, Charles
 Bar Chart
 Basal Age
 Basic Personality Inventory
 Basic Research
 Bayes Factors
 Bayesian Information Criterion
 Bayesian Statistics
 Bayley Scales of Infant Development
 Beck Depression Inventory
 Behavior Assessment System for Children
 BehrensFisher Test
 Bender Visual Motor Gestalt Test
 Bernoulli, Jakob
 Binomial Distribution/Binomial and Sign Tests
 Binomial Test
 Bioinformatics
 Biserial Correlation Coefficients
 Bivariate Distributions
 Bonferroni, Carlo Emilio
 Bonferroni Test
 Bowker Procedure
 Box Plot (Box and Whisker Plot)
 Bracken Basic Concept Scale–Revised
 Bruno, James Edward
 Buros Institute of Mental Measurements
 California Psychological Inventory
 Career Assessment Inventory
 Career Development Inventory
 Career Maturity Inventory
 Carroll Depression Scale
 Categorical Variable
 Causal Analysis
 Censored Data
 Centers for Disease Control and Prevention
 Central Limit Theorem
 Centroid
 Chance
 ChiSquare Test for Goodness of Fit
 ChiSquare Test for Independence
 Children's Academic Intrinsic Motivation Inventory
 Class Interval
 Classical Test Theory
 Classification and Regression Tree
 Clinical Assessment of Attention Deficit
 Clinical Assessment of Behavior
 Clinical Assessment of Depression
 Cluster Analysis
 Cluster Sampling
 Cochran Q Test
 Coefficient Alpha
 Coefficients of Correlation, Alienation, and Determination
 Cognitive Abilities Test
 Cognitive Psychometric Assessment
 Cohen's Kappa
 Complete Independence Hypothesis
 Completion Items
 Computational Statistics
 Computerized Adaptive Testing
 Comrey, Andrew L.
 Comrey Personality Scales
 Conditional Probability
 Confidence Intervals
 Construct Validity
 Content Validity
 Continuous Variable
 Contour Plot
 Convenience Sampling
 Coping Resources Inventory for Stress
 Correlation Coefficient
 Correspondence Analysis
 Covariance
 CriterionReferenced Test
 Criterion Validity
 Critical Value
 Cronbach, Lee J.
 Culture Fair Intelligence Test
 Cumulative Frequency Distribution
 CurriculumBased Measurement
 Curse of Dimensionality
 Curvilinear Regression
 Darwin, Charles
 Data Analysis ToolPak
 Data Collection
 Data Compression
 Data Mining
 Decision Boundary
 Decision Theory
 Delphi Technique
 Delta Method
 Deming, William Edwards
 Dependent Variable
 Descriptive Research
 Deviation Score
 Diagnostic Validity
 Difference Score
 Differential Aptitude Test
 DiggleKenward Model for Dropout
 Dimension Reduction
 Discriminant Analysis
 Discriminant Correspondence Analysis
 Dissimilarity Coefficient
 Distance
 DISTATIS
 Dixon Test for Outliers
 Dunn's Multiple Comparison Test
 Ecological Momentary Assessment
 Educational Testing Service
 Edwards Personal Preference Schedule
 Effect Size
 Eigendecomposition
 Eigenvalues
 EM Algorithm
 Embedded Figures Test
 Equivalence Testing
 Essay Items
 Estimates of the Population Median
 Ethical Issues in Testing
 Ethical Principles in the Conduct of Research With Human Participants
 EvidenceBased Practice
 Excel Spreadsheet Functions
 Exploratory Data Analysis
 Exploratory Factor Analysis
 Eyeball Estimation
 Face Validity
 Factor Analysis
 Factor Scores
 Factorial Design
 Fagan Test of Infant Intelligence
 Family Environment Scale
 File Drawer Problem
 Fisher, Ronald Aylmer
 Fisher Exact Probability Test
 FisherIrwin Test. See
 Fisher's LSD
 Fisher's Z Transformation
 Fourier Transform
 Fractal
 Fractional Randomized Block Design
 Frequency Distribution
 Friedman Test
 Galton, Sir Francis
 Gambler's Fallacy
 Gauss, Carl Friedrich
 Generalized Additive Model
 Generalized Estimating Equations
 Generalized Method of Moments
 Generalized Procrustes Analysis
 Gerontological Apperception Test
 GfGc Theory of Intelligence
 Goodenough Harris Drawing Test
 GoodnessofFit Tests
 Graduate Record Examinations
 Grand Mean
 Graphical Statistical Methods
 Gresham, Frank M.
 Grounded Theory
 Guttman Scaling
 Harmonic Mean
 Health Insurance Portability and Accountability Act
 HelloGoodbye Effect
 Heteroscedasticity and Homoscedasticity
 Hierarchical Linear Modeling
 HighStakes Tests
 Histogram
 Historiometrics
 Holden Psychological Screening Inventory
 Homogeneity of Variance
 Hypergeometric Distribution
 Hypothesis and Hypothesis Testing
 Illinois Test of Psycholinguistic Abilities
 Immediate and Delayed Memory Tasks
 Independent Variable
 Individuals with Disabilities Education Act
 Inferential Statistics
 Information Referenced Testing
 Information Systems Interaction Readiness Scales
 Informed Consent
 Instrumental Variables
 Intelligence Quotient
 Intelligence Tests
 Internal External Locus of Control Scale
 Internal Review Board
 International Assessment of Educational Progress
 Interrater Reliability
 Interval Level of Measurement
 Iowa Tests of Basic Skills
 Iowa Tests of Educational Development
 Ipsative Measure
 Item and Test Bias
 Item Response Theory
 Jackson, Douglas N.
 Jackson Personality Inventory–Revised
 Jackson Vocational Interest Survey
 Journal of the American Statistical Association
 Journal of Modern Applied Statistical Methods
 Journal of Statistics Education
 kMeans Cluster Analysis
 Kaufman Assessment Battery for Children
 Kendall Rank Correlation
 Kinetic Family Drawing Test
 Kingston Standardized Cognitive Assessment
 KolmogorovSmirnov Test for One Sample
 KolmogorovSmirnov Test for Two Samples
 KR20 and KR21
 KruskalWallis OneWay Analysis of Variance
 Kuder Occupational Interest Survey
 Kurtosis
 Laboratory Behavioral Measures of Impulsivity
 Latent Class Analysis
 Law of Large Numbers
 Law School Admissions Test
 Least Squares, Method of
 Life Values Inventory
 Likelihood Ratio Test
 Likert Scaling
 Lilliefors Test for Normality
 Line Chart
 Linear Regression
 Logistic Regression Analysis
 Loglinear Analysis
 Longitudinal/Repeated Measures Data
 Luria Nebraska Neuropsychological Battery
 Male Role Norms Inventory
 Malthus, Thomas
 MannWhitney U Test (Wilcoxon RankSum Test)
 Markov, Andrei Andreevich
 Markov Chain Monte Carlo Methods
 Matrix Analogies Test
 Matrix Operations
 Maximum Likelihood Method
 McNemar Test for Significance of Changes
 Mean
 Measurement
 Measurement Error
 Measures of Central Tendency
 Median
 Median Test
 MetaAnalysis
 Metric Multidimensional Scaling
 Millon Behavioral Medicine Diagnostic
 Millon Clinical Multiaxial InventoryIII
 Minnesota Clerical Test
 Minnesota Multiphasic Personality Inventory
 Missing Data Method
 Mixed Models
 Mixture Models
 Mixtures of Experts
 Mode
 Moderator Variable
 Monte Carlo Methods
 Mosaic Plots
 Moving Average
 Multicollinearity
 Multidimensional Aptitude Battery
 Multiple Affect Adjective Checklist–Revised
 MultipleChoice Items
 Multiple Comparisons
 Multiple Correlation Coefficient
 Multiple Correspondence Analysis
 Multiple Factor Analysis
 Multiple Imputation for Missing Data
 Multitrait Multimethod Matrix and Construct Validity
 Multivariate Analysis of Variance (MANOVA)
 Multivariate Normal Distribution
 MyersBriggs Type Indicator
 National Council on Measurement in Education
 National Science Foundation
 NEO Personality Inventory
 Neonatal Behavioral Assessment Scale
 NewmanKeuls Test
 Nominal Level of Measurement
 Nomothetic Versus Idiographic
 Nonparametric Statistics
 Nonprobability Sampling
 Normal Curve
 Null Hypothesis Significance Testing
 O'Brien Test for Homogeneity of Variance
 Observational Studies
 Ockham's Razor
 Ogive
 One and TwoTailed Tests
 OneWay Analysis of Variance
 Ordinal Level of Measurement
 Orthogonal Predictors in Regression
 Page's L Test
 Paired Samples t Test (Dependent Samples t Test)
 Pairwise Comparisons
 Parallel Coordinate Plots
 Parallel Forms Reliability
 Parameter
 Parameter Invariance
 Part and Partial Correlations
 Partial Least Square Regression
 Pascal, Blaise
 Path Analysis
 Peabody Picture Vocabulary Test
 Pearson, Karl
 Pearson ProductMoment Correlation Coefficient
 Percentile and Percentile Rank
 Performance IQ
 PerformanceBased Assessment
 Peritz Procedure
 Personal Projects Analysis
 Personality Assessment Inventory
 Personality Research Form
 Personality Tests
 Pie Chart
 PiersHarris Children's SelfConcept Scale
 Poisson, Siméon Denis
 Poisson Distribution
 Portfolio Assessment
 Post Hoc Comparisons
 Posterior Distribution
 Predictive Validity
 Preschool Language Assessment Instrument
 Principal Component Analysis
 Prior Distribution
 Probability Sampling
 Profile Analysis
 Projective Hand Test
 Projective Testing
 Propensity Scores
 Psychological Abstracts
 Psychometrics
 PsycINFO
 Q Methodology
 QQ Plot
 Quality of WellBeing Scale
 QuasiExperimental Method
 Questionnaires
 Quota Sampling
 Random Numbers
 Random Sampling
 Range
 Rasch Measurement Model
 Ratio Level of Measurement
 Raven's Progressive Matrices
 Record Linkage
 Regression Analysis
 Relative Risk
 Reliability Theory
 Repeated Measures Analysis of Variance
 Residuals
 Response to Intervention
 Reverse Scaling
 Reynolds, Cecil R.
 Roberts Apperception Test for Children
 Rorschach Inkblot Test
 RV and Congruence Coefficients
 Sample
 Sample Size
 Sampling Distribution of a Statistic
 Sampling Error
 Scaling
 Scan Statistic
 Scattergram
 Scree Plot
 Secondary Data Analysis
 Section 504 of the Rehabilitation Act of 1973
 SelfReport
 Semantic Differential
 Semantic Differential Scale
 SemiInterquartile Range
 ShapiroWilk Test for Normality
 Signal Detection Theory
 Significance Level
 Simple Main Effect
 Simpson's Paradox
 Simpson's Rule
 Simulated Annealing
 Simulation Experiments
 SingleSubject Designs
 Singular and Generalized Singular Value Decomposition
 Six Sigma
 Sixteen Personality Factor Questionnaire
 Skewness
 Smoothing
 Social Climate Scales
 Social Skills Rating System
 Society for Research in Child Development
 Sociological Abstracts
 Spatial Learning Ability Test
 Spatial Statistics
 Spearman's Rho
 Split Half Reliability
 Spreadsheet Functions
 Spurious Correlation
 Standard Deviation
 Standard Error of the Mean
 Standard Error of Measurement
 Standard Scores
 Standards for Educational and Psychological Testing
 Stanford Achievement Test
 StanfordBinet Intelligence Scales
 Stanine
 STATIS
 Statistical Significance
 StemandLeaf Display
 Stratified Random Sampling
 Strong Interest Inventory
 Stroop Color and Word Test
 Structural Equation Modeling
 Structured Clinical Interview for DSMIV
 Sunflower Plot
 Support Vector Machines
 Suppressor Variable
 Survey Weights
 Survival Analysis
 System of Multicultural Pluralistic Assessment
 T Scores
 t Test for Two Population Means
 TestRetest Reliability
 Tests of Mediating Effects
 Text Analysis
 Thematic Apperception Test
 ThreeCard Method
 Thurstone Scales
 Time Series Analysis
 Torrance, E. Paul
 Torrance Tests of Creative Thinking
 Torrance Thinking Creatively in Action and Movement
 Tree Diagram
 True/False Items
 True Score
 TukeyKramer Procedure
 Type I Error
 Type II Error
 Unbiased Estimator
 Universal Nonverbal Intelligence Test
 Validity Coefficient
 Validity Theory
 Variable
 Variable Deletion
 Variance
 Verbal IQ
 Vineland Adaptive Behavior Scales
 Vineland Social Maturity Scale
 Wechsler Adult Intelligence Scale
 Wechsler Individual Achievement Test
 Wechsler Preschool and Primary Scale of Intelligence
 West HavenYale Multidimensional Pain Inventory
 Wilcoxon, Frank
 Wilcoxon MannWhitney Test. See
 Wilcoxon Signed Ranks Test
 Woodcock Johnson Psychoeducational Battery
 Woodcock Reading Mastery Tests Revised
 z Scores
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.
 Babbage, Charles
 Bernoulli, Jakob
 Bonferroni, Carlo Emilio
 Bruno, James Edward
 Comrey, Andrew L.
 Cronbach, Lee J.
 Darwin, Charles
 Deming, William Edwards
 Fisher, Ronald Aylmer
 Galton, Sir Francis
 Gauss, Carl Friedrich
 Gresham, Frank M.
 Jackson, Douglas N.
 Malthus, Thomas
 Markov, Andrei Andreevich
 Pascal, Blaise
 Pearson, Karl
 Poisson, Siméon Denis
 Reynolds, Cecil R.
 Torrance, E. Paul
 Wilcoxon, Frank
Biographies Area Chart
 Bar Chart
 Box Plot (Box and Whisker Plot)
 Contour Plot
 Eyeball Estimation
 Frequency Distribution
 Histogram
 Line Chart
 Mosaic Plots
 Ogive
 Parallel Coordinate Plots
 Pie Chart
 QQ Plot
 Scattergram
 Scree Plot
 Smoothing
 StemandLeaf Display
 Sunflower Plot
 Tree Diagram
Charts, Graphs, and Visual Displays Babbage, Charles
 Computational Statistics
 Computerized Adaptive Testing
 Curvilinear Regression
 Data Analysis ToolPak
 Data Compression
 DISTATIS
 Excel Spreadsheet Functions
 Linear Regression
 Residuals
 Spatial Statistics
 Spreadsheet Functions
 STATIS
Computer Topics and Tools Ability Tests
 Achievement Tests
 Alternate Assessment
 Americans with Disabilities Act
 Anthropometry
 Aptitude Tests
 Artificial Neural Network
 Asymmetry of G
 Attitude Tests
 Basal Age
 Categorical Variable
 Classical Test Theory
 Coefficient Alpha
 Completion Items
 Computerized Adaptive Testing
 Construct Validity
 Content Validity
 CriterionReferenced Test
 Criterion Validity
 Cronbach, Lee J.
 CurriculumBased Measurement
 Diagnostic Validity
 Educational Testing Service
 Equivalence Testing
 Essay Items
 Ethical Issues in Testing
 Face Validity
 GfGc Theory of Intelligence
 Guttman Scaling
 Health Insurance Portability and Accountability Act
 HighStakes Tests
 Immediate and Delayed Memory Tasks
 Individuals with Disabilities Education Act
 Information Referenced Testing
 Informed Consent
 Intelligence Quotient
 Intelligence Tests
 Internal Review Board
 Interrater Reliability
 Interval Level of Measurement
 Ipsative Measure
 Item and Test Bias
 Item Response Theory
 KR20 and KR21
 Likert Scaling
 Measurement
 Measurement Error
 Metric Multidimensional Scaling
 MultipleChoice Items
 Multitrait Multimethod Matrix and Construct Validity
 Nomothetic Versus Idiographic
 Ordinal Level of Measurement
 Parallel Forms Reliability
 Performance IQ
 PerformanceBased Assessment
 Personality Tests
 Portfolio Assessment
 Predictive Validity
 Projective Testing
 Q Methodology
 Questionnaires
 Ratio Level of Measurement
 Reliability Theory
 Response to Intervention
 Reverse Scaling
 Scaling
 Section 504 of the Rehabilitation Act of 1973
 SelfReport
 Semantic Differential
 Semantic Differential Scale
 Six Sigma
 Spearman's Rho
 Split Half Reliability
 Standard Error of Measurement
 Standard Scores
 Standards for Educational and Psychological Testing
 T Scores
 TestRetest Reliability
 Thurstone Scaling
 Torrance, E. Paul
 True/False Items
 Validity Coefficient
 Validity Theory
 Verbal IQ
 z Scores
Concepts and Issues in Measurement Artificial Neural Network
 Attenuation, Correction for
 Autocorrelation
 Bayesian Statistics
 Bioinformatics
 Central Limit Theorem
 Decision Theory
 DiggleKenward Model for Dropout
 DISTATIS
 Exploratory Factor Analysis
 Factorial Design
 Fourier Transform
 Generalized Additive Model
 Generalized Method of Moments
 Generalized Procrustes Analysis
 Graphical Statistical Methods
 Hierarchical Linear Modeling
 Historiometrics
 Logistic Regression Analysis
 Loglinear Analysis
 Markov Chain Monte Carlo Methods
 Matrix Operations
 Mean
 Measurement Error
 Mixtures of Experts
 Nonparametric Statistics
 Propensity Scores
 Rasch Measurement Model
 Regression Analysis
 Sampling Distribution of a Statistic
 Signal Detection Theory
 Simpson's Paradox
 Spurious Correlation
 Standard Error of the Mean
 Standard Scores
 Support Vector Machines
 Survival Analysis
 Type I Error
 Type II Error
Concepts and Issues in Statistics Censored Data
 Data Compression
 Data Mining
 Discriminant Analysis
 Eigenvalues
 Exploratory Data Analysis
 Factor Analysis
 Factor Scores
 Missing Data Method
 Multiple Factor Analysis
 Record Linkage
 Secondary Analysis of Data
Data and Data Reduction Techniques Arithmetic Mean
 Attenuation, Correction for
 Autocorrelation
 Average
 Average Deviation
 Bayley Scales of Infant Development
 Biserial Correlation Coefficient
 Class Interval
 Coefficients of Correlation, Alienation, and Determination
 Cognitive Psychometric Assessment
 Cohen's Kappa
 Correlation Coefficient
 Cumulative Frequency Distribution
 Deviation Score
 Difference Score
 Estimates of the Population Median
 Fisher's Z Transformation
 Frequency Distribution
 Galton, Sir Francis
 Grand Mean
 Harmonic Mean
 Histogram
 Kendall Rank Correlation
 Mean
 Measures of Central Tendency
 Median
 Mode
 Moving Average
 Parameter
 Parameter Invariance
 Part and Partial Correlations
 Pearson, Karl
 Pearson ProductMoment Correlation Coefficient
 Percentile and Percentile Rank
 RV and Congruence Coefficients
 Scattergram
 SemiInterquartile Range
 Spurious Correlation
 Standard Deviation
 Survey Weights
 Text Analysis
Descriptive Statistics Achievement Tests
 EvidenceBased Practices
 Health Insurance Portability and Accountability Act
 HighStakes Tests
 Questionnaires
Evaluation Alternative Hypothesis
 American Statistical Association
 Americans with Disabilities Act
 Association for Psychological Science
 Basic Research
 Bioinformatics
 Complete Independence Hypothesis
 Continuous Variable
 Critical Value
 Data Collection
 Data Mining
 Delphi Technique
 Dependent Variable
 Descriptive Research
 Ethical Issues in Testing
 Ethical Principles in the Conduct of Research With Human Participants
 Fractional Randomized Block Design
 HelloGoodbye Effect
 Hypothesis and Hypothesis Testing
 Independent Variable
 Informed Consent
 Instrumental Variables
 Internal Review Board
 Longitudinal/Repeated Measures Data
 MetaAnalysis
 Missing Data Method
 Mixed Models
 Mixture Models
 Moderator Variable
 Monte Carlo Methods
 Null Hypothesis Significance Testing
 Ockham's Razor
 Pairwise Comparisons
 Post Hoc Comparisons
 Projective Testing
 QuasiExperimental Method
 Sample Size
 Section 504 of the Rehabilitation Act of 1973
 Significance Level
 Simple Main Effect
 Simulation Experiments
 SingleSubject Designs
 Standards for Educational and Psychological Testing
 Statistical Significance
 Suppressor Variable
 Variable
 Variable Deletion
 Variance
Experimental Methods Akaike Information Criterion
 Analysis of Covariance (ANCOVA)
 Analysis of Variance (ANOVA)
 Bayes Factors
 Bayesian Information Criterion
 Binomial Test
 Bonferroni, Carlo Emilio
 Complete Independence Hypothesis
 Data Analysis ToolPak
 Exploratory Factor Analysis
 Factorial Design
 Fisher, Ronald Aylmer
 Hierarchical Linear Modeling
 Hypothesis and Hypothesis Testing
 Inferential Statistics
 Logistic Regression Analysis
 Markov, Andrei Andreevich
 Null Hypothesis Significance Testing
 Pairwise Comparisons
 Part and Partial Correlations
 Repeated Measures Analysis of Variance
 Type I Error
 Type II Error
 Wilcoxon, Frank
Inferential Statistics Abstracts
 American Doctoral Dissertations
 American Psychological Association
 American Statistical Association
 Association for Psychological Science
 Buros Institute of Mental Measurements
 Centers for Disease Control and Prevention
 Educational Testing Service
 Journal of the American Statistical Association
 Journal of Modern Applied Statistical Methods
 Journal of Statistics Education
 National Science Foundation
 Psychological Abstracts
 Psychometrics
 PsycINFO
 Society for Research in Child Development
 Sociological Abstracts
Organizations and Publications Attributable Risk
 Bernoulli, Jakob
 Chance
 Conditional Probability
 Confidence Intervals
 Continuous Variable
 Curse of Dimensionality
 Decision Boundary
 Decision Theory
 File Drawer Problem
 Gambler's Fallacy
 Generalized Estimating Equations
 Law of Large Numbers
 Maximum Likelihood Method
 Nonprobability Sampling
 Pascal, Blaise
 Probability Sampling
 Random Numbers
 Relative Risk
 Signal Detection Theory
 Significance Level
 ThreeCard Method
Prediction and Estimation Alternate Assessment
 Audit Trail
 Authenticity
 Categorical Variable
 Essay Items
 Grounded Theory
 Observational Studies
 Portfolio Assessment
 SelfReport
 Text Analysis
Probability Active Life Expectancy
 Assessment of Interactions in Multiple Regression
 Eyeball Estimation
 Orthogonal Predictors in Regression
 Regression Analysis
 Survival Analysis
Qualitative Methods Acceptance Sampling
 Adaptive Sampling Design
 Age Norms
 Attrition Bias
 Career Maturity Inventory
 Central Limit Theorem
 Class Interval
 Cluster Sampling
 Confidence Intervals
 Convenience Sampling
 Cumulative Frequency Distribution
 Data Collection
 DiggleKenward Model for Dropout
 Gauss, Carl Friedrich
 Heteroscedasticity and Homoscedasticity
 Homogeneity of Variance
 Hypergeometric Distribution
 Kurtosis
 Malthus, Thomas
 Multicollinearity
 Multivariate Normal Distribution
 Nonprobability Sampling
 Normal Curve
 Ogive
 Parameter
 Percentile and Percentile Rank
 Poisson, Siméon Denis
 Poisson Distribution
 Posterior Distribution
 Prior Distribution
 Probability Sampling
 Quota Sampling
 Random Sampling
 Sample
 Sample Size
 SemiInterquartile Range
 Simpson's Rule
 Skewness
 Smoothing
 Stanine
 Stratified Random Sampling
 Unbiased Estimator
Samples, Sampling, and Distributions Binomial Distribution/Binomial and Sign Tests
 Bivariate Distributions
 Bonferroni Test
 Bowker Procedure
 Causal Analysis
 Centroid
 Chance
 ChiSquare Test for Goodness of Fit
 ChiSquare Test for Independence
 Classification and Regression Tree
 Cochran Q Test
 Cohen's Kappa
 Delta Method
 Dimension Reduction
 Discriminant Analysis
 Dissimilarity Coefficient
 Dixon Test for Outliers
 Dunn's Multiple Comparison Test
 Eigendecomposition
 Eigenvalues
 EM Algorithm
 Exploratory Data Analysis
 Factor Analysis
 Factor Scores
 Fisher Exact Probability Test
 Fisher's LSD
 Friedman Test
 GoodnessofFit Tests
 Grounded Theory
 kMeans Cluster Analysis
 KolmogorovSmirnov Test for One Sample
 KolmogorovSmirnov Test for Two Samples
 KruskalWallis OneWay Analysis of Variance
 Latent Class Analysis
 Likelihood Ratio Test
 Lilliefors Test for Normality
 MannWhitney U Test (Wilcoxon RankSum Test)
 McNemar Test for Significance of Changes
 Median Test
 MetaAnalysis
 Multiple Comparisons
 Multiple Factor Analysis
 Multiple Imputation for Missing Data
 Multivariate Analysis of Variance (MANOVA)
 NewmanKeuls Test
 O'Brien Test for Homogeneity of Variance
 Observational Studies
 OneWay Analysis of Variance
 Page's L Test
 Paired Samples t Test (Dependent Samples t Test)
 Path Analysis
 Peritz Procedure
 Scan Statistic
 ShapiroWilk Test for Normality
 Structural Equation Modeling
 t Test for Two Population Means
 Tests of Mediating Effects
 ThreeCard Method
 TukeyKramer Procedure
 Wilcoxon Signed Ranks Test
Statistical Techniques Analysis of Covariance (ANCOVA)
 Analysis of Variance (ANOVA)
 BehrensFisher Test
 Binomial Distribution/Binomial and Sign Tests
 Binomial Test
 Bonferroni Test
 Bowker Procedure
 ChiSquare Test for Goodness of Fit
 ChiSquare Test for Independence
 Classification and Regression Tree
 Cochran Q Test
 Dixon Test for Outliers
 Dunn's Multiple Comparison Test
 Excel Spreadsheet Functions
 Fisher Exact Probability Test
 Fisher's LSD
 Friedman Test
 GoodnessofFit Tests
 KolmogorovSmirnov Test for One Sample
 KolmogorovSmirnov Test for Two Samples
 KruskalWallis OneWay Analysis of Variance
 Latent Class Analysis
 Likelihood Ratio Test
 Lilliefors Test for Normality
 MannWhitney U Test (Wilcoxon RankSum Test)
 McNemar Test for Significance of Changes
 Median Test
 Multiple Comparisons
 Multivariate Analysis of Variance (MANOVA)
 NewmanKeuls Test
 O'Brien Test for Homogeneity of Variance
 One and TwoTailed Tests
 OneWay Analysis of Variance
 Page's L Test
 Paired Samples t Test (Dependent Samples t Test)
 Peritz Procedure
 Repeated Measures Analysis of Variance
 ShapiroWilk Test for Normality
 t Test for Two Population Means
 Tests of Mediating Effects
 TukeyKramer Procedure
 Wilcoxon Signed Ranks Test
Statistical Tests Adjective Checklist
 Alcohol Use Inventory
 Armed Forces Qualification Test
 Armed Services Vocational Aptitude Battery
 Basic Personality Inventory
 Bayley Scales of Infant Development
 Beck Depression Inventory
 Behavior Assessment System for Children
 Bender Visual Motor Gestalt Test
 Bracken Basic Concept Scale–Revised
 California Psychological Inventory
 Career Assessment Inventory
 Career Development Inventory
 Career Maturity Inventory
 Carroll Depression Scale
 Children's Academic Intrinsic Motivation Inventory
 Clinical Assessment of Attention Deficit
 Clinical Assessment of Behavior
 Clinical Assessment of Depression
 Cognitive Abilities Test
 Cognitive Psychometric Assessment
 Comrey Personality Scales
 Coping Resources Inventory for Stress
 Culture Fair Intelligence Test
 Differential Aptitude Test
 Ecological Momentary Assessment
 Edwards Personal Preference Schedule
 Embedded Figures Test
 Fagan Test of Infant Intelligence
 Family Environment Scale
 Gerontological Apperception Test
 Goodenough Harris Drawing Test
 Graduate Record Examinations
 Holden Psychological Screening Inventory
 Illinois Test of Psycholinguistic Abilities
 Information Systems Interaction Readiness
 Internal External Locus of Control Scale
 International Assessment of Educational Progress
 Iowa Tests of Basic Skills
 Iowa Tests of Educational Development
 Jackson Personality Inventory–Revised
 Jackson Vocational Interest Survey
 Kaufman Assessment Battery for Children
 Kinetic Family Drawing Test
 Kingston Standardized Cognitive Assessment
 Kuder Occupational Interest Survey
 Laboratory Behavioral Measures of Impulsivity
 Law School Admissions Test
 Life Values Inventory
 Luria Nebraska Neuropsychological Battery
 Male Role Norms Inventory
 Matrix Analogies Test
 Millon Behavioral Medicine Diagnostic
 Millon Clinical Multiaxial InventoryIII
 Minnesota Clerical Test
 Minnesota Multiphasic Personality Inventory
 Multidimensional Aptitude Battery
 Multiple Affect Adjective Checklist–Revised
 MyersBriggs Type Indicator
 NEO Personality Inventory
 Neonatal Behavioral Assessment Scale
 Peabody Picture Vocabulary Test
 Personal Projects Analysis
 Personality Assessment Inventory
 Personality Research Form
 PiersHarris Children's SelfConcept Scale
 Preschool Language Assessment Instrument
 Profile Analysis
 Projective Hand Test
 Quality of WellBeing Scale
 Raven's Progressive Matrices
 Roberts Apperception Test for Children
 Rorschach Inkblot Test
 Sixteen Personality Factor Questionnaire
 Social Climate Scales
 Social Skills Rating System
 Spatial Learning Ability Test
 Stanford Achievement Test
 StanfordBinet Intelligence Scales
 Strong Interest Inventory
 Stroop Color and Word Test
 Structured Clinical Interview for DSMIV
 System of Multicultural Pluralistic Assessment
 Thematic Apperception Test
 Torrance Tests of Creative Thinking
 Torrance Thinking Creatively in Action and Movement
 Universal Nonverbal Intelligence Test
 Vineland Adaptive Behavior Scales
 Vineland Social Maturity Scale
 Wechsler Adult Intelligence Scale
 Wechsler Individual Achievement Test
 Wechsler Preschool and Primary Scale of Intelligence
 West HavenYale Multidimensional Pain Inventory
 Woodcock Johnson Psychoeducational Battery
 Woodcock Reading Mastery Tests Revised
Tests by Name
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 treasurerelect of Division 7 of the American Psychological Association.
Contributors
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 AmreinBeardsley
Arizona State University
Lauren E. Auld
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Preface
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 ProcessThe 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 indepth 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 ReferenceWe 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 twovolume 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, stepbystep 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.
AcknowledgmentsThis 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 thankyous 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 emails 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.

Appendix A
Appendix ATen Commandments of Data CollectionThe following text is taken from Neil J. Salkind's bestselling 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, onepage questionnaire given to a group of students, parents, patients, or voters. The data collection process may very well be the most timeconsuming 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 outoftheway (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 ValuesTables of critical valuesThe following tables are taken from Neil J. Salkind's bestselling 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 the Area Between the Mean and the Area Between the Mean and the Area Between the Mean and the Area Between the Mean and the Area Between the Mean and the Area Between the Mean and the Area Between the Mean and the zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore zscore 0.00 0.00 0.50 19.15 1.00 34.13 1.50 43.32 2.00 47.72 2.50 49.38 3.00 49.87 3.50 49.98 0.01 0.40 0.52 19.50 1.01 34.38 1.51 43.45 2.01 47.78 2.51 49.40 3.01 49.87 3.51 49.98 0.02 0.50 0.53 19.85 1.02 34.61 1.52 43.57 2.02 47.83 2.52 49.41 3.02 49.87 3.52 49.98 0.03 1.20 0.54 20.19 1.03 34.85 1.53 43.70 2.03 47.88 2.53 49.43 3.03 49.88 3.53 49.98 0.04 1.60 0.55 20.54 1.04 35.08 1.54 43.82 2.04 47.93 2.54 49.45 3.04 49.88 3.54 49.98 0.05 1.99 0.56 20.88 1.05 35.31 1.55 43.94 2.05 47.98 2.55 49.46 3.05 49.89 3.55 49.98 0.06 2.39 0.57 21.23 1.06 35.54 1.56 44.06 2.06 48.03 2.56 49.48 3.06 49.89 3.56 49.98 0.07 2.79 0.58 21.57 1.07 35.77 1.57 44.18 2.07 48.08 2.57 49.49 3.07 49.89 3.57 49.98 0.08 3.19 0.59 21.90 1.08 35.99 1.58 44.29 2.08 48.12 2.58 49.51 3.08 49.9 3.58 49.98 0.09 3.59 0.60 22.24 1.09 36.21 1.59 44.41 2.09 48.17 2.59 49.52 3.09 49.9 3.59 49.98 0.10 3.98 0.61 22.57 1.10 36.43 1.60 44.52 2.10 48.21 2.60 49.53 3.10 49.9 3.60 49.98 0.11 4.38 0.62 22.91 1.11 36.65 1.61 44.63 2.11 48.26 2.61 49.55 3.11 49.91 3.61 49.98 0.12 4.78 0.63 23.24 1.12 36.86 1.62 44.74 2.12 48.30 2.62 49.56 3.12 49.91 3.62 49.98 0.13 5.17 0.64 23.57 1.13 37.08 1.63 44.84 2.13 48.34 2.63 49.57 3.13 49.91 3.63 49.98 0.14 5.57 0.65 23.89 1.14 37.29 1.64 44.95 2.14 48.38 2.64 49.59 3.14 49.92 3.64 49.98 0.15 5.96 0.66 24.54 1.15 37.49 1.65 45.05 2.15 48.42 2.65 49.60 3.15 49.92 3.65 49.98 0.16 6.36 0.67 24.86 1.16 37.70 1.66 45.15 2.16 48.46 2.66 49.61 3.16 49.92 3.66 49.98 0.17 6.75 0.68 25.17 1.17 37.90 1.67 45.25 2.17 48.50 2.67 49.62 3.17 49.92 3.67 49.98 0.18 7.14 0.69 25.49 1.18 38.10 1.68 45.35 2.18 48.54 2.68 49.63 3.18 49.93 3.68 49.98 0.19 7.53 0.70 25.80 1.19 38.30 1.69 45.45 2.19 48.57 2.69 49.64 3.19 49.93 3.69 49.98 0.20 7.93 0.71 26.11 1.20 38.49 1.70 45.54 2.20 48.61 2.70 49.65 3.20 49.93 3.70 49.99 0.21 8.32 0.72 26.42 1.21 38.69 1.71 45.64 2.21 48.64 2.71 49.66 3.21 49.93 3.71 49.99 0.22 8.71 0.73 26.73 1.22 38.88 1.72 45.73 2.22 48.68 2.72 49.67 3.22 49.94 3.72 49.99 0.23 9.10 0.74 27.04 1.23 39.07 1.73 45.82 2.23 48.71 2.73 49.68 3.23 49.94 3.73 49.99 0.24 9.48 0.75 27.34 1.24 39.25 1.74 45.91 2.24 48.75 2.74 49.69 3.24 49.94 3.74 49.99 0.25 0.99 0.76 27.64 1.25 39.44 1.75 45.99 2.25 45.78 2.75 49.70 3.25 49.94 3.75 49.99 0.26 10.26 0.77 27.94 1.26 39.62 1.76 46.08 2.26 48.81 2.76 49.71 3.26 49.94 3.76 49.99 0.27 10.64 0.78 28.23 1.27 39.80 1.77 46.16 2.27 48.84 2.77 49.72 3.27 49.94 3.77 49.99 0.28 11.03 0.79 28.52 1.28 39.97 1.78 46.25 2.28 48.87 2.78 49.73 3.28 49.94 3.78 49.99 0.29 11.41 0.80 28.81 1.29 40.15 1.79 46.33 2.29 48.90 2.79 49.74 3.29 49.94 3.79 49.99 0.30 11.79 0.81 29.10 1.30 40.32 1.80 46.41 2.30 48.93 2.80 49.74 3.30 49.95 3.80 49.99 0.31 12.17 0.82 29.39 1.31 40.49 1.81 46.49 2.31 48.96 2.81 49.75 3.31 49.95 3.81 49.99 0.32 12.55 0.83 29.67 1.32 40.66 1.82 46.56 2.32 48.98 2.82 49.76 3.32 49.95 3.82 49.99 0.33 12.93 0.84 29.95 1.33 40.82 1.83 46.64 2.33 49.01 2.83 49.77 3.33 49.95 3.83 49.99 0.34 13.31 0.85 30.23 1.34 40.99 1.84 46.71 2.34 49.04 2.84 49.77 3.34 49.95 3.84 49.99 0.35 13.68 0.86 30.51 1.35 41.15 1.85 46.78 2.35 49.06 2.85 49.78 3.35 49.96 3.85 49.99 0.36 14.06 0.87 30.78 1.36 41.31 1.86 46.86 2.36 49.09 2.86 49.79 3.36 49.96 3.86 49.99 0.37 14.43 0.88 31.06 1.37 41.47 1.87 46.93 2.37 49.11 2.87 49.79 3.37 49.96 3.87 49.99 0.38 14.80 0.89 31.33 1.38 41.62 1.88 46.99 2.38 49.13 2.88 49.80 3.38 49.96 3.88 49.99 0.39 15.17 0.90 31.59 1.39 41.77 1.89 47.06 2.39 49.16 2.89 49.81 3.39 49.96 3.89 49.99 0.40 15.54 0.91 31.86 1.40 41.92 1.90 47.13 2.40 49.18 2.90 49.81 3.40 49.97 3.90 49.99 0.41 15.91 0.92 32.12 1.41 42.07 1.91 47.19 2.41 49.20 2.91 49.82 3.41 49.97 3.91 49.99 0.42 16.28 0.93 32.38 1.42 42.22 1.92 47.26 2.42 49.22 2.92 49.82 3.42 49.97 3.92 49.99 0.43 16.64 0.94 32.64 1.43 42.36 1.93 47.32 2.43 49.25 2.93 49.83 3.43 49.97 3.93 49.99 0.44 17.00 0.95 32.89 1.44 42.51 1.94 47.38 2.44 49.27 2.94 49.84 3.44 49.97 3.94 49.99 0.45 17.36 0.96 33.15 1.45 42.65 1.95 47.44 2.45 49.29 2.95 49.84 3.45 49.98 3.95 49.99 0.46 17.72 0.97 33.40 1.46 42.79 1.96 47.50 2.46 49.31 2.96 49.85 3.46 49.98 3.96 49.99 0.47 18.08 0.98 33.65 1.47 42.92 1.97 47.56 2.47 49.32 2.97 49.85 3.47 49.98 3.97 49.99 0.48 18.44 0.99 33.89 1.48 43.06 1.98 47.61 2.48 49.34 2.98 49.86 3.48 49.98 3.98 49.99 0.49 18.79 1.00 34.13 1.49 43.19 1.99 47.67 2.49 49.36 2.99 49.86 3.49 49.98 3.99 49.99 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.
OneTailed Test TwoTailed Test df 0.10 0.05 0.01 df 0.10 0.05 0.01 1 3.078 6.314 31.821 1 6.314 12.706 63.657 2 1.886 2.92 6.965 2 2.92 4.303 9.925 3 1.638 2.353 4.541 3 2.353 3.182 5.841 4 1.533 2.132 3.747 4 2.132 2.776 4.604 5 1.476 2.015 3.365 5 2.015 2.571 4.032 6 1.44 1.943 3.143 6 1.943 2.447 3.708 7 1.415 1.895 2.998 7 1.895 2.365 3.5 8 1.397 1.86 2.897 8 1.86 2.306 3.356 9 1.383 1.833 2.822 9 1.833 2.262 3.25 10 1.372 1.813 2.764 10 1.813 2.228 3.17 11 1.364 1.796 2.718 11 1.796 2.201 3.106 12 1.356 1.783 2.681 12 1.783 2.179 3.055 13 1.35 1.771 2.651 13 1.771 2.161 3.013 14 1.345 1.762 2.625 14 1.762 2.145 2.977 15 1.341 1.753 2.603 15 1.753 2.132 2.947 16 1.337 1.746 2.584 16 1.746 2.12 2.921 17 1.334 1.74 2.567 17 1.74 2.11 2.898 18 1.331 1.734 2.553 18 1.734 2.101 2.879 19 1.328 1.729 2.54 19 1.729 2.093 2.861 20 1.326 1.725 2.528 20 1.725 2.086 2.846 21 1.323 1.721 2.518 21 1.721 2.08 2.832 22 1.321 1.717 2.509 22 1.717 2.074 2.819 23 1.32 1.714 2.5 23 1.714 2.069 2.808 24 1.318 1.711 2.492 24 1.711 2.064 2.797 25 1.317 1.708 2.485 25 1.708 2.06 2.788 26 1.315 1.706 2.479 26 1.706 2.056 2.779 27 1.314 1.704 2.473 27 1.704 2.052 2.771 28 1.313 1.701 2.467 28 1.701 2.049 2.764 29 1.312 1.699 2.462 29 1.699 2.045 2.757 30 1.311 1.698 2.458 30 1.698 2.043 2.75 35 1.306 1.69 2.438 35 1.69 2.03 2.724 40 1.303 1.684 2.424 40 1.684 2.021 2.705 45 1.301 1.68 2.412 45 1.68 2.014 2.69 50 1.299 1.676 2.404 50 1.676 2.009 2.678 55 1.297 1.673 2.396 55 1.673 2.004 2.668 60 1.296 1.671 2.39 60 1.671 2.001 2.661 65 1.295 1.669 2.385 65 1.669 1.997 2.654 70 1.294 1.667 2.381 70 1.667 1.995 2.648 75 1.293 1.666 2.377 75 1.666 1.992 2.643 80 1.292 1.664 2.374 80 1.664 1.99 2.639 85 1.292 1.663 2.371 85 1.663 1.989 2.635 90 1.291 1.662 2.369 90 1.662 1.987 2.632 95 1.291 1.661 2.366 95 1.661 1.986 2.629 100 1.29 1.66 2.364 100 1.66 1.984 2.626 Infinity 1.282 1.645 2.327 Infinity 1.645 1.96 2.576 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 (n–k).
 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 Denominator Type I Error Rate 1 2 3 4 5 6 1 .01 4052.00 4999.00 5403.00 5625.00 5764.00 5859.00 .05 162.00 200.00 216.00 225.00 230.00 234.00 .10 39.90 49.50 53.60 55.80 57.20 58.20 2 .01 98.50 99.00 99.17 99.25 99.30 99.33 05 18.51 19.00 19.17 19.25 19.30 19.33 10 8.53 9.00 9.16 9.24 9.29 9.33 3 .01 34.12 30.82 29.46 28.71 28.24 27.91 .05 10.13 9.55 9.28 9.12 9.01 8.94 10 5.54 5.46 5.39 5.34 5.31 5.28 4 .01 21.20 18.00 16.70 15.98 15.52 15.21 .05 7.71 6.95 6.59 6.39 6.26 6.16 .10 .55 4.33 4.19 4.11 4.05 4.01 5 .01 16.26 13.27 12.06 11.39 10.97 10.67 .05 6.61 5.79 5.41 5.19 5.05 4.95 .10 4.06 3.78 3.62 3.52 3.45 3.41 6 .01 13.75 10.93 9.78 9.15 8.75 8.47 .05 5.99 5.14 4.76 4.53 4.39 4.28 .10 3.78 3.46 3.29 3.18 3.11 3.06 7 .01 12.25 9.55 8.45 7.85 7.46 7.19 .05 5.59 4.74 4.35 4.12 3.97 3.87 .10 3.59 3.26 3.08 2.96 2.88 2.83 8 .01 11.26 8.65 7.59 7.01 6.63 6.37 .05 5.32 4.46 4.07 3.84 3.69 3.58 .10 3.46 3.11 2.92 2.81 2.73 2.67 9 .01 10.56 8.02 6.99 6.42 6.06 5.80 .05 5.12 4.26 3.86 3.63 3.48 3.37 .10 3.36 3.01 2.81 2.69 2.61 2.55 10 .01 10.05 7.56 6.55 6.00 5.64 5.39 .05 4.97 4.10 3.71 3.48 3.33 3.22 .10 3.29 2.93 2.73 2.61 2.52 2.46 11 .01 9.65 7.21 6.22 5.67 5.32 5.07 .05 4.85 3.98 3.59 3.36 3.20 3.10 .10 3.23 2.86 2.66 2.54 2.45 2.39 12 .01 9.33 6.93 5.95 5.41 5.07 4.82 .05 4.75 3.89 3.49 3.26 3.11 3.00 .10 3.18 2.81 2.61 2.48 2.40 2.33 13 .01 9.07 6.70 5.74 5.21 4.86 4.62 .05 4.67 3.81 3.41 3.18 3.03 2.92 .10 3.14 2.76 2.56 2.43 2.35 2.28 14 .01 8.86 6.52 5.56 5.04 4.70 4.46 .05 4.60 3.74 3.34 3.11 2.96 2.85 .10 3.10 2.73 2.52 2.40 2.31 2.24 15 .01 8.68 6.36 5.42 4.89 4.56 4.32 .05 4.54 3.68 3.29 3.06 2.90 2.79 .10 3.07 2.70 2.49 2.36 2.27 2.21 16 .01 8.53 6.23 5.29 4.77 4.44 4.20 .05 4.49 3.63 3.24 3.01 2.85 2.74 .10 3.05 2.67 2.46 2.33 2.24 2.18 17 .01 8.40 6.11 5.19 4.67 4.34 4.10 .05 4.45 3.59 3.20 2.97 2.81 2.70 .10 3.03 2.65 2.44 2.31 2.22 2.15 18 .01 8.29 6.01 5.09 4.58 4.25 4.02 .05 4.41 3.56 3.16 2.93 2.77 2.66 .10 3.01 2.62 2.42 2.29 2.20 2.13 19 .01 8.19 5.93 5.01 4.50 4.17 3.94 .05 4.38 3.52 3.13 2.90 2.74 2.63 .10 2.99 2.61 2.40 2.27 2.18 2.11 20 .01 8.10 5.85 4.94 4.43 4.10 3.87 .05 4.35 3.49 3.10 2.87 2.71 2.60 .10 2.98 2.59 2.38 2.25 2.16 2.09 21 .01 8.02 5.78 4.88 4.37 4.04 3.81 .05 4.33 3.47 3.07 2.84 2.69 2.57 .10 2.96 2.58 2.37 2.23 2.14 2.08 22 .01 7.95 5.72 4.82 4.31 3.99 3.76 .05 4.30 3.44 3.05 2.82 2.66 2.55 .10 2.95 2.56 2.35 2.22 2.13 2.06 23 .01 7.88 5.66 4.77 4.26 3.94 3.71 .05 4.28 3.42 3.03 2.80 2.64 2.53 .10 2.94 2.55 2.34 2.21 2.12 2.05 24 .01 7.82 5.61 4.72 4.22 3.90 3.67 .05 4.26 3.40 3.01 2.78 2.62 2.51 .10 2.93 2.54 2.33 2.20 2.10 2.04 25 .01 7.77 5.57 4.68 4.18 3.86 3.63 .05 4.24 3.39 2.99 2.76 2.60 2.49 .10 2.92 2.53 2.32 2.19 2.09 2.03 26 .01 7.72 5.53 4.64 4.14 3.82 3.59 .05 4.23 3.37 2.98 2.74 2.59 2.48 .10 2.91 2.52 2.31 2.18 2.08 2.01 27 .01 7.68 5.49 4.60 4.11 3.79 3.56 .05 4.21 3.36 2.96 2.73 2.57 2.46 .10 2.90 2.51 2.30 2.17 2.07 2.01 28 .01 7.64 5.45 4.57 4.08 3.75 3.53 .05 4.20 3.34 2.95 2.72 2.56 2.45 .10 2.89 2.50 2.29 2.16 2.07 2.00 29 .01 7.60 5.42 4.54 4.05 3.73 3.50 .05 4.18 3.33 2.94 2.70 2.55 2.43 .10 2.89 2.50 2.28 2.15 2.06 1.99 30 .01 7.56 5.39 4.51 4.02 3.70 3.47 .05 4.17 3.32 2.92 2.69 2.53 2.42 .10 2.88 2.49 2.28 2.14 2.05 1.98 35 .01 7.42 5.27 4.40 3.91 3.59 3.37 .05 4.12 3.27 2.88 2.64 2.49 2.37 .10 2.86 2.46 2.25 2.14 2.02 1.95 40 .01 7.32 5.18 4.31 3.91 3.51 3.29 .05 4.09 3.23 2.84 2.64 2.45 2.34 .10 2.84 2.44 2.23 2.11 2.00 1.93 45 .01 7.23 5.11 4.25 3.83 3.46 3.23 .05 4.06 3.21 2.81 2.61 2.42 2.31 .10 2.82 2.43 2.21 2.09 1.98 1.91 50 .01 7.17 5.06 4.20 3.77 3.41 3.19 .05 4.04 3.18 2.79 2.58 2.40 2.29 .10 2.81 2.41 2.20 2.08 1.97 1.90 55 .01 7.12 5.01 4.16 3.72 3.37 3.15 .05 4.02 3.17 2.77 2.56 2.38 2.27 .10 2.80 2.40 2.19 2.06 1.96 1.89 60 .01 7.08 4.98 4.13 3.68 3.34 3.12 .05 4.00 3.15 2.76 2.54 2.37 2.26 .10 2.79 2.39 2.18 2.05 1.95 1.88 65 .01 7.04 4.95 4.10 3.65 3.31 3.09 .05 3.99 3.14 2.75 2.53 2.36 2.24 .10 2.79 2.39 2.17 2.04 1.94 1.87 70 .01 7.01 4.92 4.08 3.62 3.29 3.07 .05 3.98 3.13 2.74 2.51 2.35 2.23 .10 2.78 2.38 2.16 2.03 1.93 1.86 75 .01 6.99 4.90 4.06 3.60 3.27 3.05 .05 3.97 3.12 2.73 2.50 2.34 2.22 .10 2.77 2.38 2.16 2.03 1.93 1.86 80 .01 3.96 4.88 4.04 3.56 3.26 3.04 .05 6.96 3.11 2.72 2.49 2.33 2.22 .10 2.77 2.37 2.15 2.02 1.92 1.85 85 .01 6.94 4.86 4.02 3.55 3.24 3.02 .05 3.95 3.10 2.71 2.48 2.32 2.21 .10 2.77 2.37 2.15 2.01 1.92 1.85 90 .01 6.93 4.85 4.02 3.54 3.23 3.01 .05 3.95 3.10 2.71 2.47 2.32 2.20 .10 2.76 2.36 2.15 2.01 1.91 1.84 95 .01 6.91 4.84 4.00 3.52 3.22 3.00 .05 3.94 3.09 2.70 2.47 2.31 2.20 .10 2.76 2.36 2.14 2.01 1.91 1.84 100 .01 6.90 4.82 3.98 3.51 3.21 2.99 .05 3.94 3.09 2.70 2.46 2.31 2.19 .10 2.76 2.36 2.14 2.00 1.91 1.83 Infinity .01 6.64 4.61 3.78 3.32 3.02 2.80 .05 3.84 3.00 2.61 2.37 2.22 2.10 .10 2.71 2.30 2.08 1.95 1.85 1.78 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.
OneTailed Test TwoTailed Test df .05 .01 df .05 .01 1 .9877 .9995 1 .9969 .9999 2 .9000 .9800 2 .9500 .9900 3 .8054 .9343 3 .8783 .9587 4 .7293 .8822 4 .8114 .9172 5 .6694 .832 5 .7545 .8745 6 .6215 .7887 6 .7067 .8343 7 .5822 .7498 7 .6664 .7977 8 .5494 .7155 8 .6319 .7646 9 .5214 .6851 9 .6021 .7348 10 .4973 .6581 10 .5760 .7079 11 .4762 .6339 11 .5529 .6835 12 .4575 .6120 12 .5324 .6614 13 .4409 .5923 13 .5139 .6411 14 .4259 .5742 14 .4973 .6226 15 .4120 .5577 15 .4821 .6055 16 .4000 .5425 16 .4683 .5897 17 .3887 .5285 17 .4555 .5751 18 .3783 .5155 18 .4438 .5614 19 .3687 .5034 19 .4329 .5487 20 .3598 .4921 20 .4227 .5368 25 .3233 .4451 25 .3809 .4869 30 .2960 .4093 30 .3494 .4487 35 .2746 .3810 35 .3246 .4182 40 .2573 .3578 40 .3044 .3932 45 .2428 .3384 45 .2875 .3721 50 .2306 .3218 50 .2732 .3541 60 .2108 .2948 60 .2500 .3248 70 .1954 .2737 70 .2319 .3017 80 .1829 .2565 80 .2172 .2830 90 .1726 .2422 90 .2050 .2673 100 .1638 .2301 100 .1946 .2540 Table 5 Critical Values for the ChiSquare 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 onedimensional 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 df .10 .05 .01 1 2.71 3.84 6.64 2 4.00 5.99 9.21 3 6.25 7.82 11.34 4 7.78 9.49 13.28 5 9.24 11.07 15.09 6 10.64 12.59 16.81 7 12.02 14.07 18.48 8 13.36 15.51 20.09 9 14.68 16.92 21.67 10 16.99 18.31 23.21 11 17.28 19.68 24.72 12 18.65 21.03 26.22 13 19.81 22.36 27.69 14 21.06 23.68 29.14 15 22.31 25.00 30.58 16 23.54 26.30 32.00 17 24.77 27.60 33.41 18 25.99 28.87 34.80 19 27.20 30.14 36.19 20 28.41 31.41 37.57 21 29.62 32.67 38.93 22 30.81 33.92 40.29 23 32.01 35.17 41.64 24 33.20 36.42 42.98 25 34.38 37.65 44.81 26 35.56 38.88 45.64 27 36.74 40.11 46.96 28 37.92 41.34 48.28 29 39.09 42.56 49.59 30 40.26 43.77 50.89 Appendix B
Appendix BInternet Sites about StatisticsWhat 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 factfinding 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 AppletName: 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 childoriented agency Web sites both entertaining and educational.
Name: Random Birthday Applet
Where to find it: http://wwwstat.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 selfcontained 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 bestselling 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 samplesize 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 NumbersThe 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/surfstathome/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 ScreenThere 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.
 Statistical Reference Datasets at http://www.itl.nist.gov/div898/strd/
 United States Census Bureau (a huge collection and a gold mine of data) at http://factfinder.census.gov/servlet/DatasetMainPageServlet?_lang=en
 The Data and Story Library (http://lib.stat.cmu.edu/DASL/) with great annotations about the data (look for the stories link)
 Tons of economic data sets at Growth Data Sets (at http://www.bris.ac.uk/Depts/Economics/Growth/datasets.htm)
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 earthshaking, just fun to download and play with.
The World Wide Web Virtual Library: Statistics is the name of the page, but the oneword 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, softwareoriented 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 AwayIf 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 lefthand 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
Appendix CGlossaryThe following text is taken from Neil J. Salkind's bestselling introduction to statistics text, Statistics for People Who (Think They) Hate Statistics, 2nd edition (2004).
 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. Oneway analysis of variance looks for differences between the means of more than two groups.
Analysis of variance A measure of central tendency that sums all the scores in the data sets and divides by the number of scores.
Arithmetic mean The quality of the normal curve such that the tails never touch.
Asymptotic The most representative score in a set of scores.
Average A distribution of scores that is symmetrical about the mean, median, and mode and has asymptotic tails.
Bellshaped curve The upper and lower boundaries of a set of scores used in the creation of a frequency distribution.
Class interval The amount of variance unaccounted for in the relationship between two variables.
Coefficient of alienation The amount of variance accounted for in the relationship between two variables.
Coefficient of determination See coefficient of alienation
Coefficient of nondetermination A type of validity that examines how well a test outcome is consistent with a criterion that occurs in the present.
Concurrent validity A type of validity that examines how well a test reflects an underlying construct.
Construct validity A type of validity that examines how well a test samples a universe of items.
Content validity A numerical index that reflects the relationship between two variables.
Correlation coefficient A set of correlation coefficients.
Correlation matrix Another term for the outcome variable.
Criterion 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).
Criterion validity The value necessary for rejection (or nonacceptance) of the null hypothesis.
Critical value A frequency distribution that shows frequencies for class intervals along with the cumulative frequency for each.
Cumulative frequency distribution A record of an observation or an event such as a test score, a grade in math class, or a response time.
Data An observation.
Data point A set of data points.
Data set A value that is different for different statistical tests and approximates the sample size of number of individual cells in an experimental design.
Degrees of freedom The outcome variable or the predicted variable in a regression equation.
Dependent variable Values that describe the characteristics of a sample or population.
Descriptive statistics A positive correlation where the values of both variables change in the same direction.
Direct correlation A research hypothesis that includes a statement of inequality.
Directional research hypothesis A measure of the magnitude of a particular outcome.
Effect size The difference between the actual score (Y) and the predicted score (Y¯).
Error in prediction See error in prediction
Error of estimate The part of a test score that is random and contributes to the unreliability of a test.
Error score An analysis of variance with more than one factor or independent variable.
Factorial analysis of variance A research design where there is more than one treatment variable.
Factorial design A method for illustrating the distribution of scores within class intervals.
Frequency distribution A graphical representation of a frequency distribution.
Frequency polygon A graphical representation of a frequency distribution.
Histogram An ifthen statement of conjecture that relates variables to one another.
Hypothesis The treatment variable that is manipulated or the predictor variable in a regression equation.
Independent variable A negative correlation where the values of variables move in opposite directions.
Indirect correlation Tools that are used to infer the results based on a sample to a population.
Inferential statistics The outcome where the effect of one factor is differentiated across another factor.
Interaction effect A type of reliability that examines the onedimensional nature of an assessment tool.
Internal consistency reliability A type of reliability that examines the consistency of raters.
Interrater reliability A scale of measurement that is characterized by equal distances between points on some underlying continuum.
Interval level of measurement The quality of a distribution such that it is flat or peaked.
Kurtosis The quality of a normal curve that defines its peakedness.
Leptokurtic The regression line that best fits the actual scores and minimizes the error in prediction.
Line of best fit A correlation that is best expressed as a straight line.
Linear correlation In analysis of variance, when a factor or an independent variable has a significant effect upon the outcome variable.
Main effect A type of average where scores are summed and divided by the number of observations.
Mean The average deviation for all scores from the mean of a distribution.
Mean deviation The mean, median, and mode.
Measures of central tendency The point at which 50% of the cases in a distribution fall below and 50% fall above.
Median The central point in a class interval.
Midpoint The most frequently occurring score in a distribution.
Mode A statistical technique where several variables are used to predict one.
Multiple regression A scale of measurement that is characterized by categories with no order or difference in magnitude.
Nominal level of measurement A hypothesis that posits no direction, but a difference.
Nondirectional research hypothesis Distributionfree statistics.
Nonparametric statistics See bellshaped curve
Normal curve A statement of equality between a set of variables.
Null hypothesis The score that is recorded or observed.
Observed score The value that results from the application of a statistical test.
Obtained value A visual representation of a cumulative frequency distribution.
Ogive A directional test.
Onetailed test See analysis of variance
Oneway analysis of variance A scale of measurement that is characterized by an underlying continuum that is ordered.
Ordinal level of measurement 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.
Outliers A type of reliability that examines the consistency across different forms of the same test.
Parallel forms reliability Statistics used for the inference from a sample to a population.
Parametric statistics See correlation coefficient
Pearson productmoment correlation The point at or below where a score appears.
Percentile point The quality of a normal curve that defines its flatness.
Platykurtic All the possible subjects or cases of interest.
Population After the fact, referring to tests done to determine the true source of a difference between three or more groups.
Post hoc A type of validity that examines how well a test outcome is consistent with a criterion that occurs in the future.
Predictive validity The variable that predicts an outcome.
Predictor 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.
Range A scale of measurement that is characterized by an absolute zero.
Ratio level of measurement The equation that defines the points and the line that are closest to the actual scores.
Regression equation The line drawn based on the values in the regression equation.
Regression line The quality of a test such that it is consistent.
Reliability A statement of inequality between two variables.
Research hypothesis A subset of a population.
Sample The difference between sample and population values.
Sampling error Different ways of categorizing measurement outcomes.
Scales of measurement A plot of paired data points.
Scattergram, or scatterplot The risk set by the researcher for rejecting a null hypothesis when it is true.
Significance level See analysis of variance
Simple analysis of variance 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.
Skew, or skewness A listing of sources of variance in an analysis of variance summary table.
Source table The average deviation from the mean.
Standard deviation A measure of accuracy in prediction.
Standard error of estimate See z score
Standard score See significance level
Statistical significance A set of tools and techniques used to organize and interpret information.
Statistics A type of reliability that examines consistency over time.
Testretest reliability See obtained value
Test statistic value The unobservable part of an observed score that reflects the actual ability or behavior.
True score A test of a nondirectional hypothesis where the direction of the difference is of little importance.
Twotailed test The probability of rejecting a null hypothesis when it is true.
Type I error The probability of accepting a null hypothesis when it is false.
Type II error A conservative estimate of a population parameter.
Unbiased estimate The quality of a test such that it measures what it says it does.
Validity The amount of spread or dispersion in a set of scores.
Variability The square of the standard deviation, and another measure of a distribution's spread or dispersion.
Variance The predicted Y value.
Y′ or Y prime 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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