### Study Outline for Nunnally and Bernstein, Fall 2003

#### Part One: Introduction

Chapter 1: Introduction
CONCEPTS: Scaling vs. Classification; Meaningfulness and Usefulness; Standardization; Scales of Measurement.

#### Part Two: Statistical Foundations

Chapter 2: Traditional Approaches to Scaling
CONCEPTS: The Data Matrix; Model Evaluation; Threshold; Fullerton-Cattell Law; Judgments vs. Sentiments; Preferences vs. Similarities; Law of Comparative Judgment; Multi-item Measures; Item Characteristic Curves; Difficulty and Discrimination; Guttman Scale; The Linear Model.
Chapter 3: Validity (of the first 3, this is for rereading)
CONCEPTS: Theory vs. Instrument; Theories and Models: Measurement and Structure; Construct Validity: Domain of Observables, Relations among Constructs, Campbell and Fiske's Multitrait-Multimethod Matrix; Criterion-Related Validity: (Postdictive, Concurrent, & Predictive), The Criterion Problem; Content Validity; Substantive Theory vs. Measurement Theory.
Chapter 4: Elements of Statistical Description and Estimation
CONCEPTS: Ordered vs. Categorical Variables; Variance (Ordered and Dichotomous variables); Scale Transformations; Covariance and Correlation; Variations on Pearson: phi, point-biserial, and phi; "Assumptions underlying" Pearson correlation; Factors influencing r: restriction of range, distribution form; Non-linear measure of relationship: eta (correlation ratio); Regression; Standard Error of Estimate; Partitioning variance; Estimation procedures: Least squares, Maximum likelihood; Properties of estimators.
Chapter 5: Linear Combinations, Partial and Multiple Correlation
CONCEPTS: Variance of linear combinations; Covariance of linear combinations; Within and between covariance matrices; Partial correlation (Semi-partial correlation) [Work through example on pp 178-180], Multiple correlation and multiple regression (significance, suppression, categorical predictors, multicollinearity, importance of "predictors," etc.); Selection (hierarchical inclusion or elimination, moderated multiple regression); Related topics (ANCOVA, nonlinear relations, residual analysis, canonical analysis).

#### Part Three: Construction of Multi-Item Measures

Chapter 6: The Theory of Measurement Error
CONCEPTS: The Concept of Measurement Error; Classical Test Theory; The Domain Sampling Model (multi-item measures, estimates of reliability); The Model of Parallel Tests; Test Length (Spearman-Brown prophecy formula); Coefficient Alpha; KR-20; Variance of True and Error Scores; The Standard Error of Measurement; Attenuation; Reliability as Stability over Time.
Chapter 7: The Assessment of Reliability
CONCEPTS: Sources of Error; Estimation of Reliability; Uses of the Reliability Coefficient (Correction for Attenuation, Confidence Intervals, Effects of Dispersion on Reliability); Making Measures Reliable (Test Length, Standards, Limitations); Reliability of Linear Combinations (Negative Elements, Weighted Sums, Principles); An Analysis of Variance Approach to Reliability; Generalizability Theory.
Chapter 10: Recent Developments in Test Theory
CONCEPTS: Item Response Theory (IRT) (Conditional Independence, One-Parameter Models, Two-Parameter Models, Three-Parameter Models, Item and Test Information); Differential Item Functioning (Item Bias); Tailored Tests and Computerized Adaptive Testing; Commentary on IRT.

#### Part Four: Factor Analysis

Chapter 11: Factor Analysis I: The General Model and Variance Condensation
CONCEPTS: Uses of Factor Analysis; Condensing Variance in Exploratory Factor Analysis; Centroid Condensation; Principal Component and Principal Axis Condensation; Maximum Likelihood and Related Forms of Condensation; Determining the Number of Factors; Causal Indicators.
Chapter 12: Exploratory Factor Analysis II: Rotation and Other Topics
CONCEPTS: Factor Rotation; Analytic Rotations; Estimation of Factor Scores; The Common Factor Model; Factor Analytic Designs; Ad-Lib Factoring; Higher-Order Factors.
Chapter 13: Confirmatory Factor Analysis
CONCEPTS: Spearman's General Factor Solution; Comparing Factors in Different Analyses; Testing Weak Theories; Factoring Categorical Variables (Item Level Factoring); Testing Strong Theories.
Factor Analysis Using SAS PROC FACTOR (Stat Services, UT-Austin)
Factor Analysis (Bertram Malle, University of Oregon)
A compilation of SEM resources (AERA SIG: Structural Equation Modeling)

I stole the following from an email msg posted to STAT-L by Eric Bohlman (ebohlman@netcom.com):

"H.G. Wells once said that he expected that in his lifetime, learning to think statistically would become as important as learning to read. Harold Hotelling once questioned how anyone could consider himself (sic) in possession of a liberal education if he (sic) didn't understand the nature of variation."

If you have difficulty with any of the concepts presented in the text or lectures, please consult the syllabus for one or more of the courses listed on my home page