Applied Univariate, Bivariate, and Multivariate Statistics. Daniel J. Denis

      1  COVER

      2  TITLE PAGE

      3  COPYRIGHT PAGE

      4  DEDICATION PAGE

      5  PREFACE ACKNOWLEDGMENTS

      6  ABOUT THE COMPANION WEBSITE

      7  1 PRELIMINARY CONSIDERATIONS 1.1 THE PHILOSOPHICAL BASES OF KNOWLEDGE: RATIONALISTIC VERSUS EMPIRICIST PURSUITS 1.2 WHAT IS A “MODEL”? 1.3 SOCIAL SCIENCES VERSUS HARD SCIENCES 1.4 IS COMPLEXITY A GOOD DEPICTION OF REALITY? ARE MULTIVARIATE METHODS USEFUL? 1.5 CAUSALITY 1.6 THE NATURE OF MATHEMATICS: MATHEMATICS AS A REPRESENTATION OF CONCEPTS 1.7 AS A SCIENTIST, HOW MUCH MATHEMATICS DO YOU NEED TO KNOW? 1.8 STATISTICS AND RELATIVITY 1.9 EXPERIMENTAL VERSUS STATISTICAL CONTROL 1.10 STATISTICAL VERSUS PHYSICAL EFFECTS 1.11 UNDERSTANDING WHAT “APPLIED STATISTICS” MEANS Review Exercises Further Discussion and Activities

      8  2 INTRODUCTORY STATISTICS 2.1 DENSITIES AND DISTRIBUTIONS 2.2 CHI‐SQUARE DISTRIBUTIONS AND GOODNESS‐OF‐FIT TEST 2.3 SENSITIVITY AND SPECIFICITY 2.4 SCALES OF MEASUREMENT: NOMINAL, ORDINAL, INTERVAL, RATIO 2.5 MATHEMATICAL VARIABLES VERSUS RANDOM VARIABLES 2.6 MOMENTS AND EXPECTATIONS 2.7 ESTIMATION AND ESTIMATORS 2.8 VARIANCE 2.9 DEGREES OF FREEDOM 2.10 SKEWNESS AND KURTOSIS 2.11 SAMPLING DISTRIBUTIONS 2.12 CENTRAL LIMIT THEOREM 2.13 CONFIDENCE INTERVALS 2.14 MAXIMUM LIKELIHOOD 2.15 AKAIKE'S INFORMATION CRITERIA 2.16 COVARIANCE AND CORRELATION 2.17 PSYCHOMETRIC VALIDITY, RELIABILITY: A COMMON USE OF CORRELATION COEFFICIENTS 2.18 COVARIANCE AND CORRELATION MATRICES 2.19 OTHER CORRELATION COEFFICIENTS 2.20 STUDENT'S t DISTRIBUTION 2.21 STATISTICAL POWER 2.22 POWER ESTIMATION USING R AND G^*POWER 2.23 PAIRED‐SAMPLES t‐TEST: STATISTICAL TEST FOR MATCHED‐PAIRS (ELEMENTARY BLOCKING) DESIGNS 2.24 BLOCKING WITH SEVERAL CONDITIONS 2.25 COMPOSITE VARIABLES: LINEAR COMBINATIONS 2.26 MODELS IN MATRIX FORM 2.27 GRAPHICAL APPROACHES 2.28 WHAT MAKES A p‐VALUE SMALL? A CRITICAL OVERVIEW AND PRACTICAL DEMONSTRATION OF NULL HYPOTHESIS SIGNIFICANCE TESTING 2.29 CHAPTER SUMMARY AND HIGHLIGHTS Review Exercises Further Discussion and Activities

      9  3 ANALYSIS OF VARIANCE: FIXED EFFECTS MODELS 3.1 WHAT IS ANALYSIS OF VARIANCE? FIXED VERSUS RANDOM EFFECTS 3.2 HOW ANALYSIS OF VARIANCE WORKS: A BIG PICTURE OVERVIEW 3.3 LOGIC AND THEORY OF ANOVA: A DEEPER LOOK 3.4 FROM SUMS OF SQUARES TO UNBIASED VARIANCE ESTIMATORS: DIVIDING BY DEGREES OF FREEDOM 3.5 EXPECTED MEAN SQUARES FOR ONE‐WAY FIXED EFFECTS MODEL: DERIVING THE F‐RATIO 3.6 THE NULL HYPOTHESIS IN ANOVA 3.7 FIXED EFFECTS ANOVA: MODEL ASSUMPTIONS 3.8 A WORD ON EXPERIMENTAL DESIGN AND RANDOMIZATION 3.9 A PREVIEW OF THE CONCEPT OF NESTING 3.10 BALANCED VERSUS UNBALANCED DATA IN ANOVA MODELS 3.11 MEASURES OF ASSOCIATION AND EFFECT SIZE IN ANOVA: MEASURES OF VARIANCE EXPLAINED 3.12 THE F‐TEST