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Daniel J. Denis
Applied Univariate, Bivariate, and Multivariate Statistics
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Страница 1
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Страница 7
Страница 8
Страница 9
Страница 10
Страница 11
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
Notes
2 INTRODUCTORY STATISTICS
2.1 DENSITIES AND DISTRIBUTIONS
2.1.1 Plotting Normal Distributions
2.1.2 Binomial Distributions
2.1.3 Normal Approximation
2.1.4 Joint Probability Densities: Bivariate and Multivariate Distributions
2.2 CHI‐SQUARE DISTRIBUTIONS AND GOODNESS‐OF‐FIT TEST
2.2.1 Power for Chi‐Square Test of Independence
2.3 SENSITIVITY AND SPECIFICITY
2.4 SCALES OF MEASUREMENT: NOMINAL, ORDINAL, INTERVAL, RATIO
2.4.1 Nominal Scale
2.4.2 Ordinal Scale
2.4.3 Interval Scale
2.4.4 Ratio Scale
2.5 MATHEMATICAL VARIABLES VERSUS RANDOM VARIABLES
2.6 MOMENTS AND EXPECTATIONS
2.6.1 Sample and Population Mean Vectors
2.7 ESTIMATION AND ESTIMATORS
2.8 VARIANCE
2.9 DEGREES OF FREEDOM
2.10 SKEWNESS AND KURTOSIS
2.11 SAMPLING DISTRIBUTIONS
2.11.1 Sampling Distribution of the Mean
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
2.20.1
t
‐Tests for One Sample
2.20.2
t
‐Tests for Two Samples
2.20.3 Two‐Sample
t
‐Tests in R
2.21 STATISTICAL POWER
2.21.1 Visualizing Power
2.22 POWER ESTIMATION USING R AND G
*
POWER
2.22.1 Estimating Sample Size and Power for Independent Samples
t
‐Test
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
2.27.1 Box‐and‐Whisker Plots
2.28 WHAT MAKES A
p
‐VALUE SMALL? A CRITICAL OVERVIEW AND PRACTICAL DEMONSTRATION OF NULL HYPOTHESIS SIGNIFICANCE TESTING
2.28.1 Null Hypothesis Significance Testing (NHST): A Legacy of Criticism
2.28.2 The Make‐Up of a
p
‐Value: A Brief Recap and Summary
2.28.3 The Issue of Standardized Testing: Are Students in Your School Achieving More Than the National Average?
2.28.4 Other Test Statistics
2.28.5 The Solution
2.28.6 Statistical Distance: Cohen's d
2.28.7 What Does Cohen's d Actually Tell Us?
2.28.8 Why and Where the Significance Test Still Makes Sense
2.29 CHAPTER SUMMARY AND HIGHLIGHTS
Review Exercises
Further Discussion and Activities
Notes
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