Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences

Preface ix

About the Companion Website xiii

1 Introduction 1

Basis of How All Quantitative Statistical Based Research 1

Data Analysis, Not Statistical Analysis 3

Quantitative Versus Qualitative Research 8

What the Book Covers and What It Does Not Cover 9

Book Structure 10

References 11

Part I Data Analysis Approaches 13

2 Statistics Terminology 15

Statistically Testing a Hypothesis 15

Statistical Significance and p-Value 19

Confidence Intervals 26

Effect Size 27

Statistical Power of a Test 31

Practical Significance Versus Statistical Significance 34

Statistical Independence 34

Degrees of Freedom 36

Measures of Central Tendency 37

Percentile and Percentile Rank 41

Central Limit Theorem 42

Law of Large Numbers 44

References 48

3 Analysis Issues and Potential Pitfalls 49

Effects of Variables 49

Outliers in the Dataset 53

Relationships Between Variables 53

A Single Contradictory Example Does Not Invalidate a Statistical Relationship 60

References 62

4 Graphically Representing Data 63

Data Distributions 63

Bell Curves 64

Skewed Curves 68

Bimodal Distributions 71

Poisson Distributions 75

Binomial Distribution 77

Histograms 79

Scatter Plots 80

Box Plots 81

Ranges of Values and Error Bars 82

References 85

5 Statistical Tests 87

Inter-Rater Reliability 87

Regression Models 92

Parametric Tests 93

Nonparametric Tests 95

One-Tailed or Two-Tailed Tests 96

Tests Must Make Sense 99

References 103

Part II Data Analysis Examples 105

6 Overview of Data Analysis Process 107

Know How to Analyze It Before Starting the Study 107

Perform an Exploratory Data Analysis 108

Perform the Statistical Analysis 109

Analyze the Results and Draw Conclusions 110

Writing Up the Study 111

References 112

7 Analysis of a Study on Reading and Lighting Levels 113

Lighting and Reading Comprehension 113

Know How the Data Will Be Analyzed Before Starting the Study 113

Perform an Exploratory Data Analysis 115

Perform an Inferential Statistical Analysis 122

Exercises 132

8 Analysis of Usability of an E-Commerce Site 135

Usability of an E-Commerce Site 135

Study Overview 135

Know How You Will Analyze the Data Before Starting the Study 136

Perform an Exploratory Data Analysis 138

Perform an Inferential Statistical Analysis 147

Follow-Up Tests 151

Performing Follow-Up Tests 153

Exercises 157

Reference 158

9 Analysis of Essay Grading 159

Analysis of Essay Grading 159

Exploratory Data Analysis 160

Inferential Statistical Data Analysis 165

Exercises 173

Reference 175

10 Specific Analysis Examples 177

Handling Outliers in the Data 177

Floor/Ceiling Effects 182

Order Effects 183

Data from Stratified Sampling 184

Missing Data 184

Noisy Data 186

Transform the Data 187

References 188

11 Other Types of Data Analysis 189

Time-Series Experiment 189

Analysis for Data Clusters 192

Low-Probability Events 193

Metadata Analysis 193

Reference 195

A Research Terminology 197

Independent, Dependent, and Controlled Variables 197

Between Subjects and Within Subjects 199

Validity and Reliability 200

Variable Types 201

Type of Data 201

Independent Measures and Repeated Measures 203

Variation in Data Collection 205

Probability-What 30% Chance Means 212

References 214

Index 215

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• Matemática

quantitative data analysis; contextualizing data; statistical tests; exploratory analysis; decision-making for performing parametric or non-parametric analysis; practical significance determination