Preface xv

Acknowledgments xix

**1 Introduction 1**

Big Data Analysis 1

Visual Data Analysis 2

Importance of Statistics for the Social and Health Sciences and Medicine 3

Historical Notes: Early Use of Statistics 4

Approach of the Book 6

Cases from Current Research 7

Research Design 9

Focus on Interpretation 9

**2 Descriptive Statistics: Central Tendency 13**

What is the Whole Truth? Research Applications (Spuriousness) 13

Descriptive and Inferential Statistics 16

The Nature of Data: Scales of Measurement 16

Descriptive Statistics: Central Tendency 23

Using SPSS^{®} and Excel to Understand Central Tendency 28

Distributions 35

Describing the Normal Distribution: Numerical Methods 37

Descriptive Statistics: Using Graphical Methods 41

Terms and Concepts 47

Data Lab and Examples (with Solutions) 49

Data Lab: Solutions 51

**3 Descriptive Statistics: Variability 55**

Range 55

Percentile 56

Scores Based on Percentiles 57

Using SPSS^{®} and Excel to Identify Percentiles 57

Standard Deviation and Variance 60

Calculating the Variance and Standard Deviation 61

Population SD and Inferential SD 66

Obtaining SD from Excel and SPSS^{®} 67

Terms and Concepts 70

Data Lab and Examples (with Solutions) 71

Data Lab: Solutions 73

**4 The Normal Distribution 77**

The Nature of the Normal Curve 77

The Standard Normal Score: *Z Score* 79

The *Z *Score Table of Values 80

Navigating the *Z *Score Distribution 81

Calculating Percentiles 83

Creating Rules for Locating *Z *Scores 84

Calculating *Z *Scores 87

Working with Raw Score Distributions 90

Using SPSS^{®} to Create *Z *Scores and Percentiles 90

Using Excel to Create *Z *Scores 94

Using Excel and SPSS^{®} for Distribution Descriptions 97

Terms and Concepts 99

Data Lab and Examples (with Solutions) 99

Data Lab: Solutions 101

**5 Probability and the ***Z *Distribution 105

The Nature of Probability 106

Elements of Probability 106

Combinations and Permutations 109

Conditional Probability: Using Bayes’ Theorem 111

*Z *Score Distribution and Probability 112

Using SPSS^{®} and Excel to Transform Scores 117

Using the Attributes of the Normal Curve to Calculate Probability 119

“Exact” Probability 123

From Sample Values to Sample Distributions 126

Terms and Concepts 127

Data Lab and Examples (with Solutions) 128

Data Lab: Solutions 129

**6 Research Design and Inferential Statistics 133**

Research Design 133

Experiment 136

Non-Experimental or Post Facto Research Designs 140

Inferential Statistics 143

*Z *Test 154

The Hypothesis Test 154

Statistical Significance 156

Practical Significance: Effect Size 156

*Z *Test Elements 156

Using SPSS^{®} and Excel for the *Z *Test 157

Terms and Concepts 158

Data Lab and Examples (with Solutions) 161

Data Lab: Solutions 162

**7 The ***T *Test for Single Samples 165

Introduction 166

*Z *Versus *T*: Making Accommodations 166

Research Design 167

Parameter Estimation 169

The *T *Test 173

The *T *Test: A Research Example 176

Interpreting the Results of the *T *Test for a Single Mean 180

The *T *Distribution 181

The Hypothesis Test for the Single Sample *T *Test 182

Type I and Type II Errors 183

Effect Size 187

Effect Size for the Single Sample *T *Test 187

Power Effect Size and Beta 188

One- and Two-Tailed Tests 189

Point and Interval Estimates 192

Using SPSS^{®} and Excel with the Single Sample *T *Test 196

Terms and Concepts 201

Data Lab and Examples (with Solutions) 201

Data Lab: Solutions 203

**8 Independent Sample ***T *Test 207

A Lot of “Ts” 207

Research Design 208

Experimental Designs and the Independent *T *Test 208

Dependent Sample Designs 209

Between and Within Research Designs 210

Using Different *T *Tests 211

Independent *T *Test: The Procedure 213

Creating the Sampling Distribution of Differences 215

The Nature of the Sampling Distribution of Differences 216

Calculating the Estimated Standard Error of Difference with Equal Sample Size 218

Using Unequal Sample Sizes 219

The Independent *T *Ratio 221

Independent *T *Test Example 222

Hypothesis Test Elements for the Example 222

Before–After Convention with the Independent *T *Test 226

Confidence Intervals for the Independent *T *Test 227

Effect Size 228

The Assumptions for the Independent *T *Test 230

SPSS^{®} Explore for Checking the Normal Distribution Assumption 231

Excel Procedures for Checking the Equal Variance Assumption 233

SPSS^{®} Procedure for Checking the Equal Variance Assumption 237

Using SPSS^{®} and Excel with the Independent *T *Test 239

SPSS^{® }Procedures for the Independent *T *Test 239

Excel Procedures for the Independent *T *Test 243

Effect Size for the Independent *T *Test Example 245

Parting Comments 245

Nonparametric Statistics: The Mann–Whitney *U *Test 246

Terms and Concepts 249

Data Lab and Examples (with Solutions) 249

Data Lab: Solutions 251

Graphics in the Data Summary 254

**9 Analysis of Variance 255**

A Hypothetical Example of ANOVA 255

The Nature of ANOVA 257

The Components of Variance 258

The Process of ANOVA 259

Calculating ANOVA 260

Effect Size 268

Post Hoc Analyses 269

Assumptions of ANOVA 274

Additional Considerations with ANOVA 275

The Hypothesis Test: Interpreting ANOVA Results 276

Are the Assumptions Met? 276

Using SPSS^{®} and Excel with One-Way ANOVA 282

The Need for Diagnostics 289

Non-Parametric ANOVA Tests: The Kruskal–Wallis Test 289

Terms and Concepts 292

Data Lab and Examples (with Solutions) 293

Data Lab: Solutions 294

**10 Factorial ANOVA 297**

Extensions of ANOVA 297

ANCOVA 298

MANOVA 299

MANCOVA 299

Factorial ANOVA 299

Interaction Effects 299

Simple Effects 301

2XANOVA: An Example 302

Calculating Factorial ANOVA 303

The Hypotheses Test: Interpreting Factorial ANOVA Results 306

Effect Size for 2XANOVA: Partial 𝜂^{2} 308

Discussing the Results 309

Using SPSS^{® }to Analyze 2XANOVA 311

Summary Chart for 2XANOVA Procedures 319

Terms and Concepts 319

Data Lab and Examples (with Solutions) 320

Data Lab: Solutions 320

**11 Correlation 329**

The Nature of Correlation 330

The Correlation Design 331

Pearson’s Correlation Coefficient 332

Plotting the Correlation: The Scattergram 334

Using SPSS^{®} to Create Scattergrams 337

Using Excel to Create Scattergrams 339

Calculating Pearson’s *r* 341

The *Z *Score Method 342

The Computation Method 344

The Hypothesis Test for Pearson’s *r* 345

Effect Size: the Coefficient of Determination 347

Diagnostics: Correlation Problems 349

Correlation Using SPSS^{®} and Excel 352

Nonparametric Statistics: Spearman’s Rank Order Correlation (*r*_{s}) 358

Terms and Concepts 363

Data Lab and Examples (with Solutions) 364

Data Lab: Solutions 365

**12 Bivariate Regression 371**

The Nature of Regression 372

The Regression Line 374

Calculating Regression 376

Effect Size of Regression 379

The *Z *Score Formula for Regression 380

Testing the Regression Hypotheses 382

The Standard Error of Estimate 383

Confidence Interval 385

Explaining Variance Through Regression 386

A Numerical Example of Partitioning the Variation 389

Using Excel and SPSS^{®} with Bivariate Regression 390

The SPSS^{®} Regression Output 390

The Excel Regression Output 396

Complete Example of Bivariate Linear Regression 398

Assumptions of Bivariate Regression 398

The Omnibus Test Results 404

Effect Size 404

The Model Summary 405

The Regression Equation and Individual Predictor Test of Significance 405

Advanced Regression Procedures 406

Detecting Problems in Bivariate Linear Regression 408

Terms and Concepts 409

Data Lab and Examples (with Solutions) 410

Data Lab: Solutions 411

**13 Introduction to Multiple Linear Regression 417**

The Elements of Multiple Linear Regression 417

Same Process as Bivariate Regression 418

Some Differences between Bivariate Linear Regression and Multiple Linear Regression 419

Stuff not Covered 420

Assumptions of Multiple Linear Regression 421

Analyzing Residuals to Check MLR Assumptions 422

Diagnostics for MLR: Cleaning and Checking Data 423

Extreme Scores 424

Distance Statistics 428

Influence Statistics 429

MLR Extended Example Data 430

Assumptions Met? 431

Analyzing Residuals: Are Assumptions Met? 433

Interpreting the SPSS^{®} Findings for MLR 436

Entering Predictors Together as a Block 437

Entering Predictors Separately 442

Additional Entry Methods for MLR Analyses 447

Example Study Conclusion 448

Terms and Concepts 448

Data Lab and Example (with Solution) 450

Data Lab: Solution 450

**14 Chi-Square and Contingency Table Analysis 455**

Contingency Tables 455

The Chi-square Procedure and Research Design 456

Chi-square Design One: Goodness of Fit 457

A Hypothetical Example: Goodness of Fit 458

Effect Size: Goodness of Fit 462

Chi-square Design Two: The Test of Independence 463

A Hypothetical Example: Test of Independence 464

Special 2 × 2 Chi-square 468

Effect Size in 2 × 2 Tables: PHI 470

Cramer’s *V*: Effect Size for the Chi-square Test of Independence 471

Repeated Measures Chi-square: Mcnemar Test 472

Using SPSS® and Excel with Chi-square 474

Using SPSS® for the Chi-square Test of Independence 475

Using Excel for Chi-square Analyses 481

Terms and Concepts 483

Data Lab and Examples (with Solutions) 483

Data Lab: Solutions 484

**15 Repeated Measures Procedures: ***T*_{dep} **and ANOVA**_{WS} **489**

Independent and Dependent Samples in Research Designs 490

Using Different *T *Tests 491

The Dependent *T *Test Calculation: The “Long” Formula 491

Example: The Long Formula 492

The Dependent *T *Test Calculation: The “Difference” Formula 494

*T*_{dep} and Power 496

Conducting The *T*_{dep} Analysis Using SPSS^{®} 496

Conducting The *T*_{dep} Analysis Using Excel 498

Within-Subject ANOVA (ANOVA_{WS}) 498

Experimental Designs 499

Post Facto Designs 500

Within-Subject Example 501

Using SPSS^{®} for Within-Subject Data 501

The SPSS^{®} Procedure 502

The SPSS^{®} Output 504

Nonparametric Statistics 508

Terms and Concepts 508

**Appendices**

**Appendix A SPSS**^{®} Basics 509

Using SPSS^{® }509

General Features 510

Management Functions 513

Additional Management Functions 517

**Appendix B Excel Basics 531**

Data Management 531

The Excel Menus 533

Using Statistical Functions 541

Data Analysis Procedures 543

Missing Values and “0” Values in Excel Analyses 544

Using Excel with “Real Data” 544

**Appendix C Statistical Tables 545**

Table C.1: *Z*-Score Table (Values Shown are Percentages – %) 545

Table C.2: Exclusion Values for the *T*-Distribution 547

Table C.3: Critical (Exclusion) Values for the Distribution of *F* 548

Table C.4: Tukey’s Range Test (Upper 5% Points) 551

Table C.5: Critical (Exclusion) Values for Pearson’s Correlation Coefficient *r* 552

Table C.6: Critical Values of the *𝜒*^{2} (Chi-Square) Distribution 553

References 555

Index 557