Statistics for Exercise Science and Health with Microsoft Office Excel

J. P. Verma, PhD, is Professor of Statistics and Director of the Center for Advanced Studies at Lakshmibai National Institute of Physical Education in Gwalior, India. Professor Verma is an active researcher in sports modeling and data analysis and has conducted many workshops on research methodology, research designs, multivariate analysis, statistical modeling, and data analysis for students of management, physical education, social science, and economics.

Preface xxi

1 Scope of Statistics in Exercise Science and Health 1

1.1 Introduction, 1

1.2 Understanding Statistics, 2

1.3 What Statistics Does?, 3

1.4 Statistical Processes, 4

1.5 Need for Statistics, 5

1.6 Statistics in Exercise Science and Health, 8

1.7 Computing with Excel, 9

2 Understanding the Nature of Data 19

2.1 Introduction, 19

2.2 Important Terminologies, 20

2.3 Measurement of Data, 22

2.4 Parametric and Nonparametric Statistics, 24

2.5 Frequency Distribution, 25

2.6 Summation Notation, 28

2.7 Measures of Central Tendency, 34

2.8 Comparison of the Mean, Median, and Mode, 46

2.9 Measures of Variability, 53

2.10 Standard Error, 72

2.11 Coefficient of Variation, 72

2.12 Absolute and Relative Variability, 74

2.13 Box-And-Whisker Plot, 79

2.14 Skewness, 81

2.15 Percentiles, 82

2.16 Computing with Excel, 86

3 Working with Graphs 101

3.1 Introduction, 101

3.2 Guidelines for Constructing a Graph, 102

3.3 Bar Diagram, 104

3.4 Histogram, 105

3.5 Frequency Polygon, 107

3.6 Frequency Curve, 107

3.7 Cumulative Frequency Curve, 108

3.8 Ogive, 110

3.9 Pie Diagram, 111

3.10 Stem and Leaf Plot, 113

3.11 Computing with Excel, 117

4 Probability and its Application 130

4.1 Introduction, 130

4.2 Application of Probability, 131

4.3 Set Theory, 132

4.4 Terminologies Used in Probability, 136

4.5 Basic Definitions of Probability, 142

4.6 Some Results on Probability, 145

4.7 Computing Probability, 145

4.8 Types of Probability, 151

4.9 Theorems of Probability, 152

4.10 Computing with Excel, 162

5 Statistical Distributions and their Application 176

5.1 Introduction, 176

5.2 Terminologies used in Statistical Distribution, 177

5.3 Discrete Distribution, 182

5.4 Binomial Distribution, 183

5.5 Poisson Distribution, 189

5.6 Continuous Distribution, 194

5.7 Normal Distribution, 195

5.8 Standard Score, 198

5.9 Normal Approximation to the Binomial Distribution, 199

5.10 Testing Normality of the Data, 200

5.11 The Central Limit Theorem, 204

5.12 Solving Problems Based on Normal Distribution, 204

5.13 Uses of Normal Distribution, 216

5.14 Computing with Excel, 217

6 Sampling and Sampling Distribution 234

6.1 Introduction, 234

6.2 Population and Sample, 235

6.3 Parameter and Statistics, 235

6.4 Sampling Frame, 236

6.5 Sampling, 236

6.6 Census, 238

6.7 Probability and Nonprobability Sampling, 238

6.8 Probability Sampling, 239

6.9 Nonprobability Sampling, 246

6.10 When to Use Probability Sampling, 249

6.11 When to Use Nonprobability Sampling, 250

6.12 Characteristics of a Good Sample, 250

6.13 Sources of Data, 251

6.14 Methods of Data Collection, 252

6.15 Biases in Data Collection, 254

6.16 Sampling Error, 255

6.17 Nonsampling Errors, 255

6.18 Sampling Distribution, 255

6.19 Criteria in Deciding Sample Size, 262

6.20 Computing with Excel, 266

7 Statistical Inference for Decision-Making in Exercise Science and Health 277

7.1 Introduction, 277

7.2 Theory of Estimation, 278

7.3 Point Estimation, 278

7.4 Characteristics of a Good Estimator, 279

7.5 The t-Distribution, 280

7.6 Interval Estimation, 281

7.7 Testing of Hypothesis, 295

7.8 Types of Hypothesis, 296

7.9 Test Statistic, 297

7.10 Concept used in Hypothesis Testing, 298

7.11 Type I and Type II Errors, 299

7.12 Level of Significance, 300

7.13 Power of the Test, 301

7.14 Rejection Region and Critical Value, 301

7.15 p-Value, 302

7.16 One-Tailed and Two-Tailed Tests, 303

7.17 Degrees of Freedom, 305

7.18 Strategy in Selecting the Test Statistic, 306

7.19 Steps in Hypothesis Testing, 307

7.20 One-Sample Testing, 312

7.21 Two-Sample Testing, 324

7.22 Test of Significance about Two Population Proportions, 338

7.23 Test of Significance about Two Population Variances, 341

7.24 Computing with Excel, 346

8 Analysis of Variance and Designing Research Experiments 375

8.1 Introduction, 375

8.2 Understanding Analysis of Variance, 376

8.3 Design of Experiment, 378

8.4 One-way Analysis of Variance, 379

8.5 Completely Randomized Design, 384

8.6 Two-way Analysis of Variance (N Observations Per Cell), 391

8.7 Two-way Analysis of Variance (One Observation Per Cell), 397

8.8 Randomized Block Design, 401

8.9 Factorial Design, 407

8.10 Analysis of Covariance, 414

8.11 Computing with Excel, 428

9 Understanding Relationships and Developing Regression Models 461

9.1 Introduction, 461

9.2 Types of Relationship, 462

9.3 Correlation Coefficient, 463

9.4 Partial Correlation, 476

9.5 Multiple Correlation, 480

9.6 Suppression Variable, 483

9.7 Regression Analysis, 485

9.8 The Multiple Regression Model, 510

9.9 Different Ways of Testing a Regression Model, 515

9.10 Law of Diminishing Returns, 523

9.11 Different Approaches in Developing Multiple Regression Models, 524

9.12 Computing with Excel, 528

10 Statistical Tests for Nonparametric Data 556

10.1 Introduction, 556

10.2 Merits and Demerits of Nonparametric Tests, 557

10.3 Chi-Square Test, 557

10.4 Runs Test, 571

10.5 Mann–Whitney U-Test for Two Samples, 577

10.6 Wilcoxon Matched-Pairs Signed-Ranks Test, 584

10.7 Kruskal–Wallis Test (One-Way ANOVA for Nonparametric Data), 589

10.8 The Friedman Test, 593

10.9 Computing with Excel, 599

11 Measuring Associations in Nonparametric Data 615

11.1 Introduction, 615

11.2 Rank Correlation (Measure of Association Between Ranked Data), 616

11.3 Bi-Serial Correlation (Measure of Association Between a Dichotomous and a Continuous Variable), 622

11.4 Point Bi-Serial Correlation (Measure of Correlation Between a True Dichotomous Variable and a Continuous Variable), 624

11.5 Tetrachoric Correlation (Measure of Association Between Dichotomous Variables), 629

11.6 Phi Coefficient (Measure of Association Between Naturally Dichotomous Variables), 636

11.7 Contingency Coefficient (Measure of Association Between Categorical Variables), 640

11.8 Computing with Excel, 646

12 Developing Norms for Assessing Performance 657

12.1 Introduction, 657

12.2 Percentiles, 658

12.3 Z-Scale, 663

12.4 T-Scale, 664

12.5 Stanine Scale, 664

12.6 Composite Scale Based on Z-Score, 666

12.7 Scaling of Ratings in Terms of the Normal Curve, 671

12.8 Developing Norms Based on Difficulty Ratings, 674

12.9 Computing with Excel, 677

Appendix: Statistical Tables 688

Table A.1 Trigonometric Function, 688

Table A.2 Binomial Probability Distribution, 691

Table A.3 Poisson Probability Distribution, 695

Table A.4 The Normal Curve Area Between the Mean and a Given z Value, 700

Table A.5 Ordinates at Different Values of z-Score in the Standard Normal Distribution, 701

Table A.6 Standard Scores (or Deviates) and Ordinates Corresponding to Divisions of the Area under the Normal Curve into a Larger Proportion (B) and a Smaller Proportion (C), 704

Table A.7 Critical Values of “t”, 707

Table A.8 Critical Values of the Correlation Coefficient, 708

Table A.9 F-Table: Critical Values = 0.05, 709

Table A.10 F-Table: Critical Values = 0.01, 710

Table A.11 The Chi-square Table, 711

Table A.12 Critical Values for Number of Runs R, 712

Table A.13 Critical Values for the Mann–Whitney U-Test, 713

Table A.14 Critical Values of T for the Wilcoxon Matched-pairs Signed-ranks Test (Small Samples), 713

Table A.15 Critical Values of Studentized Range Distribution(q) for Familywise = .05, 714

Index 717