Statistics for Exercise Science and Health with Microsoft Office Excel

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 alpha = 0.05, 709 Table A.10 F-Table: Critical Values alpha = 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 alpha = .05, 714 Index 717