Statistics for Exercise Science and Health with Microsoft Office Excel

Delivers the statistical skill set for a solid foundation for research work and data analysis in exercise science and health   Featuring an introduction to the basic concepts of statistics, Statistics for Exercise Science and Health with Microsoft(R) Office Excel(R) serves as an excellent guide to the use of Excel in exercise science and health related research. The author begins with simplified concepts and subsequently builds into a more complex approach. This structure allows readers from disciplines outside of statistics to follow the chapters in a sequential order, while facilitating an in depth understanding of the intricacies of the various concepts discussed. The book’s approach aides readers in the analysis of their own data by combining the presented statistical techniques with the use of Excel. Coverage includes a comprehensive treatment of hypothesis testing, regression models, and binomial and Poisson distributions as well as: • Chapter–by–chapter Excel tutorials to enhance reader competency in data analysis and experimental designs • Multiple examples, practice exercises, case studies, and illustrations to demonstrate the presented concepts and analytical techniques • Key definitions and formulas throughout for easy reference within the text • Select solutions at the end of the chapters to reinforce reader understanding Statistics for Exercise Science and Health with Microsoft(R) Office Excel(R) is an ideal textbook for graduate and PhD–level courses in exercise, sport, and health sciences including sports psychology, sports kinesiology, sports management, sports biomechanics, health education, and nutrition. The book is also recommended as a reference for professionals and scientists in physical education, sports, and allied disciplines.

Chapter 1: Scope of Statistics in Exercise Science and Health Preface Introduction Basic Concepts of Statistics What Statistics Does? Statistical Processes Descriptive Process Comparative Process Relationship Process Inferential Process Predictive Process Need of Statistics To understand the literature To fabricate the research problems To develop scientific temper To assess the authenticity of research findings and to contradict the unjustifiable claims To develop the indices on various characteristics and performances To develop norms on various traits To conduct research Statistics in Exercise Science and Health Check your progress Computing with Excel Installing Analysis ToolPak Formatting Cell Entries in Excel Initiating Computation with Excel Important Definitions Key Terms Exercise Answers Check your progress References Chapter 2: Understanding Nature of Data Introduction Important Terminologies Raw scores Single scores Variable and attribute Independent and Dependent Variable Continuous and Discrete Variable Measurement of Data Nominal Level Ordinal Level Interval Level Ratio Level Parametric and Non–parametric Statistics Frequency distribution Assumptions in Calculating the Statistics from the Grouped Data Summation Notation Double Summation Triple Summation Measures of central tendency The Mean Mean for Raw Data Mean for Grouped data Mean for Grouped data using Deviation method Properties of Mean Effect of change of Origin and Scale on mean The Median Median for ungrouped data Median for Grouped Data Properties of Median The Mode Mode for Ungrouped Data Mode for Grouped Data Properties of mode Limitations of Mode Comparison of the Mean, Median and Mode Check your progress Practice Exercise Measures of Variability The Range The Quartile Deviation Quartile Deviation for Ungrouped Data Quartile Deviation for Grouped Data Properties of quartile deviation Drawbacks of quartile deviation The Mean Deviation Mean Deviation for Raw Data Mean Deviation for Grouped Data Properties of mean deviation Drawbacks of mean deviation The Standard Deviation Standard Deviation for Ungrouped Data Standard Deviation for Grouped Data Effect of change of origin and scale on standard deviation Properties of standard deviation Grouping Error Variance Standard Error Coefficient of Variation Absolute and Relative Variability Box–and–Whisker Plot Skewness Percentiles Check your progress Practice Exercise Computing with Excel Computing Descriptive Statistics With Excel Key terms Important definitions Important formulas Chapter Exercises Answers Check your progress Chapter Exercise Chapter 3: Working with Graph Introduction Guidelines for constructing the graph Defining X–Y Axis Take Origin as Zero Use Single Vertical Scale Deciding the Scale Unit Plotting the Data Labeling the Graph Highlighting the Lines Bar Diagram Histogram Frequency polygon Frequency curve Cumulative frequency curve Ogive Pie diagram Stem and leaf plot Check your progress Practice Exercise Computing with Excel Constructing Histogram for Understanding Distribution of the Data Key terms Important definitions Important formulas Chapter Exercise Answers Check your progress Chapter Exercise Chapter 4: Probability and its Application Introduction Application of Probability Set Theory Set Null Set Complement Subset Operations on Sets Union Intersection Difference Algebra of Sets Terminologies used in Probability Experiment Sample Space Event Elementary Events Exhaustive cases Trial Equally Likely Events Mutually Exclusive Events Independent Events Factorial Combination Check your progress Practice Exercise Basic Definitions of Probability Classical Definition of Probability Empirical Definition of Probability Subjective Definition of Probability Axiomatic Definition of Probability Some Results on Probability Computing Probability Types of Probability Marginal Probability Union Probability Joint Probability Conditional Probability Theorems of Probability Law of Addition of Probabilities Law of Multiplication of Probability Conditional Probability Bayes’ Theorem Check your progress Practice Exercise Computing with Excel Finding the probability Key terms Important definitions Important formulas Chapter Exercise Answers Check your progress Practice Exercise Chapter Exercise Chapter 5: Statistical Distributions and their Application Introduction Importance of Statistical Distribution Terminologies used in Statistical Distribution Random Variable Discrete Random Variable Continuous Random Variable Probability Distribution Function Properties of Probability Distribution Function Probability Density Function Properties of Probability Density Function Binomial Experiment Expectation Mean and variance of discrete distributions Mean and variance of continuous distributions Check your progress Discrete Distribution Binomial Distribution Mean and Standard Deviation of the Binomial distribution Solving problems using Binomial tables Poisson distribution Mean and Standard Deviation of the Poisson distribution Solving problems using Poisson tables Check your progress Practice Exercise Continuous Distribution Normal Distribution Family of Normal Curve Characteristics of Normal Curve Standard Normal Distribution Standard Score Normal Approximation to the Binomial Distribution Testing normality of the data Skewness Kurtosis Test for normality Normal Q–Q plot for normality The Central Limit Theorem Solving problems based on normal distribution How to use standard normal area table Check your progress Chapter Exercise Uses of Normal Distribution Computing with Excel Finding the probability Important formulas Important Definitions Chapter Exercises Answers Check your progress Practice Exercise References Chapter 6: Sampling and Sampling Distribution Introduction Population and sample Parameter and Statistics Sampling Frame Sampling Advantages of sampling Census Probability and Non Probability Sampling Probability Sampling Simple Random Sampling Lottery method Random number table method Computer generated method Features of simple random sampling Stratified random Sampling Features of stratified random sampling Systematic Sampling Features of stratified random sampling Cluster Sampling Features of stratified random sampling Multistage sampling Features of Multistage Sampling Check your progress Non Probability Sampling Sequential sampling Features of Sequential Sampling Convenience Sampling Consecutive Sampling Quota Sampling Purposive Sampling Snowball Sampling When to use the probability sampling When to use the non probability sampling Characteristics of good sample Sources of Data Primary data Secondary Data Methods of data collection Observation method Interview method Questionnaire methods Experimental method Biases in data collection Biases due to procedure Biases due to sampling Sampling error Non sampling errors Sampling Distribution Central Limit Theorem Standard Error Sampling Distribution of sample mean Sampling Distribution of Proportion Check your progress Criteria in deciding sample size Cost Factor Accuracy factor Practice Exercise Computing with Excel Finding random sample using Excel Important Definitions Important formulas Chapter Exercises Answers Check your progress Practice Exercise References Chapter 7: Statistical Inference for decision making in Exercise Science and Health Introduction Theory of Estimation Point estimation Characteristics of a good Estimator Unbiasedness Consistency Efficiency Sufficiency The t distribution Interval estimation Factors that Affects the Confidence Interval Confidence Intervals for Population Mean Confidence Intervals for Population Proportion Check your progress Practice Exercise Testing of Hypothesis Types of Hypothesis Null hypothesis Alternative hypothesis Test Statistic Concept Used in Hypothesis Testing Type I and Type II error Level of Significance Power of the test Rejection region and Critical value The p–value One tailed and two tailed test Degrees of freedom Strategy in selecting test statistic Steps in Hypothesis Testing Finding critical value in z test Finding critical value in t test Testing with p–value One sample testing Test of Significance about a population mean With the z Test (σ known) Test of Significance about a population mean With the t test (σ unknown) Test of Significance about a proportion Test of Significance about a variance Two samples testing Test of Significance About The Difference in Two Means: With z–Test for two Independent Samples (σ 1 and σ 2 Known) Test of Significance About The Difference in Two Means: With t–Test (σ 1 and σ 2 Unknown) Case I: Two sample t–test for Independent Samples Case II: Paired t–test for two dependent sample Test of Significance About two Population Proportions Test of Significance About two Population Variances Check your progress Practice Exercise Computing with Excel Using Excel in comparing group Means z–Test for Comparing the Means of two Samples t–Test for comparing two independent samples Paired t–test for two dependent samples Important Definitions Important formulas Chapter Exercise Answers Check your progress Practice Exercise Chapter Exercise Chapter 8: Analysis of Variance and Designing Research Experiments Introduction Understanding Analysis of Variance Design of Experiment One way Analysis of Variance One–way ANOVA Model Procedure in One–Way ANOVA Post hoc Tests LSD Test Tukey HSD Test Scheffe’s Test Assumptions in one–way ANOVA Using multiple t–tests instead of one way ANOVA Completely Randomized Design Example of one–way ANOVA For Solving Completely Randomized Design Check your progress Practice Exercise Two–way Analysis of Variance (n observations per cell) Advantages of two–way ANOVA Terminologies used in Two–Way ANOVA Factors Treatment conditions Main effect Simple Effect Interaction effect Two–way ANOVA model Procedure in two–way ANOVA Assumptions in two way Analysis of Variance Two–way Analysis of Variance (one observation per cell) Two–way ANOVA model Procedure in two–way ANOVA(one observation per cell) Randomized Block Design Example of Two–way ANOVA with One Observation Per Cell For Solving Randomized Block Design Practice Exercise Factorial Design Example of Two–way ANOVA with n Observations per Cell For Solving Factorial Design Analysis of Covariance Steps in the analysis of Covariance Check your progress Practice Exercise Computing with Excel Solving Experimental designs with Excel Solving Completely Randomized Design(One way ANOVA) Solving Randomized Block Design(Two–way ANOVA with 1 observation per cell) Solving Factorial Design(Two–way ANOVA with n observation per cell) Important Definitions Important formulas Chapter Exercise Answers Check your progress Practice Exercise Chapter Exercise Reference Chapter 9: Understanding Relationships and Developing Regression Models Introduction Types of relationship Correlation Coefficient Testing the significance of correlation coefficient Interpreting correlation coefficient Application of correlation coefficient Effect of change of origin and scale on the correlation coefficient Limitations of the correlation coefficient Check your progress Practice Exercise Partial correlation General Formula for Partial Correlation Limitations of Partial Correlation Utilities of Partial Correlation Multiple correlation Suppression Variable Check your progress Practice Exercise Regression Analysis Simple Regression Analysis Alternate formula of intercept and slope Computing intercept and slope in a simple regression analysis Analyzing the residuals Residual Plot Testing assumptions in the regression model Standard error of estimate Testing the significance of slope Testing the significance of model Coefficient of Determination (R 2 ) Check your progress Practice Exercise The Multiple Regression model Procedure of developing the regression equation with two independent variables Developing a Multiple Regression Model Standardized regression coefficients Different ways of testing a regression model Testing the significance of overall model Testing the significance of regression coefficients Analyzing the residuals Standard Error of the Estimate The coefficient of determination(R 2 ) Adjusted R 2 Testing the significance of R 2 Law of Diminishing Return Different approaches in developing multiple regression model Stepwise Regression Forward Regression Backward Regression Enter method Check your progress Practice Exercise Computing with Excel Computing Correlation Matrix in Excel Regression Analysis with Excel Important Definitions Important formulas Chapter Exercise Answers Check your progress Practice Exercise Chapter Exercise Reference Chapter 10: Statistical Tests for Non Parametric Data Introduction Merits and demerits of Non parametric tests Chi–square Test Application of Chi–square test Assumptions in Chi–Square test Testing Goodness of Fit Test for Independence of Attributes Yates Correction Additive Property of Chi–Square Check your progress Runs Test Test Statistic Critical value Decision rule Large Sample size Check your progress Practice Exercise Mann–Whitney U test for two Samples Test Statistic Critical value Decision rule Large Sample size Wilcoxon Match–Pairs Signed Ranks Test Test Statistic Critical value Decision rule Large Sample size Kruskal Wallis Test (One–Way ANOVA for Non–Parametric Data) Test Statistic Critical value Decision rule The Friedman test Test Statistic Critical value Decision rule Check your progress Practice Exercise Computing with Excel Computing Chi Square with Excel Important definitions Important Formulas Chapter Exercise Answers Check your progress Practice exercise Chapter Exercise Bibliography Chapter 11: Measuring Associations in non parametric data Introduction Rank Correlation: Measure of association between ranked data Assumptions Testing significance Merits and demerits Bi–serial Correlation: measure of association between dichotomous and continuous variable Assumptions Testing significance Merits and demerits Point Bi–serial Correlation: measure of correlation between true dichotomous and continuous variable Testing significance Check your progress Tetrachoric correlation: measure of association between dichotomous variables Assumptions Testing significance Merits and demerits Phi Coefficient: measure of association between naturally dichotomous variables Assumptions Testing significance Merits and demerits Contingency coefficient: measure of association between any categorical variables Merits and demerits Check your progress Practice exercise Computing with Excel Computing Rank Correlation with Excel Important definitions Important formulas Chapter Exercise Answers Check your progress Practice exercise Chapter Exercise References Chapter 12: Developing Norms For Assessing Performance Introduction Percentiles Merits and Demerits of the Percentile Scale Percentile Rank Z–scale Merits and Demerits of Z Scale T–scale Stanine Scale Composite Scale Based on Z–Score Conditions for using Z–score Check your progress Practice Exercise Scaling of Ratings in Terms of Normal Curve Developing Norms Based Upon Difficulty Ratings Computing with Excel Computing Z and T scores with Excel Important Definitions Important formulas Chapter Exercise Answers Check your progress Practice exercise Chapter Exercise Appendix: Tables Table A.1: Trigonometric functions Table A.2: Binomial Probability Distribution Table A.3:Poisson Probability Distribution Table A.4:Normal curve area table Table A.5: Ordinates of the distribution of normal deviate Table A.6:Standard scores and ordinates corresponding to divisions of the area under the normal curve into a larger proportion (B) and a smaller proportion (C) Table A.7:Critical values of t–distribution Table A.8: Critical values of the correlation coefficient Table A.9: Critical values of F–distribution at .05 level of significance Table A.10:Critical values of F–distribution at .01 level of significance Table A.11:Critical Values of Chi–square distribution Table A.12:Critical Values of R in the Runs test Table A.13: Critical Values of U in Mann–Whitney Test Table A.14:Critical value of T for the Wilcoxon matched–pairs signed–ranks test (Small Samples)

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.