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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
This book introduces the use of statistics to solve a variety of problems in exercise science and health and provides readers with a solid foundation for future research and data analysis. Statistics for Exercise Science and Health with Microsoft Office Excel: * Aids readers in analyzing their own data using the presented statistical techniques combined with Excel * Features comprehensive coverage of hypothesis testing and regression models to facilitate modeling in sports science * Utilizes Excel to enhance reader competency in data analysis and experimental designs * Includes coverage of both binomial and poison distributions with applications in exercise science and health * Provides solved examples and plentiful practice exercises throughout in addition to case studies to illustrate the discussed analytical techniques * Contains all needed definitions and formulas to aid readers in understanding different statistical concepts and developing the needed skills to solve research problems
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
Chapter 1: Scope of Statistics in Exercise Science and Health
1.1 Introduction
1.2 Understanding Statistics
1.3 What Statistics Does?
1.4 Statistical Processes
1.5 Need for Statistics
1.6
Statistics in Exercise Science
and Health
Check Your Progress
1.7 Computing With Excel
Important Definitions
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 2: Understanding the Nature of Data
2.1 Introduction
2.2 Important Terminologies
2.3 Measurement of Data
2.4 Parametric and Nonparametric Statistics
2.5 Frequency Distribution
2.6 Summation Notation
2.7 Measures of Central Tendency
2.8 Comparison of the Mean, Median, and Mode
Check Your Progress
Practice Exercise
2.9 Measures of Variability
2.10 Standard Error
2.11 Coefficient of Variation
2.12 Absolute and Relative Variability
2.13 Box-And-Whisker Plot
2.14 Skewness
2.15 Percentiles
Check Your Progress
Practice Exercise
2.16 Computing With Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 3: Working with Graphs
3.1 Introduction
3.2 Guidelines for Constructing a Graph
3.3 Bar Diagram
3.4 Histogram
3.5 Frequency Polygon
3.6 Frequency Curve
3.7 Cumulative Frequency Curve
3.8 Ogive
3.9 Pie Diagram
3.10 Stem and Leaf Plot
Check Your Progress
Practice Exercise
3.11 Computing With Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 4: Probability and its Application
4.1 Introduction
4.2 Application of Probability
4.3 Set Theory
4.4 Terminologies Used in Probability
Check Your Progress
Practice Exercise
4.5 Basic Definitions of Probability
4.6 Some Results on Probability
4.7 Computing Probability
4.8 Types of Probability
4.9 Theorems of Probability
Check Your Progress
Practice Exercise
4.10 Computing with Excel
Important Definitions
Important formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 5: Statistical Distributions and their Application
5.1 Introduction
5.2 Terminologies used in Statistical Distribution
Check Your Progress
5.3 Discrete Distribution
5.4 Binomial Distribution
5.5 Poisson Distribution
Check Your Progress
Practice Exercise
5.6 Continuous Distribution
5.7 Normal Distribution
5.8 Standard Score
5.9 Normal Approximation to the Binomial Distribution
5.10
Testing Normality
of the Data
5.11 The Central Limit Theorem
5.12 Solving Problems Based on Normal Distribution
Check Your Progress
Practice Exercise
5.13 Uses of Normal Distribution
5.14 Computing with Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 6: Sampling and Sampling Distribution
6.1 Introduction
6.2 Population and Sample
6.3 Parameter and Statistics
6.4 Sampling Frame
6.5 Sampling
6.6 Census
6.7 Probability and Nonprobability Sampling
6.8 Probability Sampling
Check Your Progress
6.9 Nonprobability Sampling
6.10 When to Use Probability Sampling
6.11 When to Use Nonprobability Sampling
6.12 Characteristics of a Good Sample
6.13 Sources of Data
6.14 Methods of Data Collection
6.15 Biases in Data Collection
6.16 Sampling Error
6.17 Nonsampling Errors
6.18 Sampling Distribution
Check Your Progress
6.19 Criteria in Deciding Sample Size
Practice Exercise
6.20 Computing with Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 7: Statistical Inference for Decision-Making in Exercise Science and Health
7.1 Introduction
7.2 Theory of Estimation
7.3 Point Estimation
7.4 Characteristics of a Good Estimator
7.5 The -Distribution
7.6 Interval Estimation
Check Your Progress
Practice Exercise
7.7 Testing of Hypothesis
7.8 Types of Hypothesis
7.9 Test Statistic
7.10 Concept used in Hypothesis Testing
7.11
Type I and Type II Errors
7.12 Level of Significance
7.13 Power of the Test
7.14 Rejection Region and Critical Value
7.15
p
-Value
7.16 One-Tailed and Two-Tailed Tests
7.17 Degrees of Freedom
7.18 Strategy in Selecting the Test Statistic
7.19 Steps in Hypothesis Testing
7.20 One-Sample Testing
7.21 Two-Sample Testing
7.22 Test of Significance about Two Population Proportions
7.23 Test of Significance about Two Population Variances
Check Your Progress
Practice Exercise
7.24 Computing with Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 8: Analysis of Variance And Designing Research Experiments
8.1 Introduction
8.2 Understanding Analysis of Variance
8.3 Design of Experiment
8.4 One-way Analysis of Variance
8.5 Completely Randomized Design
Check Your Progress
Practice Exercise
8.6 Two-Way Analysis of Variance (
N
Observations Per Cell)
8.7 Two-Way Analysis of Variance (One Observation Per Cell)
8.8 Randomized Block Design
Practice Exercise
8.9 Factorial Design
8.10 Analysis of Covariance
Check Your Progress
Practice Exercise
8.11 Computing With Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 9: Understanding Relationships and Developing Regression Models
9.1 Introduction
9.2 Types of Relationship
9.3 Correlation Coefficient
Check Your Progress
Practice Exercise
9.4 Partial Correlation
9.5 Multiple Correlation
9.6 Suppression Variable
Check Your Progress
Practice Exercise
9.7 Regression Analysis
Check Your Progress
Practice Exercise
9.8 The Multiple Regression Model
9.9 Different Ways of Testing a Regression Model
9.10 Law of Diminishing Returns
9.11 Different Approaches in Developing Multiple Regression Models
Check Your Progress
Practice Exercise
9.12 Computing with Excel
Important Definitions
Important Formulas
Chapter Exercise
Answers
Further Reading
Chapter 10: Statistical Tests for Nonparametric Data
10.1 Introduction
10.2 Merits and Demerits of Nonparametric Tests
10.3 Chi-Square Test
Check Your Progress
10.4
Runs Test
Check Your Progress
Practice Exercise
10.5 Mann–Whitney-Test for Two Samples
10.6 Wilcoxon Matched-Pairs Signed-Ranks Test
10.7 Kruskal–Wallis Test (One-Way ANOVA for Nonparametric Data)
10.8 The
Friedman Test
Check Your Progress
Practice Exercise
10.9 Computing with Excel
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 11: Measuring Associations in Nonparametric Data
11.1 Introduction
11.2 Rank Correlation (Measure of Association Between Ranked Data)
11.3 Bi-Serial Correlation (Measure of Association Between a Dichotomous and a Continuous Variable)
11.4 Point Bi-Serial Correlation (Measure of Correlation Between a True Dichotomous Variable and a Continuous Variable)
Check Your Progress
11.5 Tetrachoric Correlation (Measure of Association Between Dichotomous Variables)
11.6 Phi Coefficient (Measure of Association Between Naturally Dichotomous Variables)
11.7 Contingency Coefficient (Measure of Association Between Categorical Variables)
Check Your Progress
Practice Exercise
11.8 Computing with Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Chapter 12: Developing Norms For Assessing Performance
12.1 Introduction
12.2 Percentiles
12.3
Z
-Scale
12.4
T
-Scale
12.5 Stanine Scale
12.6 Composite Scale Based on
Z
-Score
Check Your Progress
Practice Exercise
12.7 Scaling of Ratings in Terms of the Normal Curve
12.8 Developing Norms Based on Difficulty Ratings
12.9 Computing with Excel
Important Definitions
Important Formulas
Key Terms
Chapter Exercise
Answers
Further Reading
Appendix
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Chapter 1: Scope of Statistics in Exercise Science and Health
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 1.8
Figure 1.9
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 3.12
Figure 3.13
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 5.15
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
Figure 7.15
Figure 7.16
Figure 7.17
Figure 7.18
Figure 7.19
Figure 7.20
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.14
Figure 8.13
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 9.10
Figure 9.11
Figure 9.12
Figure 9.13
Figure 9.14
Figure 9.15
Figure 9.16
Figure 9.17
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 11.1
Figure 11.2
Figure 11.3
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
List of Tables
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 2.5
Table 2.6
Table 2.7
Table 2.8
Table 2.9
Table 2.10
Table 2.11
Table 2.12
Table 2.13
Table 2.14
Table 2.15
Table 2.16
Table 2.17
Table 2.18
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 3.5
Table 3.6
Table 3.7
Table 3.8
Table 5.1
Table 5.2
Table 5.4
Table 5.5
Table 5.6
Table 6.1
Table 6.2
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 7.5
Table 7.6
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 8.5
Table 8.6
Table 8.7
Table 8.8
Table 8.9
Table 8.10
Table 8.11
Table 8.12
Table 8.13
Table 8.14
Table 8.15
Table 8.16
Table 8.17
Table 8.18
Table 8.19
Table 8.20
Table 8.21
Table 8.22
Table 8.23
Table 8.24
Table 8.25
Table 8.26
Table 8.27
Table 8.28
Table 8.29
Table 8.30
Table 8.31
Table 8.32
Table 8.33
Table 8.34
Table 9.1
Table 9.2
Table 9.3
Table 9.4
Table 9.5
Table 9.6
Table 9.7
Table 9.8
Table 9.9
Table 9.10
Table 9.11
Table 9.12
Table 9.13
Table 9.14
Table 9.15
Table 9.16
Table 9.17
Table 9.18
Table 9.19
Table 9.20
Table 9.21
Table 10.1
Table 10.2
Table 10.3
Table 10.4
Table 10.5
Table 10.6
Table 10.7
Table 10.8
Table 10.9
Table 10.10
Table 10.11
Table 10.12
Table 10.13
Table 10.14
Table 10.15
Table 10.16
Table 10.17
Table 10.18
Table 10.18b
Table 11.1
Table 11.2
Table 11.3
Table 11.4
Table 11.5
Table 11.6
Table 11.7
Table 11.8
Table 11.9
Table 11.10
Table 11.11
Table 11.12
Table 11.13
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Table 12.5
Table 12.6
Statistics for Exercise Science and Health with Microsoft Office Excel
J. P. Verma
Centre for Advanced Studies,
Lakshmibai National Institute of Physical Education,
Gwalior, India
Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Verma, J. P., author.
Statistics for exercise science and health with Microsoft Office Excel / J.P. Verma, Centre for Advanced Studies, Lakshmibai National Institute of Physical Education, Gwalior, India.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-85521-8 (hardback)
1. Microsoft Excel (Computer file) 2. Sports sciences. 3. Sports sciences–Statistical methods–
Computer programs. 4. Exercise–Statistical methods. I. Title.
GV741.V47 2014
613.7′1–dc23
2013047834
This book is dedicated to
my mother,
whose loving spirit sustains me still
Preface
Statistics is tough. Statistics is boring. Statistics is dry. These are the preconceived notions of most students about the subject. After considerable experience in my teaching career, I have realized that almost all difficult concepts of statistics can be taught well in a simple manner. This book is primarily meant for students of Exercise Science and Health, as a text book of statistics for their graduate, predoctoral, and doctoral course work. It can be used by students of any of the applied branches of physical education and sports sciences such as sport psychology, sport kinesiology, sport management, sport pedagogy, sport biomechanics, nutrition, and yoga. Since Excel® computing has been discussed in each chapter, this makes the book more useful for all those students who are required to analyze data in their thesis or project.
This book is the result of my experience in teaching statistics for the last three decades at the Lakshmibai National Institute of Physical Education, Gwalior and of my interaction with professionals while conducting workshops in many Indian and foreign universities. Being the only faculty of statistics in India working in the field of physical education and sports, scarcity of study material in statistics in these areas was a hindrance to teaching. This compelled me to produce a much needed text for the students. I strongly believe that if you teach statistics to students of Exercise Science and Health using illustrations from their own domain, they understand it better. Although writing this book took around two years, the contents and concepts included in it have been accrued based on deliberations with my students and research scholars during my entire teaching career.
The purpose of this book is to provide readers with a basic understanding of statistics and to help them in solving a variety of problems in exercise science and health. Besides serving as a textbook for students, this book will also give them a solid foundation for their future research work. One of the main features of this book is that it follows the “simple to complex” approach. Even students with no prior knowledge of statistics can understand the text if they refer its chapters in sequential order.
After writing this book, I think I have become more disciplined in my approach. It was my desire to create a book that students of Exercise Science and Health would love to read, and I worked with the minutest possible detail to enhance the clarity of the topics in each chapter.
As you go through the text, you will find sections such as “Check Your Progress” and “Practice Exercise” that follow the discussion of major topics. There is also an exhaustive list of exercises at the end of each chapter. In order to comprehend the discussed topics and concepts well, students must solve the problems listed in these three sections. This will help them in understanding the intricacies of different concepts discussed in the chapter. The solutions for all the questions in the sections “Check Your Progress,” “Practice Exercise,” and “Chapter Exercise” given at the end of the chapter can be used by students to check the correctness of their answers. For easy reference, all the important definitions and formulas used have been given in each chapter.
Excel computing for most of the statistical techniques discussed in each chapter has been shown by means of different examples. Students should master the statistical techniques discussed in the chapter by manual process first and may verify the results later by using the Excel methods. The Excel facility of statistical computing discussed in different chapters of the text will enable the masters' degree students, PhD scholars, and research personnel to solve their research problems in the area of statistical inference, regression models, research designs, and applied research.
The faculty who uses this as a textbook will find it useful as it presents many illustrative studies with real or simulated realistic data in different chapters to clarify and illustrate the analytical techniques covered in the text. Some of the examples cited in the text are from my own as well as my colleagues' research studies.
This book has been organized in 12 chapters. Each chapter is self-contained and includes enough solved exercises for students to understand the procedure of computation in a systematic manner.
In Chapter 1, students learn what statistics is, how it is useful in research, and its application in exercise science and health. Deliberations are made about the ways in which research data can be analyzed by using different types of statistics. The readers are introduced to Excel computing in this chapter.
Chapter 2 discusses the characteristics of different data types and the procedure for investigating the nature of data. It discusses the situations where one can identify the suitable measure of central tendency and variability for drawing conclusions. For instance, why the median is preferred over the mean in case of skewed data although the mean is the most suitable measure of central tendency in the case of interval or ratio data. A detailed discussion has been made on developing a profile chart, which invariably forms the part of every thesis. This chapter also discusses procedures to compute various descriptive statistics by means of Excel.
In Chapter 3, the procedure for drawing different graphs and charts has been discussed. The stem and leaf diagram has been discussed to understand the distribution of data. Developing histograms with Excel has been shown for understanding the distribution of data.
Chapter 4 discusses the importance of probability in decision making. Computing probability in different situations has been shown by means of many solved examples. One can learn to compute the probability of various events by using Excel functionality if the data are also normally distributed.
In Chapter 5, students are introduced to some very important distributions such as the binomial, Poisson, and normal distributions. Students may learn how to test the normality of data, which is one of the main assumptions in using any of the statistical tests for hypothesis testing.
In Chapter 6, the importance of sampling over population has been discussed at great length. The chapter includes different types of probability and non-probability sampling techniques. Another important feature of this chapter is discussion on the two different considerations for deciding the sample size in conducting research. Students have been shown why the sample mean follows a normal distribution in case of a large sample irrespective of the population distribution.
Chapter 7 discusses statistical inference, which includes the theory of estimation and testing of hypothesis. Different parametric tests such as the z, t, F, and have been discussed in detail. Students are shown why the null hypothesis is rejected if the calculated value of z is greater than its critical value. Using the p-value for testing of hypothesis has been extensively discussed. Besides manual computation by means of examples, the step-by-step procedure of using Excel in computing z, t, and F have been shown as well. This will help the students to analyze their dataset for their thesis work and research articles.
In Chapter 8, the completely randomized design and randomized block design and one factorial experiment have been discussed. The solutions to these designs have been shown by means of the one-way ANOVA, two-way ANOVA with one observation per cell, and two–way ANOVA with n observations per cell. The chapter also includes discussion on the ANCOVA design by means of a solved example. The most important feature of this chapter is that the students can learn to solve these designs by using the Excel functionalities.
Chapter 9 enables the students to understand the relationships among different variables by means of product moment correlation, partial correlation, and multiple correlation. This chapter includes simple and multiple regression. The students can learn to develop a regression model for estimating the criterion variable on the basis of explanatory variables. The chapter also discusses various assumptions in regression analysis and how to test the model as well. The important feature of this chapter is that one can develop the regression model and test its significance as well by using Excel features.
Chapter 10 deals with various types of nonparametric tests for hypothesis testing in a situation where the normality assumption is not satisfied. The researchers can use these tests for testing hypotheses for parametric data also in a situation where assumptions for the parametric tests fail.
In Chapter 11, different types of nonparametric associations have been discussed. Many situations arise in research where such associations are required to be computed.
Finally, Chapter 12 is devoted to the development of norms. A detailed procedure has been discussed for developing a weighted scale for assessing the performance of an individual. This scale can be used in many situations in physical education because human performance improves at a faster rate in the beginning; however, at a higher level, a lot of effort is required for even a slight enhancement in performance. Therefore, a slight improvement at the higher level may be rewarded more by using this weighted scale.
I am indebted to many of my colleagues who have helped me professionally over the years. Particularly, I would like to show my gratitude to Prof. Gupta YP, Prof. Sekhar, Prof. Prasad J, and Prof. Khare D for providing some of the crucial inputs in completing this text. All my research scholars and graduate students deserve special thanks for providing me the food for thought throughout my whole teaching career. Their insightful queries and difficulties in understanding different concepts have helped me to incorporate all those deliberations and solutions in this text.
I am very much thankful to Susanne Steitz-Filler, Senior Editor, John Wiley & Sons, and her team for providing me all the support and encouragement in presenting this book to the audience in its present form. My sincere thanks to Sari Friedman for providing me all the guidance in the publication of this text. She was very prompt and supportive of all my queries during the whole process of publication. At last, I would like to place on record the efforts made by Gowri Vasanth, Project Manager at SPi-Global, and her team in typesetting and editing this book.
I wish to thank my brother, Verma Pankaj, who helped me in resolving certain issues in preparing this manuscript. I must appreciate the effort of my children, Priyam and Prachi, for making available their skill sets and time in helping me to modify the language of the manuscript quite often.
At last, a special mark of appreciation to my wonderful wife, Haripriya, for her patience and good nature in understanding the long hours of work that necessitated my being locked away in my study room at “LNIPE” for endless hours, night after night, and on weekends, working on the manuscript. She is really a remarkable lady.
For each topic, considerable effort has been made to describe each and every step, so that on going through any topic, students can grasp its concept well. I hope that the book will provide students and researchers with a useful material for their course work and research activity. Suggestions and queries from readers are most welcome via email at [email protected]. A timely response to them shall be ensured.
J. P. Verma, PhD
Professor of Statistics
Director, Centre for Advanced Studies
Chapter 1Scope of Statistics in Exercise Science and Health
1.1 Introduction
The use of statistics has become very popular in exercise science and health research because of the availability of many statistical packages. Researchers have begun to use advanced statistical techniques to draw meaningful conclusions. Exercise scientists use statistical techniques to refine their exercise schedule for different categories of people. Using a statistical model helps the researcher to fine-tune his research. The assessment of fitness status is based on the statistical model where different components of health-related fitness are given an appropriate weight to develop a fitness index. By using computer software, the exercise scientists can begin to assess the functional fitness of an individual. Knowledge of statistics empowers research scientists to develop customized fitness prescriptions.
Identification of talent in sports is one of the major thrust areas of research. Knowledge of cause-and-effect relationships provides a scientific basis to develop strategies for talent identification at an early age in different sports. Exercise scientists play an important role in nurturing these young players in different sports. By understanding the nature of different sports, these scientists can develop different exercise programs. By understanding statistical techniques, one can test the appropriateness of the developed schedule. Thus, the use of statistics provides a scientific basis for developing any exercise regimen.
Fitness and health are complementary to each other. Hence, health scientists are always engaged in propagating the need for fitness activities along with proper nutritional intake. The main issue is to identify the optimum level of fitness regimen and the nutritional intake for different categories of people. Such knowledge is created by designing an appropriate research experiment and analyzing its findings. By using advanced statistical techniques, one can understand the fitness status and health deficiency of the people in a particular community. Obesity is a menace; hence, health scientists are always interested in identifying the parameters that cause it in different communities. By using statistical modeling, one can identify the lifestyle parameters that are responsible for the increase in the body mass index (BMI) of individuals.
Statistics plays an important role not only in exercise science and health but also in its applied areas such as physical education, sports biomechanics, sports psychology, and sports sciences. For instance, indices can be developed for assessing different parameters such as flexibility, muscular endurance, and muscular strength by using the regression model. Several researchers have developed a methodology for assessing fat percentage on the basis of a few skin folds or bodily circumference by using statistical techniques. One can also use statistical tests in estimating the accuracy of such an assessment. Similarly, researchers in the area of sports biomechanics can use statistical tools to identify the specific muscles used by high performance players. Sports psychologists can identify the specific psychological traits required for being successful in sports. By using some advanced statistical techniques, one can identify the traits that help an individual win in a particular sport. Sports has become very competitive in nature, and scientists now focus on methods to enhance the performance of the players. The researcher can develop a model for maximizing a sportsman's performance by enhancing other parameters to optimal levels. Thus, it is clear that there is tremendous scope for statistics not only in exercise science and health but also in their applied areas.
1.2 Understanding Statistics
The term statistics is used to denote the data as well as the subject. The important thing is the context in and the purpose for which it is used. This text is about statistics; hence, one should understand its definition first. Statistics can be defined as an applied science that deals with the collection, compilation, analysis, and interpretation of data. It is also considered a branch of mathematics because most of the statistical techniques are based on mathematical concepts and derivations. A main purpose of statistics is to understand the characteristics of a large group of subjects or entities based on a small subset drawn from it. In other words, one wishes to investigate population characteristics on the basis of the sample drawn from it. The meaning of population depends on the context in which it is used. For instance, if it is required to estimate the BMI of people over 40 years of age in a locality, then all those whose age is more than 40 years shall constitute the population. On the other hand, if one wishes to understand the fitness culture in the schools of a state, then all the schools will constitute the population. To know the characteristics of the population, one needs to define some parameters on the basis of which its nature can be understood. Two such parameters that are generally used by researchers are mean μ and standard deviation σ, where μ indicates the central value of the dataset and σ is used for understanding the variation of the data in the population. Owing to the large size of the population and various other reasons (as discussed in Chapter 6), these population parameters μ and σ are estimated by the sample statistics and , respectively. Thus, the term statistics is also used to denote the function of sample observations.
FACTS TO KNOW
Statistics provides authenticity in research findings
Research studies on statistics can be broadly classified into descriptive and inferential. In descriptive studies, researchers gather data on a group of people or organization to understand their characteristics. For instance, collecting data on the height of the players in a tournament can reveal several interesting features. The mean height can reveal what the average athlete's height is, whereas the range can indicate the maximum variation among the athletes' height. The statistics that are used for descriptive studies are usually mean, standard deviation, variance, coefficient of variation, skewness, kurtosis, and so on.
In inferential studies, a researcher uses those statistical techniques on the basis of which a conclusion about the population characteristics can be drawn from the sample data. Consider a situation where it is necessary to know the impact of a weight training program on back strength. A study may be conducted on a randomly drawn sample of athletes. The data so obtained from the sample may be analyzed by using inferential statistics to draw a conclusion, which can be generalized for the population. The most important aspect of any inferential study is to draw the sample randomly, without which the conclusion drawn about the population characteristics cannot be considered to be authentic. Some statistical techniques used for inferential studies are hypothesis testing, correlation, regression analysis, and so on.
1.3 What Statistics Does?
A main advantage of using statistics in analyzing data is that the reliability of findings can be verified. In addition to this, one can also be sure that the results obtained from the experiment are authentic and, hence, more acceptable to the scientific community. There are ways and means by which one can also test the accuracy of the findings. Let us try and understand what statistics does. A teacher conducts a few statistical tests in which the average performances of the students A and B are given by 55 and 58 marks, respectively. Can it be concluded that the student B is better than student A in statistics. For some it may be, and for others it may not be. But if the difference between their performances is 10 in favor of B, then majority of the people would say that B is better than A but still some may think otherwise. To conclude, all these decisions are subjective in nature and lack authenticity. But if these two averages are compared by using the statistical test, the difference of 3 marks in their averages may provide 95% confidence to the researcher to believe that B's performance is better than A. What does “the researcher is 95% confident in favor of B” mean? It simply indicates that if you conduct 100 such tests of statistics, at least 95 times B's performance would be better than A's.
1.4 Statistical Processes
A statistical process can be defined as the type of statistical analysis that is used by the researcher in his research study. Before discussing the different types of statistical techniques, let us first see how many types of statistical processes can be encountered in research, and what are the appropriate statistical techniques used in these processes. Broadly, the research processes can be divided into the following five categories.
1.4.1 Descriptive Process
The descriptive process refers to describing the characteristics of a group of individuals, an organization, or a group of similar entities. In such studies, one describes various characteristics of the subjects under study. These studies not only provide interesting information but also help in decision-making. Findings in the descriptive studies may at times provide new topics for research and investigation. The statistics that are used in descriptive studies are known as descriptive statistics. Such statistics are the mean, standard deviation, coefficient of variation, range, skewness, kurtosis, and so on. There are many situations in which descriptive studies may be undertaken. For instance, one may take up a study to prepare a profile of Indian wrestlers. In this case, statistics such as the mean, range, standard deviation, skewness, and kurtosis of different parameters such as height, weight, total body fat, endurance, flexibility, and strength may be computed to understand the different characteristics of Indian wrestlers. Another example of a descriptive study can be the case study of any particular celebrity in sports. In such a case, different descriptive statistics are calculated on the data obtained from the same subject at different points of time.
1.4.2 Comparative Process
All those studies where the researcher is interested in comparing two or more groups come under this category. Often there is interest in comparing the effect of two training programs, the anxiety levels among male and female players, or the IQ of high and low performers in sports. Such studies can be categorized as the comparative process. The statistics that are used in comparative studies are known as comparative statistics. Such statistics are Z, t, F, and chi-square. In comparing more than two groups, analysis of variance is used to analyze the data.
1.4.3 Relationship Process
In the relationship process, the researcher is usually more interested in exploring the relationships among different parameters. For instance, one may be interested in the relationship between the leg length, reaction time, and leg strength with that of the 100 m performance. Similarly, one may like to determine the relationship between the fat percentage and age with cardio respiratory endurance. In such studies, the relationship statistics such as correlation coefficient, partial correlation, and multiple correlation are used to investigate the relationship.
FACTS TO KNOW
In the inferential process the phenomenon that is investigated exists but is unknown, whereas in the predictive process the phenomenon is not known and nor does it exists as well.
1.4.4 Inferential Process
In the inferential process, a conclusion about the population characteristics is drawn on the basis of the information from a sample. Techniques such as statistical estimation and testing of hypothesis are used to draw inferences about the population characteristics. Studies such as estimating students' IQ in a college on the basis of a sample of students, or comparing the agility of gymnasts and basketball players on the basis of two samples obtained from the college gymnasts and basketball players, come under the inferential process. Statistical techniques such as point estimation; interval estimation; s, t, F, and Z tests; and analysis of variance are used to analyze the data in such studies.
1.4.5 Predictive Process
The predictive process is used in studies where we try to predict a future event on the basis of the information from a sample. There is a difference between the inferential process and the predictive process. In the predictive process, a phenomenon that does not exist as of now is predicted on the basis of the information from a sample. On the other hand, in the inferential process, a phenomenon about the population that exists but is not known is estimated on the basis of the information from a sample. Consider a study in which it is of interest to know whether a particular student would qualify in a competitive examination on the basis of his mathematical ability, reasoning ability, and IQ scores. In such a study, the predictive process is used because the happening of the event, that is, the result of the competitive examination, is not known at the time of predicton. Statistical techniques such as regression analysis, logistic regression, and discriminant analysis are used to analyze the data in such situations.
1.5 Need for Statistics
The following are reasons why students should take a course in statistics and develop mastery of this subject.
1.5.1 To Understand Research Literature
One cannot read much of the literature in research journals without encountering statistical concepts, methods, and techniques. Without understanding the concepts and fundamentals of statistics, it becomes difficult to interpret the findings mentioned in research articles, as a result of which one loses interest in research activities and is discouraged from undertaking research problems.
1.5.2 To Construct a Research Problem
There is a huge difference between abstract thinking and rational thinking. A researcher is required to convert an abstract thought into a feasible research study. This requires knowledge of various statistical designs without which it becomes impossible to frame an experimental study. Further, knowledge of advance statistical techniques gives insight to the researcher in developing the hypotheses for investigation in the study. In the absence of knowledge about various statistical techniques, it is just not possible to develop a meaningful research study.
1.5.3 To Develop a Scientific Temper
Using statistics in decision-making helps an individual to inculcate scientific temper. A scientific temper is required at each and every step in life. It helps an individual to think rationally in any situation. For instance, during a match, a player's decision for any move is based purely upon his earlier experience. A coach plans the training schedule for his trainee on the basis of his previous experience. While taking a shot, the batsman always calculates the risk on the basis of his scientific judgment. Thus, the development of a scientific temper helps an individual to take decisions rationally all the time.
1.5.4 To Assess the Authenticity of Research Findings and to Contradict Unjustifiable Claims
Several researchers publicly announce findings based on their research work. In order to assess the authenticity of their statements, one can read their research report. But to satisfy oneself about the conformity between their statements and the actual fact, one should be able to understand the statistical techniques used in the report. Many companies make a claim about their product by using the research findings of their scientists. These claims may be tested by conducting an experiment under controlled conditions and analyzing the data. For example, if a fitness lab announces that their oral tablets reduce 10 lbs weight in 15 days, this claim may be tested by actually conducting an experiment. Normally while making such claims, companies hide certain facts that are required to justify their claims. For instance, they may not reveal for which age group and weight category the finding is true. Thus, knowledge of designing an experiment and various statistical techniques are essential to write-off the unjustifiable claims.
FACTS TO KNOW
Learning statistics sharpens your faculties and helps in developing a good research problem
1.5.5 To Develop Indices for Various Characteristics and Performances
Certain concepts in exercise science cannot be directly measured. For instance, to measure the body strength there is no single test. Instead, one may test arm strength, back strength, leg strength, and shoulder strength separately. One may develop a single index for body strength by giving appropriate weight to these components. Similarly, an index can be prepared to measure the flexibility, health-related fitness, or endurance of an individual. To develop such indices, some advanced statistical techniques such as regression analysis and factor analysis can be used. Thus, knowledge of these techniques equips the researcher to take up such studies in exercise science and health.
1.5.6 To Develop Norms on Various Traits
Norms on different test items provide motivation to an individual. In developing norms for parameters such as sit-ups, pull-ups, push-ups, and so on in different age and sex categories, performance of these parameters needs to be converted into a score by using a scale ranging from 0 to 100. Such norms are easily understood by a lay man and can be used as a selection criteria for certain courses and programs. The norms for the test items are developed by assuming normality of the data. In a situation when the data is not normal, a certain transformation is used before using different scaling techniques. Statistical techniques such as percentile scale, T-scale, and weighted scale are used to develop such norms. Thus, the knowledge of these techniques will equip the researcher to take up normative studies for developing norms for different physical, physiological, and psychological traits in people of different age and sex categories.
1.5.7 To Conduct Research
An important reason to understand the concepts of statistics and learn advanced statistical techniques is to equip an individual for research. The knowledge of sampling techniques allows the researcher to select a representative sample that represents the population. Similarly, knowledge of the different statistical designs helps researchers to choose an appropriate methodology for the experiment and identify the proper statistical test to analyze the data. Thus, it is extremely important to have appropriate knowledge of statistical concepts, methods, and techniques to conduct research in an efficient manner and to draw valid conclusions.
1.6 Statistics in Exercise Science and Health
No academic discipline can grow without advancement in research; this is true for exercise science and health as well. One of the important dimensions of research is the design of the experiment. Proper statistical design used in a study helps the researcher to isolate the factors responsible for the performance in any event. Further, using appropriate statistical design reduces overall error in the experiment, giving more reliable conclusions. New techniques in different sports can be tested against the existing technique for better results by using an appropriate statistical technique. For instance, in comparing the effectiveness of three different warm-up exercises on a 400 m performance, one may plan a completely randomized design where the subjects may be randomly assigned to three different warm-up exercises. One-way analysis of the variance technique can be used to identify the best warm-up program for the 400 m event. Similar experiments can help to determine the best duration of the warm-up program for the 100 m event. Thus, the development of new techniques and strategies in sports is the result of research experiments conducted over a period of time.
Different statistical techniques are used to solve varieties of research problems in exercise science. For instance, development of test batteries for measuring the concept of motor fitness, athletic fitness, general fitness, and specific fitness in different sports requires factor analysis technique to solve the problem. Similarly, norms construction requires identification of the appropriate scaling procedure. Further, if a coach is interested in the extent of relationships between performance and independent parameters, partial correlation may be used whereas multiple correlation allows him to find the reliability in estimating the performance on the basis of certain known characteristics. To find the optimum training load for different levels of athletes, the experiment can be planned by using the proper statistical design.
To measure qualitative characteristics such as competitive anxiety, attitude toward sports, knowledge of health education, and self concept, questionnaires can be developed. These questionnaires are developed using statistical techniques such as item analysis including difficulty rating and index of discrimination along with the reliability analysis. Further, keys may be developed by using statistical techniques such as factor analysis. Most of the statistical techniques mentioned in this chapter are discussed in detail in different chapters of the book. Thus, we see that any advancement in exercise science and health is not possible without statistical aids.
Every academic discipline has different research requirements; exercise science and health too demand separate attention from a statistical point of view. To give specific focus to the problems in this area this book has been titled Statistics for Exercise Science and Health with Microsoft® Office Excel®.
Check Your Progress
Note: Tick the correct answer by using the sign (√ )
True
False
1.
Statistics is the function of population values
–
–
2.
t
-statistics is used for testing of hypothesis
–
–
3.
Population is an aggregate of all the items
–
–
4.
Statistics can be used to denote the distribution used in the analysis of data
–
–
5.
If the sample is not random, population characteristics cannot be estimated from the statistics computed from sample observations
–
–
6.
Inferential statistics is used for drawing conclusions about population characteristics
–
–
7.
Descriptive statistics describes population characteristics
–
–
8.
The mean
μ
and standard deviation
σ
are known as population statistics
–
–
9.
Statistics describes sample characteristics
–
–
10.
The mean,
, and sample standard deviation,
s
, are known as sample statistics
–
–
11.
Statistics provides scientific explanation to research findings
–
–
12.
The statistics
t
,
F
, and
Z
are known as comparative statistics
–
–
13.
Multiple correlation is a predictive statistics
–
–
1.7 Computing With Excel
1.7.1 Installing Analysis ToolPak
While using Excel for analyzing data you must check that the Add-ins “Analysis ToolPak” is already installed in your Excel. Without its installation, you cannot use the functionality discussed in various chapters of this book. Follow the steps given while installing this ToolPak in your Excel:
After starting the Excel in your system, click the sequence of commands.
Office
button
Excel Options
Add-Ins
While clicking these commands, you will see the following screens in sequence as shown in Figure 1.1(a–c).
Figure 1.1 (a–c) Sequence of commands in installing Analysis ToolPak.
Figure 1.2 (a,b) Options for installing Analysis ToolPak.
After clicking the
OK
in
Figure 1.1
(c) you will get the screen as shown in
Figure 1.2
(a). By scrolling choose the option
Analysis ToolPak
and then select the option
Excel Add-Ins
. Click
OK
to get the screen as shown in
Figure 1.2
(b). Select the
Analysis ToolPak
and then click
OK
to get it installed.
Restart the Excel to use the functionality of Analysis ToolPak.
1.7.2 Formatting Cell Entries in Excel
Most of the time when you compute various statistics using Excel, it shows you long scores in fraction such as 1.087811258, 3.43996124, 11.83333333, and −0.716014396. This disturbs the whole formatting. You can format the cell entries by the following command sequence. Let us consider the following output generated in Excel while computing descriptive statistics as shown in Figure 1.3.
Figure 1.3 Dataset in the column B which is required to be formatted.
Let us see how scores in the second column as shown in Figure 1.3 can be formatted.
Select the second column by clicking the mouse on the column label B and right click the mouse to get the option Format Cells as shown in Figure 1.4
Figure 1.4 Choosing the option for formatting data.
Clicking the option Format Cells in Figure 1.4 will take you to Figure 1.5 to decide on the number of decimal places in your output. Select 2 or anything else as per your requirement. Let other options be selected by default. Click OK to get your desired formatted output as shown in Figure 1.6.
Figure 1.5 Choosing the option for deciding decimal places and other specifications.
Figure 1.6 Final output in a formatted form.
After choosing the option in Figure 1.5, the final output looks like what is shown in Figure 1.6.
1.7.3 Initiating Computation with Excel
Excel can be used for simple as well as advanced computing. One must understand its basics to exploit its full potential. The following example will make you learn how to add, subtract, multiply, divide, and compute mathematical expressions.
Example 1.1
Following are the data on height (cms), weight (lbs), and arm length (cms) obtained on male athletes in a college.
Height (
X
)
185
190
188
180
178
172
168
Weight (
Y
)
189
165
169
178
184
169
167
Arm length (
Z
)
82
84
81
83
79
80
78
Compute the following:
X
+
Y
+
Z
X
−
Y
X
×
Y
,
, and
,
Solution
Computing
X
+
Y
+
Z
To find the value of this expression, do the following:
Type the formula
= (
A
2+
B
2+
C
2)
in the cell
E
2 as shown in
Figure 1.7
(a).
A
2,
B
2, and
C
2 are the cell addresses of the first athlete's data on the three variables
X
,
Y
, and
Z
, respectively.
Click Enter key after the command to get the first subject's data on three variables added in the
E
2 location as shown in
Figure 1.7
(b). Kindly note that unless the = sign is typed, Excel will not understand this as a formula.
Drag the black dot located in the right corner at the bottom of the cell
E
2 downward to compute the expression for other subjects as shown in
Figure 1.7
(c).
