Sports Research with Analytical Solution using SPSS
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Preface xv
About the Companion Website xviii
Acknowledgments xix
1 Introduction to Data Types and SPSS Operations 1
1.1 Introduction 1
1.2 Types of data 2
1.2.1 Qualitative Data 2
1.2.2 Quantitative Data 3
1.3 Important definitions 4
1.3.1 Variable 4
1.4 Data Cleaning 4
1.5 Detection of Errors 5
1.5.1 Using Frequencies 5
1.5.2 Using Mean and Standard Deviation 5
1.5.3 Logic Checks 5
1.5.4 Outlier Detection 5
1.6 How to Start Spss? 6
1.6.1 Preparing Data File 7
1.7 Exercise 10
1.7.1 Short Answer Questions 10
1.7.2 Multiple Choice Questions 11
2 Descriptive Profile 14
2.1 Introduction 14
2.2 Explanation of Various Descriptive Statistics 16
2.2.1 Mean 16
2.2.2 Variance 16
2.2.3 Standard Error of Mean 17
2.2.4 Skewness 17
2.2.5 Kurtosis 18
2.2.6 Percentiles 19
2.3 Application of Descriptive Statistics 19
2.3.1 Testing Normality of Data and Identifying Outliers 20
2.4 Computation of Descriptive Statistics Using Spss 25
2.4.1 Preparation of Data File 25
2.4.2 Defining Variables 26
2.4.3 Entering Data 26
2.4.4 SPSS Commands 26
2.5 Interpretations of the Results 29
2.6 Developing Profile Chart 31
2.7 Summary of Spss Commands 33
2.8 Exercise 33
2.8.1 Short Answer Questions 33
2.8.2 Multiple Choice Questions 34
2.9 Case Study on Descriptive Analysis 36
3 Correlation Coefficient and Partial Correlation 41
3.1 Introduction 41
3.2 Correlation Matrix and Partial Correlation 43
3.2.1 Product Moment Correlation Coefficient 43
3.2.2 Partial Correlation 45
3.3 Application of Correlation Matrix and Partial Correlation 46
3.4 Correlation Matrix with Spss 46
3.4.1 Computation in Correlation Matrix 46
3.4.2 Interpretations of Findings 51
3.5 Partial Correlation with Spss 51
3.5.1 Computation of Partial Correlations 52
3.5.2 Interpretation of Partial Correlation 55
3.6 Summary of the Spss Commands 56
3.6.1 For Computing Correlation Matrix 56
3.6.2 For Computing Partial Correlations 57
3.7 Exercise 57
3.7.1 Short Answer Questions 57
3.7.2 Multiple Choice Questions 57
3.7.3 Assignment 60
3.8 Case Study on Correlation 60
4 Comparing Means 65
4.1 Introduction 65
4.2 One-Sample t-Test 66
4.2.1 Application of One-Sample t-Test 67
4.3 Two-Sample t-Test for Unrelated Groups 67
4.3.1 Assumptions While Using t-Test 67
4.3.2 Case I: Two-Tailed Test 68
4.3.3 Case II: Right Tailed Test 68
4.3.4 Case III: Left Tailed Test 69
4.3.5 Application of Two-Sample t-Test 70
4.4 Paired t-Test for Related Groups 70
4.4.1 Case I: Two-Tailed Test 71
4.4.2 Case II: Right Tailed Test 71
4.4.3 Case III: Left Tailed Test 72
4.4.4 Application of Paired t-Test 73
4.5 One-Sample t-Test with Spss 73
4.5.1 Computation in t-Test for Single Group 74
4.5.2 Interpretation of Findings 77
4.6 Two-Sample t-Test for Independent Groups with Spss 78
4.6.1 Computation in Two-Sample t-Test 79
4.6.2 Interpretation of Findings 83
4.7 Paired t-Test for Related Groups with Spss 85
4.7.1 Computation in Paired t-Test 86
4.7.2 Interpretation of Findings 89
4.8 Summary of Spss Commands for t-Tests 90
4.8.1 One-Sample t-Test 90
4.8.2 Two-Sample t-Test for Independent Groups 90
4.8.3 Paired t-Test 91
4.9 Exercise 91
4.9.1 Short Answer Questions 91
4.9.2 Multiple Choice Questions 91
4.9.3 Assignment 93
4.10 Case Study 94
5 Independent Measures Anova 100
5.1 Introduction 101
5.2 One-Way Analysis of Variance 101
5.2.1 One-Way ANOVA Model 102
5.2.2 Post Hoc Test 102
5.2.3 Application of One-Way ANOVA 103
5.3 One-Way Anova with Spss (Equal Sample Size) 103
5.3.1 Computation in One-Way ANOVA (Equal Sample Size) 104
5.3.2 Interpretation of Findings 107
5.4 One-Way Anova with Spss (Unequal Sample Size) 110
5.4.1 Computation in One-Way ANOVA (Unequal Sample Size) 111
5.4.2 Interpretation of Findings 114
5.5 Two-Way Analysis of Variance 115
5.5.1 Assumptions in Two-Way Analysis of Variance 116
5.5.2 Hypotheses in Two-Way ANOVA 116
5.5.3 Factors 117
5.5.4 Treatment Groups 117
5.5.5 Main Effect 117
5.5.6 Interaction Effect 117
5.5.7 Within-Groups Variation 117
5.5.8 F-Statistic 117
5.5.9 Two-Way ANOVA Table 118
5.5.10 Interpretation 118
5.5.11 Application of Two-Way Analysis of Variance 118
5.6 Two-Way Anova Using Spss 119
5.6.1 Computation in Two-Way ANOVA 121
5.6.2 Interpretation of Findings 126
5.7 Summary of the Spss Commands 137
5.7.1 One-Way ANOVA 137
5.7.2 Two-Way ANOVA 138
5.8 Exercise 138
5.8.1 Short Answer Questions 138
5.8.2 Multiple Choice Questions 139
5.8.3 Assignment 142
5.9 Case Study on One-Way Anova Design 143
5.10 Case Study on Two-Way Anova 147
6 Repeated Measures Anova 153
6.1 Introduction 153
6.2 One-Way Repeated Measures Anova 154
6.2.1 Assumptions in One-Way Repeated Measures ANOVA 155
6.2.2 Application in Sports Research 155
6.2.3 Steps in Solving One-Way Repeated Measures ANOVA 156
6.3 One-Way Repeated Measures Anova Using Spss 157
6.3.1 Computation in the One-Way Repeated Measures ANOVA 157
6.3.2 Interpretation of Findings 161
6.3.3 Findings of the Study 165
6.3.4 Inference 166
6.4 Two-Way Repeated Measures Anova 166
6.4.1 Assumptions in Two-Way Repeated Measures ANOVA 166
6.4.2 Application in Sports Research 167
6.4.3 Steps in Solving Two-Way Repeated Measures ANOVA 167
6.5 Two-Way Repeated Measures Anova Using Spss 168
6.5.1 Computation in Two-Way Repeated Measures ANOVA 170
6.5.2 Interpretation of Findings 173
6.5.3 Findings of the Study 181
6.5.4 Inference 181
6.6 Summary of the Spss Commands for One-Way Repeated Measures Anova 182
6.7 Summary of the Spss Commands for Two-Way Repeated Measures Anova 182
6.8 Exercise 183
6.8.1 Short Answer Questions 183
6.8.2 Multiple Choice Questions 183
6.8.3 Assignment 185
6.9 Case Study on Repeated Measures Design 186
7 Analysis of Covariance 190
7.1 Introduction 190
7.2 Conceptual Framework of Analysis of Covariance 191
7.3 Application of ANCOVA 192
7.4 ANCOVA with Spss 193
7.4.1 Computation in ANCOVA 194
7.5 Summary of the Spss Commands 201
7.6 Exercise 202
7.6.1 Short Answer Questions 202
7.6.2 Multiple Choice Questions 202
7.6.3 Assignment 203
7.7 Case Study on ANCOVA Design 204
8 Nonparametric Tests in Sports Research 209
8.1 Introduction 209
8.2 Chi-Square Test 211
8.2.1 Testing Goodness of Fit 211
8.2.2 Yates' Correction 212
8.2.3 Contingency Coefficient 212
8.3 Goodness of Fit with Spss 212
8.3.1 Computation in Goodness of Fit 213
8.3.2 Interpretation of Findings 216
8.4 Testing Independence of Two Attributes 216
8.4.1 Interpretation 218
8.5 Testing Association with Spss 219
8.5.1 Computation in Chi-Square 219
8.5.2 Interpretation of Findings 223
8.6 Mann-Whitney U Test: Comparing Two Independent Samples 224
8.6.1 Computation in Mann-Whitney U Statistic Using SPSS 224
8.6.2 Interpretation of Findings 226
8.7 Wilcoxon Signed-Rank Test: For Comparing Two Related Groups 227
8.7.1 Computation in Wilcoxon Signed-Rank Test Using SPSS 228
8.7.2 Interpretation of Findings 230
8.8 Kruskal-Wallis Test 231
8.8.1 Computation in Kruskal-Wallis Test Using SPSS 232
8.8.2 Interpretation of Findings 234
8.9 Friedman Test 234
8.9.1 Computation in Friedman Test Using SPSS 235
8.9.2 Interpretation of Findings 237
8.10 Summary of the Spss Commands 237
8.10.1 Computing Chi-Square Statistic (for Testing Goodness of Fit) 237
8.10.2 Computing Chi-Square Statistic (for Testing Independence) 238
8.10.3 Computation in Mann-Whitney U Test 238
8.10.4 Computation in Wilcoxon Signed-Rank Test 239
8.10.5 Computation in Kruskal-Wallis Test 239
8.10.6 Computation in Friedman Test 239
8.11 Exercise 240
8.11.1 Short Answer Questions 240
8.11.2 Multiple Choice Questions 241
8.11.3 Assignment 243
8.12 Case Study on Testing Independence of Attributes 243
9 Regression Analysis and Multiple Correlations 246
9.1 Introduction 246
9.2 Understanding Regression Equation 247
9.2.1 Methods of Regression Analysis 247
9.2.2 Multiple Correlation 248
9.3 Application of Regression Analysis 248
9.4 Multiple Regression Analysis with Spss 249
9.4.1 Computation in Regression Analysis 249
9.4.2 Interpretation of Findings 254
9.5 Summary of Spss Commands for Regression Analysis 259
9.6 Exercise 259
9.6.1 Short Answer Questions 259
9.6.2 Multiple Choice Questions 260
9.6.3 Assignment 261
9.7 Case Study on Regression Analysis 263
10 Application of Discriminant Function Analysis 267
10.1 Introduction 268
10.2 Basics of Discriminant Function Analysis 268
10.2.1 Discriminating Variables 268
10.2.2 Dependent Variable 268
10.2.3 Discriminant Function 268
10.2.4 Classification Matrix 269
10.2.5 Stepwise Method of Discriminant Analysis 269
10.2.6 Power of Discriminating Variable 269
10.2.7 Canonical Correlation 269
10.2.8 Wilks' Lambda 270
10.3 Assumptions in Discriminant Analysis 270
10.4 Why to Use Discriminant Analysis 270
10.5 Steps in Discriminant Analysis 271
10.6 Application of Discriminant Function Analysis 272
10.7 Discriminant Analysis Using Spss 274
10.7.1 Computation in Discriminant Analysis 274
10.7.2 Interpretation of Findings 279
10.8 Summary of the Spss Commands for Discriminant Analysis 284
10.9 Exercise 284
10.9.1 Short Answer Questions 284
10.9.2 Multiple Choice Questions 285
10.9.3 Assignment 286
10.10 Case Study on Discriminant Analysis 288
11 Logistic Regression for Developing Logit Model in Sport 293
11.1 Introduction 293
11.2 Understanding Logistic Regression 294
11.3 Application of Logistic Regression in Sports Research 295
11.4 Assumptions in Logistic Regression 297
11.5 Steps in Developing Logistic Model 297
11.6 Logistic Analysis Using Spss 297
11.6.1 Block 0 299
11.6.2 Block 1 299
11.6.3 Computation in Logistic Regression with SPSS 299
11.7 Interpretation of Findings 304
11.7.1 Case Processing and Coding Summary 304
11.7.2 Analyzing Logistic Models 305
11.8 Summary of the Spss Commands for Logistic Regression 310
11.9 Exercise 310
11.9.1 Short Answer Questions 310
11.9.2 Multiple Choice Questions 311
11.9.3 Assignment 312
11.10 Case Study on Logistic Regression 313
12 Application of Factor Analysis 319
12.1 Introduction 319
12.2 Terminologies Used in Factor Analysis 320
12.2.1 Principal Component Analysis 320
12.2.2 Eigenvalue 320
12.2.3 Kaiser Criterion 321
12.2.4 The Scree Test 321
12.2.5 Communality 321
12.2.6 Factor Loading 322
12.2.7 Varimax Rotation 322
12.3 Assumptions in Factor Analysis 322
12.4 Steps in Factor Analysis 323
12.5 Application of Factor Analysis 323
12.6 Factor Analysis with Spss 324
12.6.1 Computation in Factor Analysis Using SPSS 326
12.7 Summary of the Spss Commands for Factor Analysis 336
12.8 Exercise 336
12.8.1 Short Answer Questions 336
12.8.2 Multiple Choice Questions 337
12.8.3 Assignment 338
12.9 Case Study on Factor Analysis 339
Appendix 346
Bibliography 360
Index 368
1
INTRODUCTION TO DATA TYPES AND SPSS OPERATIONS
LEARNING OBJECTIVES
After completing this chapter, you should be able to do the following:
- Understand different data types generated in research
- Learn the nature of variables
- Know various data cleaning methods
- Learn to install SPSS package in computer
- Prepare data file in SPSS
1.1 INTRODUCTION
Due to large stake involved in sports, research in this area is gaining momentum in different universities of the world. Even developing countries have started introducing sports sciences in different universities. The sole purpose is to create specific knowledge required for enhancing sports performance. Everyday, enormous data is being generated in the area of sports all over the world, which can be used to draw meaningful conclusions. Scientists have started organizing experiments by taking athletes as subjects. It is therefore required to support these scientists with analytical skill set to carry out their business. Since they deal with the data, it is essential that they are aware of its nature. Depending upon the data types, one identifies the relevant analytical technique for addressing research issues. Sports research can broadly be classified into two categories: descriptive and analytical. In descriptive research, the nature of dataset is investigated from different perspectives. Several statistics like mean, standard deviation, coefficient of variation, skewness, kurtosis, and percentiles are used to describe the characteristics of the dataset. Many interesting facts about the population can be investigated by using these descriptive statistics. Analytical research broadly follows two approach: exploratory and confirmatory. In explorative research, focus is on discovering the hidden relationships. It is done by hypothesis testing, data modeling, and using multivariate analysis. On the other hand, in confirmatory studies, some of the facts are either confirmed or denied on the basis of hypothesis testing.
Numerous statistical techniques are available to the researchers for analyzing their research data. Selection of an appropriate technique depends upon the research questions being investigated in the study. Due to complexities of different analytical solutions in sports research, one needs to use some user-friendly software package. This chapter will acquaint you with different types of data that are generated in sports research and some of the widely used statistical techniques by the research scholars to solve them for answering different research questions by using the most popular IBM SPSS Statistics package.
1.2 TYPES OF DATA
It is essential to know the types of data generated in research studies because choosing statistical test for analyzing data depends upon its type. Data can be classified into two categories: metric and nonmetric. Metric data is analyzed by using parametric tests such as t, F, Z, correlation coefficient, etc., whereas nonparametric tests such as Wilcoxon signed-ranked, Chi-square, Mann-Whitney U, and Kruskal Wallis are used to analyze nonmetric data.
Parametric tests are more reliable than the nonparametric, but to use such tests certain assumptions must be satisfied. On the other hand, nonparametric tests are more flexible, easy to use, and not many assumptions are required to use them.
Nonmetric and metric data are also known as qualitative and quantitative data, respectively. Nonmetric data is further classified into nominal and ordinal. On the other hand, metric data is classified into interval and ratio. These classification is based on the level of measurements. The details of these four types of data have been discussed under two categories: qualitative data and quantitative data.
1.2.1 Qualitative Data
Qualitative data is a categorical measurement and is expressed not in terms of numbers, rather by means of a natural language description. It is often known as "categorical" data. For instance, smoking habit = "smoker" and gender = "male" are the examples of categorical data. These data can be measured on two different scales: nominal and ordinal.
1.2.1.1 Nominal Scale
Variables measured on this scale are known as categorical variables. Categorical variables result from a selection of categories. Examples might be response (agree, disagree), sports specialization, race, religion, etc. If in a class 30 subjects are male and 20 are female, no gradation is possible. In other words, 30 do not indicate that the males are better than the female in some sense.
1.2.1.2 Ordinal Scale
Variables that are assessed on the ordinal scale are also known as categorical variables, but here the categories are ordered. Such variables are also called "ordinal variables." Categorical variables that assess performance (good, average, poor, etc.) are ordinal variables. Similarly, the variables that measure attitude (strongly agree, agree, undecided, disagree, and strongly disagree) are also ordinal variables. On the basis of the order of these variables, we may not know the magnitude of the measured phenomenon of an individual, but we can always grade them. For instance, if A's playing ability in soccer is good and B's is average, we can always conclude that the A is better than B, but how much is not known. Moreover, the distance between the ordered categories is also not same and measurable.
1.2.2 Quantitative Data
Quantitative data is a numerical measurement expressed in terms of numbers. It is not necessary that all numbers are continuous and measurable. For instance, the roll number is a number, but not something that one can add or subtract. Quantitative data are always associated with a scale measure. These data can be measured on two different types of scales: interval and ratio.
1.2.2.1 Interval Scale
The interval scale is a quantitative measure. It also has an equidistant measure. But the doubling principle breaks down in this scale. The 4 marks given to an individual for his creativity do not explain that his nature is twice as good as the person with 2 marks. This is so because on this scale zero cannot be exactly located. Thus, variables measured on an interval scale have values in which differences are uniform, but ratios are not.
1.2.2.2 Ratio Scale
The data on ratio scale has a meaningful zero value and has an equidistant measure (i.e., the difference between 30 and 40 is the same as the difference between 60 and 70). For example, 60 marks obtained in a test is twice that of 30. This is so because zero exists in the ratio scale. Height is another ratio scale quantitative measure. Observations that are counted or measured are ratio data (e.g., number of goals, runs, height, and weight).
1.3 IMPORTANT DEFINITIONS
1.3.1 Variable
A variable is a phenomenon that changes from time to time, place to place, and individual to individual. It can be numeric or attribute. Numeric variable can further be classified into discrete and continuous. Discrete variable is a numeric variable that assumes value from a limited set of numbers and is always represented in whole number. Examples of such variables are number of goals, runs scored in cricket, scores in basketball match, etc. Continuous variable is also a numeric variable, but it can take any value within a range and is usually represented in fraction. Examples of such variables are height, weight, and timings.
On the other hand, an attribute is a qualitative variable that takes sub-values of a variable, such as "male" and "female," "student" and "teacher," etc. An attribute is said to be mutually exclusive if its sub-values do not occur at the same time. For instance, gender is a mutually exclusive variable because it can take value either "male" or "female" but not both. Similarly in a survey, a person can choose only one option from a list of alternatives (as opposed to selecting as many that might apply).
1.3.1.1 Independent Variable
An independent variable can be defined as the one that can be manipulated by a researcher. In planning a research experiment to see the effect of different intensities of exercise on the performance, exercise intensity is an independent variable because the researcher is free to manipulate it.
1.3.1.2 Dependent Variable
A variable is said to be dependent if it changes as a result of the change in the independent variable. In the previous example, performance is a dependent variable because it is affected by the change in exercise intensity. In fact dependent variable can be defined as the variable of interest. In creating the graph, the dependent variable is taken along the Y-axis, whereas the independent variable is plotted on the X-axis.
1.3.1.3 Extraneous Variable
Any additional variable that may provide alternative explanation or create some doubt on the conclusions in an experimental study is known as extraneous variable. If the effect of three different teaching methods on the performance is to be compared, IQ of the subjects may be considered as an extraneous variable as it might affect the final outcomes in the experiment, if IQ of all the groups are not equal...
