Fundamental Concepts In Inferential Fundamental concepts in inferential statistics 1 2. Descriptive

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  • Fundamental Concepts In Inferential Statistics1

  • ___Published by European Centre for Research Training and Development UK (www.eajournals.org)

    BRIEF CONTENTS

    1. Fundamental concepts in inferential statistics 1

    2. Descriptive statistics 52

    3. Comparison of two means with z-test and t-test 117

    4. Comparison of means with analysis of variance (ANOVA) 164

    5. Comparison of means with two-way analysis of variance 199

    6. Hypothesis testing with analysis of covariance 229

    7. Correlation 247

    8. Simple regression 284

    9. Information and communication technology in data analyses: SPSS in action 300

    10. Correlation and regression analyses, using SPSS 354

    11. Execution of ANOVA, two-way ANOVA and ANCOVA

    with SPSS 398

    12. Nonparametric statistics with SPSS 433

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    DETAILED CONTENTS

    CHAPTER 1: FUNDAMENTAL CONCEPTS IN INFERENTIAL STATISTICS

    Inferential Statistics 1

    Population 4

    Sample 5

    Qualities of a good sample 6

    Merits of sampling 7

    Nature of population elements: 7

    Cost reduction: 8

    Accuracy of results: 8

    Data collection speed: 8

    Sampling Techniques 8

    Probability sampling techniques 9

    Simple Random Sampling Technique 9

    Example of Simple Random Sampling 10

    Stratified Random Sampling Technique 10

    Advantages of stratified random sampling 11

    Systematic Sampling Technique 12

    Cluster Random Sampling Technique 13

    Nonprobability Sampling Procedures 14

    Convenience Sampling Technique 15

    Purposive Judgment Sampling 15

    Purposive Quota Sampling 16

    Sample Size Suitability 16

    Hypothesis 21

    Uses of Hypothesis in Research 22

    Characteristics of Hypothesis 26

    Types of Hypothesis 30

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    The Research Hypothesis 30

    The Null Hypothesis 31

    Steps for Testing Hypothesis 33

    Level of Significance 34

    Decision Errors 37

    Type I Error 39

    Type II Error 40

    Balancing of Type I error and Type II error 41

    Central Limit Theorem 42

    The Normal Curve 45

    One-Tailed and Two-Tailed Tests 47

    One-Tailed Test of Significance 48

    Two-Tailed Test of Significance 49

    CHAPTER 2: DESCRIPTIVE STATISTICS

    Scales of Measurement 53

    Nominal Scale 53

    Ordinal Scale 54

    Interval Scale 55

    Ratio Scale 56

    Organization of Research Data 57

    Grouped frequency distribution 61

    Organization of Nominal Scale Data 63

    Graphic Presentation of Data 70

    Histogram 71

    Frequency polygon 72

    Cumulative frequency curve 74

    Characteristics of Distribution 75

    Normal Curve 75

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    Positively Skewed Curve 75

    Negatively Skewed Curve 76

    Leptokurtic Curve 77

    Platykurtic Curve 77

    Bimodal Curve 78

    Pie Chart 79

    Bar Chart 80

    Measures of Central Tendency 81

    The Mean 82

    Midpoint Method of Finding Mean 83

    Assumed Mean Method of Finding Mean 84

    The Mode 86

    The Median 86

    Measures of Variability 89

    Standard Deviation 91

    Raw Scores Method 91

    Deviation from the Mean Method 95

    Grouped Frequency Distribution Method 98

    Variance 99

    Range 102

    Semi-Interquartile Range 103

    Measures of Relative Position 106

    The Z-score 107

    T-Score 108

    Stanine Scores 111

    Percentile Ranks 113

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    CHAPTER 3: COMPARISON OF TWO MEANS WITH Z-TEST AND T-TEST

    Distribution of means 117

    The Z-Test for Difference Between One Sample Mean And 117

    Population Mean When the Population Standard Deviation Is Known 121

    The T-Test for Difference between One Sample Mean and

    Population Mean When the Population Standard Deviation is Unknown 125

    The T-Test for Difference Between Means from Two Independent

    Samples 131

    Corrected Sum of Squares Method for Computation of Two

    Independent Samples T-Test 138

    Unbiased Variance Method for Computation of Two Independent

    Samples T-Test 140

    Summary of Results for Research Articles 143

    The Z-Test for Difference Between Two Independent Samples 144

    The T-Test for Dependent Samples 150

    Difference Scores Standard Deviation Method 152

    Direct Difference Scores Method 156

    Standard Error of the Difference Between Two Dependent Means Method 158

    CHAPTER 4: COMPARISON OF MEANS WITH ANALYSIS OF VARIANCE

    (ANOVA)

    Assumptions that Underlie ANOVA 165

    Normal Distribution of the Population 165

    Independence of Observations 165

    Homoscedasticity 166

    Example of ANOVA for Hypothesis Testing 166

    Raw-Scores Method of ANOVA Computation 168

    The F-Ratio 168

    Mean square 168

    Degrees of freedom 169

    Sources of variation 170

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    Summary of ANOVA Equations 172

    Sources of variation 173

    Degrees of freedom 174

    Mean squares 175

    The F-ratio 175

    Summary of ANOVA Results 175

    Deviation from Grand Mean Method of Computing ANOVA 177

    The F-ratio 177

    Mean squares 177

    Degrees of freedom 178

    Sources of variation 178

    Degrees of freedom 181

    Mean squares 181

    The F-ratio 182

    Multiple Comparisons 183

    Post Hoc or a Posteriori Tests 183

    Fisher’s Protected T-Tests (ť) 184

    Fisher’s LSD 185

    Application of Fisher’s LSD: 189

    Scheffé’s Test (Fs) 190

    Tukey’s HSD (q) 196

    CHAPTER 5: COMPARISON OF MEANS WITH TWO-WAY ANALYSIS OF

    VARIANCE

    Advantages of Two-Way ANOVA 199

    Greater generalizability of results 200

    Determination of Interaction Effect 200

    Two-way ANOVA is more economical 201

    Example of Two-Way ANOVA for Hypothesis Testing 201

    Raw-Scores Method of Computing Two-Way ANOVA 204

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    The F ratios in two-way ANOVA 204

    Mean squares in two-way ANOVA 206

    Degrees of freedom in two-way ANOVA 208

    Sources of variation in two-way ANOVA 208

    Summary of two-way ANOVA equations 212

    Calculation of Sources of Variation in Two-Way ANOVA with

    Raw-Scores Method 213

    Calculation of degrees of freedom in Two-Way ANOVA 216

    Calculation of Two-way ANOVA Mean Squares 216

    Calculation of F ratios in two-way ANOVA 217

    Deviation from Grand Mean Method of Calculating Two-Way ANOVA 220

    The F ratios 221

    Sources of variation 221

    The mean squares 222

    Degrees of freedom 223

    CHAPTER 6: HYPOTHESIS TESTING WITH ANALYSIS OF COVARIANCE

    Uses of Analysis of Covariance 229

    Determination of change 230

    Elimination of nuisance variables effects 230

    ANCOVA reduces the error term 230

    ANCOVA adjusts the group means 231

    ANCOVA uses randomization 231

    Assumptions that Underlie ANCOVA 232

    Valid and reliable measurement of the covariate 232

    Linearity of the dependent variable and covariate relationship

    Homogeneity of regression 233

    Example of Analysis of Covariance 233

    The F ratio of ANCOVA 23