Preface xi
Foreword to Students xv
1 Introduction 1
1.1 What Do we Mean by Statistics? 1
1.2 Why Is Statistics Necessary? 1
1.3 The Limitations of Statistics 2
1.4 Performing Statistical Calculations 2
1.5 The Purpose of this Text 2
2 Health Care Investigations: Measurement and Sampling Concepts 5
2.1 Introduction 5
2.2 Populations, Samples and Observations 5
2.3 Counting Things – The Sampling Unit 6
2.4 Sampling Strategy 6
2.5 Target and Study Populations 7
2.6 Sample Designs 7
2.7 Simple Random Sampling 8
2.8 Systematic Sampling 9
2.9 Stratified Sampling 9
2.10 Quota Sampling 10
2.11 Cluster Sampling 11
2.12 Sampling Designs – Summary 11
2.13 Statistics and Parameters 11
2.14 Descriptive and Inferential Statistics 12
2.15 Parametric and Non-Parametric Statistics 12
3 Processing Data 13
3.1 Scales of Measurement 13
3.2 The Nominal Scale 13
3.3 The Ordinal Scale 14
3.4 The Interval Scale 14
3.5 The Ratio Scale 15
3.6 Conversion of Interval Observations to an Ordinal Scale 15
3.7 Derived Variables 16
3.8 Logarithms 17
3.9 The Precision of Observations 18
3.10 How Precise Should We Be? 19
3.11 The Frequency Table 19
3.12 Aggregating Frequency Classes 21
3.13 Frequency Distribution of Count Observations 23
3.14 Bivariate Data 23
4 Presenting Data 25
4.1 Introduction 25
4.2 Dot Plot or Line Plot 25
4.3 Bar Graph 26
4.4 Histogram 28
4.5 Frequency Polygon and Frequency Curve 29
4.6 Centiles and Growth Charts 29
4.7 Scattergram 32
4.8 Circle or Pie Graph 32
5 Clinical Trials 35
5.1 Introduction 35
5.2 The Nature of Clinical Trials 35
5.3 Clinical Trial Designs 36
5.4 Psychological Effects and Blind Trials 37
5.5 Historical Controls 38
5.6 Ethical Issues 38
5.7 Case Study: Leicestershire Electroconvulsive Therapy Study 38
5.8 Summary 40
6 Introduction to Epidemiology 41
6.1 Introduction 41
6.2 Measuring Disease 42
6.3 Study Designs – Cohort Studies 43
6.4 Study Designs – Case-Control Studies 45
6.5 Cohort or Case-Control Study? 46
6.6 Choice of Comparison Group 46
6.7 Confounding 47
6.8 Summary 48
7 Measuring the Average 49
7.1 What Is an Average? 49
7.2 The Mean 49
7.3 Calculating the Mean of Grouped Data 51
7.4 The Median – A Resistant Statistic 52
7.5 The Median of a Frequency Distribution 53
7.6 The Mode 54
7.7 Relationship between Mean, Median and Mode 55
8 Measuring Variability 57
8.1 Variability 57
8.2 The Range 57
8.3 The Standard Deviation 58
8.4 Calculating the Standard Deviation 59
8.5 Calculating the Standard Deviation from Grouped Data 60
8.6 Variance 61
8.7 An Alternative Formula for Calculating the Variance and Standard Deviation 61
8.8 Degrees of Freedom 62
8.9 The Coefficient of Variation 63
9 Probability and the Normal Curve 65
9.1 The Meaning of Probability 65
9.2 Compound Probabilities 66
9.3 Critical Probability 67
9.4 Probability Distribution 68
9.5 The Normal Curve 69
9.6 Some Properties of the Normal Curve 70
9.7 Standardizing the Normal Curve 71
9.8 Two-Tailed or One-Tailed? 72
9.9 Small Samples: The t-Distribution 74
9.10 Are our Data Normally Distributed? 75
9.11 Dealing with ‘Non-normal’ Data 77
10 How Good Are our Estimates? 81
10.1 Sampling Error 81
10.2 The Distribution of a Sample Mean 81
10.3 The Confidence Interval of a Mean of a Large Sample 83
10.4 The Confidence Interval of a Mean of a Small Sample 85
10.5 The Difference between the Means of Two Large Samples 86
10.6 The Difference between the Means of Two Small Samples 88
10.7 Estimating a Proportion 89
10.8 The Finite Population Correction 90
11 The Basis of Statistical Testing 91
11.1 Introduction 91
11.2 The Experimental Hypothesis 91
11.3 The Statistical Hypothesis 92
11.4 Test Statistics 93
11.5 One-Tailed and Two-Tailed Tests 93
11.6 Hypothesis Testing and the Normal Curve 94
11.7 Type 1 and Type 2 Errors 95
11.8 Parametric and Non-parametric Statistics: Some Further Observations 96
11.9 The Power of a Test 97
12 Analysing Frequencies 99
12.1 The Chi-Square Test 99
12.2 Calculating the Test Statistic 99
12.3 A Practical Example of a Test for Homogeneous Frequencies 102
12.4 One Degree of Freedom – Yates’ Correction 103
12.5 Goodness of Fit Tests 104
12.6 The Contingency Table – Tests for Association 105
12.7 The ‘Rows by Columns’ (r × c) Contingency Table 108
12.8 Larger Contingency Tables 109
12.9 Advice on Analysing Frequencies 111
13 Measuring Correlations 113
13.1 The Meaning of Correlation 113
13.2 Investigating Correlation 113
13.3 The Strength and Significance of a Correlation 115
13.4 The Product Moment Correlation Coefficient 116
13.5 The Coefficient of Determination r2 118
13.6 The Spearman Rank Correlation Coefficient rs 118
13.7 Advice on Measuring Correlations 120
14 Regression Analysis 121
14.1 Introduction 121
14.2 Gradients and Triangles 121
14.3 Dependent and Independent Variables 122
14.4 A Perfect Rectilinear Relationship 123
14.5 The Line of Least Squares 125
14.6 Simple Linear Regression 126
14.7 Fitting the Regression Line to the Scattergram 128
14.8 Regression for Estimation 128
14.9 The Coefficient of Determination in Regression 129
14.10 Dealing with Curved Relationships 129
14.11 How Can We ‘Straighten Up’ Curved Relationships? 132
14.12 Advice on Using Regression Analysis 133
15 Comparing Averages 135
15.1 Introduction 135
15.2 Matched and Unmatched Observations 136
15.3 The Mann–Whitney U-Test for Unmatched Samples 136
15.4 Advice on Using the Mann–Whitney U-Test 137
15.5 More than Two Samples – The Kruskal–Wallis Test 138
15.6 Advice on Using the Kruskal–Wallis Test 140
15.7 The Wilcoxon Test for Matched Pairs 140
15.8 Advice on Using the Wilcoxon Test for Matched Pairs 143
15.9 Comparing Means – Parametric Tests 143
15.10 The z-Test for Comparing the Means of Two Large Samples 144
15.11 The t-Test for Comparing the Means of Two Small Samples 145
15.12 The t-Test for Matched Pairs 146
15.13 Advice on Comparing Means 147
16 Analysis of Variance – ANOVA 149
16.1 Why Do We Need ANOVA? 149
16.2 How ANOVA Works 149
16.3 Procedure for Computing ANOVA 151
16.4 The Tukey Test 154
16.5 Further Applications of ANOVA 155
16.6 Advice on Using ANOVA 157
Appendices
Appendix A: Table of Random Numbers 159
Appendix B: t-Distribution 160
Appendix C: χ2-Distribution 162
Appendix D: Critical Values of Spearman’s Rank Correlation Coefficient 164
Appendix E: Critical Values of the Product Moment Correlation Coefficient 166
Appendix F: Mann–Whitney U-test Values (Two-Tailed Test) P =0.05 169
Appendix G: Critical Values of T in the Wilcoxon Test for Matched Pairs 170
Appendix H: F-Distribution 173
Appendix I: Tukey Test 178
Appendix J: Symbols 180
Appendix K: Leicestershire ECT Study Data: Subgroup with Depressive Illness 183
Appendix L: How Large Should Our Samples Be? 187
Bibliography 193
Index 195
