Practical Statistics for Nursing and Health Care

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