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 3

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 7

2.5 Target and study populations 8

2.6 Sample designs 8

2.7 Simple random sampling 9

2.8 Systematic sampling 9

2.9 Stratified sampling 10

2.10 Quota sampling 11

2.11 Cluster sampling 12

2.12 Sampling designs – summary 12

2.13 Statistics and parameters 13

2.14 Descriptive and inferential statistics 13

2.15 Parametric and non-parametric statistics 14

3 PROCESSING DATA 15

3.1 Scales of measurement 15

3.2 The nominal scale 15

3.3 The ordinal scale 16

3.4 The interval scale 17

3.5 The ratio scale 17

3.6 Conversion of interval observations to an ordinal scale 17

3.7 Derived variables 19

3.8 Logarithms 20

3.9 The precision of observations 21

3.10 How precise should we be? 22

3.11 The frequency table 22

3.12 Aggregating frequency classes 24

3.13 Frequency distribution of count observations 26

3.14 Bivariate data 27

4 PRESENTING DATA 29

4.1 Introduction 29

4.2 Dot plot or line plot 29

4.3 Bar graph 30

4.4 Histogram 32

4.5 Frequency polygon and frequency curve 33

4.5 Centiles and growth charts 35

4.7 Scattergram 35

4.8 Circle or pie graph 35

5 CLINICAL TRIALS 39

5.1 Introduction 39

5.2 The nature of clinical trials 39

5.3 Clinical trial designs 40

5.4 Psychological effects and blind trials 41

5.5 Historical controls 42

5.6 Ethical issues 43

5.7 Case study: Leicestershire Electroconvulsive Therapy (ECT) study 43

5.8 Summary 45

6 INTRODUCTION TO EPIDEMIOLOGY 47

6.1 Introduction 47

6.2 Measuring disease 48

6.3 Study designs – cohort studies 50

6.4 Study designs – case-control studies 51

6.5 Cohort or case-control study? 53

6.6 Choice of comparison group 54

6.7 Confounding 55

6.8 Summary 56

7 MEASURING THE AVERAGE 57

7.1 What is an average? 57

7.2 The mean 57

7.3 Calculating the mean of grouped data 59

7.4 The median – a resistant statistic 60

7.5 The median of a frequency distribution 61

7.6 The mode 62

7.7 Relationship between mean, median and mode 64

8 MEASURING VARIABILITY 65

8.1 Variability 65

8.2 The range 65

8.3 The standard deviation 66

8.4 Calculating the standard deviation 67

8.5 Calculating the standard deviation from grouped data 68

8.6 Variance 69

8.7 An alternative formula for calculating the variance and standard deviation 70

8.8 Degrees of freedom 71

8.9 The Coefficient of Variation (CV) 72

9 PROBABILITY AND THE NORMAL CURVE 75

9.1 The meaning of probability 75

9.2 Compound probabilities 76

9.3 Critical probability 78

9.4 Probability distribution 79

9.5 The normal curve 81

9.6 Some properties of the normal curve 82

9.7 Standardizing the normal curve 83

9.8 Two-tailed or one-tailed? 84

9.9 Small samples: the t-distribution 86

9.10 Are our data normally distributed? 88

9.11 Dealing with ‘non-normal’ data 91

10 HOW GOOD ARE OUR ESTIMATES? 95

10.1 Sampling error 95

10.2 The distribution of a sample mean 95

10.3 The confidence interval of a mean of a large sample 98

10.4 The confidence interval of a mean of a small sample 99

10.5 The difference between the means of two large samples 100

10.6 The difference between the means of two small samples 102

10.7 Estimating a proportion 103

10.8 The finite population correction 105

11 THE BASIS OF STATISTICAL TESTING 107

11.1 Introduction 107

11.2 The experimental hypothesis 107

11.3 The statistical hypothesis 108

11.4 Test statistics 110

11.5 One-tailed and two-tailed tests 110

11.6 Hypothesis testing and the normal curve 111

11.7 Type 1 and type 2 errors 113

11.8 Parametric and non-parametric statistics: some further observations 113

11.9 The power of a test 114

12 ANALYSING FREQUENCIES 115

12.1 The chi-squared test 115

12.2 Calculating the test statistic 115

12.3 A practical example of a test for homogeneous frequencies 118

12.4 One degree of freedom – Yates’ correction 119

12.5 Goodness of fit tests 120

12.6 The contingency table – tests for association 121

12.7 The ‘rows by columns’ (r × c) contingency table 125

12.8 Larger contingency tables 127

12.9 Advice on analysing frequencies 129

13 MEASURING CORRELATIONS 131

13.1 The meaning of correlation 131

13.2 Investigating correlation 131

13.3 The strength and significance of a correlation 133

13.4 The Product Moment Correlation Coefficient 134

13.5 The coefficient of determination r2 136

13.6 The Spearman Rank Correlation Coefficient rs 137

13.7 Advice on measuring correlations 139

14 REGRESSION ANALYSIS 141

14.1 Introduction 141

14.2 Gradients and triangles 142

14.3 Dependent and independent variables 143

14.4 A perfect rectilinear relationship 144

14.5 The line of least squares 146

14.6 Simple linear regression 147

14.7 Fitting the regression line to the scattergram 150

14.8 Regression for estimation 150

14.9 The coefficient of determination in regression 151

14.10 Dealing with curved relationships 152

14.11 How we can ‘straighten up’ curved relationships? 155

14.12 Advice on using regression analysis 155

15 COMPARING AVERAGES 157

15.1 Introduction 157

15.2 Matched and unmatched observations 158

15.3 The Mann–Whitney U-test for unmatched samples 158

15.4 Advice on using the Mann–Whitney U-test 160

15.5 More than two samples – the Kruskal–Wallace test 161

15.6 Advice on using the Kruskal–Wallace test 163

15.7 The Wilcoxon test for matched pairs 164

15.8 Advice on using the Wilcoxon test for matched pairs 167

15.9 Comparing means – parametric tests 168

15.10  The z-test for comparing the means of two large samples 168

15.11  The t-test for comparing the means of two small samples 170

15.12 The t-test for matched pairs 171

15.13 Advice on comparing means 173

16 ANALYSIS OF VARIANCE -ANOVA 175

16.1 Why do we need ANOVA? 175

16.2 How ANOVA works 176

16.3 Procedure for computing ANOVA 178

16.4 The Tukey test 181

16.5 Further applications of ANOVA 183

16.6 Advice on using ANOVA 185

APPENDICES 187

Appendix 1: Table of random numbers 187

Appendix 2: t-distribution 188

Appendix 3: χ2-distribution 189

Appendix 4: Critical values of Spearman’s Rank Correlation Coefficient 190

Appendix 5: Critical values of the product moment correlation coefficient 191

Appendix 6: Mann–Whitney U-test values (two-tailed test) 192

Appendix 7: Critical values of T in the Wilcoxon test for matched pairs 193

Appendix 8: F-distribution 194

Appendix 9: Tukey test 198

Appendix 10: Symbols 200

Appendix 11: Leicestershire ECT study data 201

Appendix 12: How large should our samples be? 203

BIBLIOGRAPHY 209

INDEX 211

Now in its second edition, Practical Statistics for Nursing and Health Care provides a sound foundation for nursing, midwifery and other health care students and early career professionals, guiding readers through the often daunting subject of statistics ‘from scratch’. Making no assumptions about one’s existing knowledge, the text develops in complexity as the material and concepts become more familiar, allowing readers to build the confidence and skills to apply various formula and techniques to their own data.

The authors explain common methods of interpreting data sets and explore basic statistical principles that enable nurses and health care professionals to decide on suitable treatment, as well as equipping readers with the tools to critically appraise clinical trials and epidemiology journals.

• Offers information on statistics presented in a clear, straightforward manner 
• Covers all basic statistical concepts and tests, and includes worked examples, case studies, and data sets 
• Provides an understanding of how data collected can be processed for the patients’ benefit 
• Contains a new section on how to calculate and use percentiles 

Written for students, qualified nurses and other healthcare professionals, Practical Statistics for Nursing and Health Care is a hands-on guide to gaining rapid proficiency in statistics.

Jim Fowler, former Principal Lecturer, Department of Biological Sciences, De Montfort University, Leicester, UK. 

Philip Jarvis, Statistician, Novartis Pharma AG, Basel, Switzerland. 

Mel Chevannes, Emeritus Professor of Nursing, University of Wolverhampton, Wolverhampton, UK.