DAVID BOWERS, Leeds Institute of Health Sciences, School of Medicine, University of Leeds, Leeds, UK.

Preface to the 4th Edition xix

Preface to the 3rd Edition xxi

Preface to the 2nd Edition xxiii

Preface to the 1st Edition xxv

Introduction xxvii

I Some Fundamental Stuff 1

1 First things first - the nature of data 3

Variables and data 3

Where are we going ...? 5

The good, the bad, and the ugly - types of variables 5

Categorical data 6

Nominal categorical data 6

Ordinal categorical data 7

Metric data 8

Discrete metric data 8

Continuous metric data 9

How can I tell what type of variable I am dealing with? 10

The baseline table 11

II Descriptive Statistics 15

2 Describing data with tables 17

Descriptive statistics. What can we do with raw data? 18

Frequency tables - nominal data 18

The frequency distribution 19

Relative frequency 20

Frequency tables - ordinal data 20

Frequency tables - metric data 22

Frequency tables with discrete metric data 22

Cumulative frequency 24

Frequency tables with continuous metric data - grouping the raw data 25

Open¿ended groups 27

Cross¿tabulation - contingency tables 28

Ranking data 30

3 Every picture tells a story - describing data with charts 31

Picture it! 32

Charting nominal and ordinal data 32

The pie chart 32

The simple bar chart 34

The clustered bar chart 35

The stacked bar chart 37

Charting discrete metric data 39

Charting continuous metric data 39

The histogram 39

The box (and whisker) plot 42

Charting cumulative data 44

The cumulative frequency curve with discrete metric data 44

The cumulative frequency curve with continuous metric data 44

Charting time¿based data - the time series chart 47

The scatterplot 48

The bubbleplot 49

4 Describing data from its shape 51

The shape of things to come 51

Skewness and kurtosis as measures of shape 52

Kurtosis 55

Symmetric or mound¿shaped distributions 56

Normalness - the Normal distribution 56

Bimodal distributions 58

Determining skew from a box plot 59

5 Measures of location - Numbers R us 62

Numbers, percentages, and proportions 62

Preamble 63

N umbers, percentages, and proportions 64

Handling percentages - for those of us who might need a reminder 65

Summary measures of location 67

The mode 68

The median 69

The mean 70

Percentiles 71

Calculating a percentile value 72

What is the most appropriate measure of location? 73

6 Measures of spread - Numbers R us - (again) 75

Preamble 76

The range 76

The interquartile range (IQR) 76

Estimating the median and interquartile range from the cumulative frequency curve 77

The boxplot (also known as the box and whisker plot) 79

Standard deviation 82

Standard deviation and the Normal distribution 84

Testing for Normality 86

Using SPSS 86

Using Minitab 87

Transforming data 88

7 Incidence, prevalence, and standardisation 92

Preamble 93

The incidence rate and the incidence rate ratio (IRR) 93

The incidence rate ratio 94

Prevalence 94

A couple of difficulties with measuring incidence and prevalence 97

Some other useful rates 97

Crude mortality rate 97

Case fatality rate 98

Crude maternal mortality rate 99

Crude birth rate 99

Attack rate 99

Age¿specific mortality rate 99

Standardisation - the age¿standardised mortality rate 101

The direct method 102

The standard population and the comparative mortality ratio (CMR) 103

The indirect method 106

The standardised mortality rate 107

III The Confounding Problem 111

8 Confounding - like the poor, (nearly) always with us 113

Preamble 114

What is confounding? 114

Confounding by indication 117

Residual confounding 119

Detecting confounding 119

Dealing with confounding - if confounding is such a problem, what can we do about it? 120

Using restriction 120

Using matching 121

Frequency matching 121

One¿to¿one matching 121

Using stratification 122

Using adjustment 122

Using randomisation 122

IV Design and Data 125

9 Research design - Part I: Observational study designs 127

Preamble 128

Hey ho! Hey ho! it's off to work we go 129

Types of study 129

Observational studies 130

Case reports 130

Case series studies 131

Cross¿sectional studies 131

Descriptive cross¿sectional studies 132

Confounding in descriptive cross¿sectional studies 132

Analytic cross¿sectional studies 133

Confounding in analytic cross¿sectional studies 134

From here to eternity - cohort studies 135

Confounding in the cohort study design 139

Back to the future - case-control studies 139

Confounding in the case-control study design 141

Another example of a case-control study 142

Comparing cohort and case-control designs 143

Ecological studies 144

The ecological fallacy 145

10 Research design - Part II: getting stuck in - experimental studies 146

Clinical trials 147

Randomisation and the randomised controlled trial (RCT) 148

Block randomisation 149

Stratification 149

Blinding 149

The crossover RCT 150

Selection of participants for an RCT 153

Intention to treat analysis (ITT) 154

11 Getting the participants for your study: ways of sampling 156

From populations to samples - statistical inference 157

Collecting the data - types of sample 158

The simple random sample and its offspring 159

The systematic random sample 159

The stratified random sample 160

The cluster sample 160

Consecutive and convenience samples 161

How many participants should we have? Sample size 162

Inclusion and exclusion criteria 162

Getting the data 163

V Chance Would Be a Fine Thing 165

12 The idea of probability 167

Preamble 167

Calculating probability - proportional frequency 168

Two useful rules for simple probability 169

Rule 1. The multiplication rule for independent events 169

Rule 2. The addition rule for mutually exclusive events 170

Conditional and Bayesian statistics 171

Probability distributions 171

Discrete versus continuous probability distributions 172

The binomial probability distribution 172

The Poisson probability distribution 173

The Normal probability distribution 174

13 Risk and odds 175

Absolute risk and the absolute risk reduction (ARR) 176

The risk ratio 178

The reduction in the risk ratio (or relative risk reduction (RRR)) 178

A general formula for the risk ratio 179

Reference value 179

N umber needed to treat (NNT) 180

What happens if the initial risk is small? 181

Confounding with the risk ratio 182

Odds 183

Why you can't calculate risk in a case-control study 185

The link between probability and odds 186

The odds ratio 186

Confounding with the odds ratio 189

Approximating the risk ratio from the odds ratio 189

VI The Informed Guess - An Introduction to Confidence Intervals 191

14 Estimating the value of a single population parameter - the idea of confidence intervals 193

Confidence interval estimation for a population mean 194

The standard error of the mean 195

How we use the standard error of the mean to calculate a confidence interval for a population mean 197

Confidence interval for a population proportion 200

Estimating a confidence interval for the median of a single population 203

15 Using confidence intervals to compare two population parameters 206

What's the difference? 207

Comparing two independent population means 207

An example using birthweights 208

Assessing the evidence using the confidence interval 211

Comparing two paired population means 215

Within¿subject and between¿subject variations 215

Comparing two independent population proportions 217

Comparing two independent population medians - the Mann-Whitney rank sums method 219

Comparing two matched population medians - the Wilcoxon signed¿ranks method 220

16 Confidence intervals for the ratio of two population parameters 224

Getting a confidence interval for the ratio of two independent population means 225

Confidence interval for a population risk ratio 226

Confidence intervals for a population odds ratio 229

Confidence intervals for hazard ratios 232

VII Putting it to the Test 235

17 Testing hypotheses about the difference between two population parameters 237

Answering the question 238

The hypothesis 238

The null hypothesis 239

The hypothesis testing process 240

The p¿value and the decision rule 241

A brief summary of a few of the commonest tests 242

Using the p¿value to compare the means of two independent populations 244

Interpreting computer hypothesis test results for the difference in two independent population means - the two¿sample t test 245

Output from Minitab - two¿sample t test of difference in mean...