Essential Statistics for the Pharmaceutical Sciences (eBook)

Dr Philip Rowe. Reader in Pharmaceutical Computing, School of Pharmacy and Chemistry, Liverpool,?UK In addition to Dr Rowe's teaching and research at LJMU he also works on a consultancy basis offering advice and assistance with pharmacokinetic or general data analysis problems for the pharmaceutical industry, professional organizations and hospitals. He has recently secured a post delivering statistics training for the Institute of Clinical Research.

Essential Statistics for the Pharmaceutical Sciences 5
Contents 9
Preface 15
Statistical packages 21
PART 1: DATA TYPES 1 23
1 Data types 25
1.1 Does it really matter? 25
1.2 Interval scale data 26
1.3 Ordinal scale data 26
1.4 Nominal scale data 27
1.5 Structure of this book 28
1.6 Chapter summary 28
PART 2: INTERVAL-SCALE DATA 29
2 Descriptive statistics 31
2.1 Summarizing data sets 31
2.2 Indicators of central tendency - mean, median and mode 32
2.3 Describing variability - standard deviation and coefficient of variation 38
2.4 Quartiles – another way to describe data 42
2.5 Using computer packages to generate descriptive statistics 45
2.6 Chapter summary 47
3 The normal distribution 49
3.1 What is a normal distribution? 49
3.2 Identifying data that are not normally distributed 50
3.3 Proportions of individuals within one or two standard deviations of the mean 53
3.4 Chapter summary 56
4 Sampling from populations - the SEM 57
4.1 Samples and populations 57
4.2 From sample to population 58
4.3 Types of sampling error 59
4.4 What factors control the extent of random sampling error? 61
4.5 Estimating likely sampling error - The SEM 64
4.6 Offsetting sample size against standard deviation 68
4.7 Chapter summary 68
5 Ninety-five per cent confidence interval for the mean 71
5.1 What is a confidence interval? 72
5.2 How wide should the interval be? 72
5.3 What do we mean by ‘95 per cent’ confidence? 73
5.4 Calculating the interval width 74
5.5 A long series of samples and 95 per cent confidence intervals 75
5.6 How sensitive is the width of the confidence interval to changesin the SD, the sample size or the required level of confidence? 76
5.7 Two statements 78
5.8 One-sided 95 per cent confidence intervals 79
5.9 The 95 per cent confidence interval for the difference between two treatments 82
5.10 The need for data to follow a normal distribution and data transformation 83
5.11 Chapter summary 87
6 The two-samplet-test (1). Introducing hypothesis tests 89
6.1 The two samplet-test - an example of a hypothesis test 90
6.2 'Significance' 96
6.3 The risk of a false positive finding 97
6.4 What factors will influence whether or not we obtain a significant outcome? 98
6.5 Requirements for applying a two-samplet-test 101
6.6 Chapter summary 102
7 The two-samplet-test (2). The dreadedP value 105
7.1 Measuring how significant a result is 105
7.2 P values 106
7.3 Two ways to define significance? 107
7.4 Obtaining theP value 108
7.5 P values or 95 per cent confidence intervals? 108
7.6 Chapter summary 109
8 The two-samplet-test (3). False negatives, power and necessary sample sizes 111
8.1 What else could possibly go wrong? 112
8.2 Power 113
8.3 Calculating necessary sample size 116
8.4 Chapter summary 123
9 The two-samplet-test (4). Statistical significance, practical significance and equivalence 125
9.1 Practical significance - is the difference big enough to matter? 126
9.2 Equivalence testing 129
9.3 Non-inferiority testing 133
9.4 P values are less informative and can be positively misleading 135
9.5 Setting equivalence limits prior to experimentation 137
9.6 Chapter summary 138
10 The two-samplet-test (5). One-sided testing 139
10.1 Looking for a change in a specified direction 140
10.2 Protection against false positives 142
10.3 Temptation! 143
10.4 Using a computer package to carry out a one-sided test 147
10.5 Should one-sided tests be used more commonly? 148
10.6 Chapter summary 148
11 What does a statistically significant result really tell us? 149
11.1 Interpreting statistical significance 149
11.2 Starting from extreme scepticism 153
11.3 Chapter summary 154
12 The pairedt-test - comparing two related sets of measurements 155
12.1 Paired data 155
12.2 We could analyse the data using a two-samplet-test 157
12.3 Using a pairedt-test instead 157
12.4 Performing a pairedt-test 158
12.5 What determines whether a pairedt-test will be significant? 160
12.6 Greater power of the pairedt-test 161
12.7 The pairedt-test is only applicable to naturally paired data 161
12.8 Choice of experimental design 162
12.9 Requirements for applying a pairedt-test 163
12.10 Sample sizes, practical significance and one-sided tests 163
12.11 Summarizing the differences between the paired and two-samplet-tests 165
12.12 Chapter summary 166
13 Analyses of variance - going beyondt-tests 167
13.1 Extending the complexity of experimental designs 168
13.2 One-way analysis of variance 168
13.3 Two-way analysis of variance 178
13.4 Multi-factorial experiments 186
13.5 Keep it simple - Keep it powerful 187
13.6 Chapter summary 189
14 Correlation and regression - relationships between measured values 191
14.1 Correlation analysis 192
14.2 Regression analysis 200
14.3 Multiple regression 207
14.4 Chapter summary 214
PART 3: NOMINAL-SCALE DATA 217
15 Describing categorized data 219
15.1 Descriptive statistics 220
15.2 Testing whether the population proportion might credibly be some pre-determined figure 224
15.3 Chapter summary 229
16 Comparing observed proportions - the contingency chi-square test 231
16.1 Using the contingency chi-square test to compare observed proportions 232
16.2 Obtaining a 95 per cent CI for the change in the proportion of expulsions – is the difference large enough to be of practical significance? 235
16.3 Larger tables - attendance at diabetic clinics 236
16.4 Planning experimental size 239
16.5 Chapter summary 241
PART 4: ORDINAL-SCALE DATA 243
17 Ordinal and non-normally distributed data. Transformations and non-parametric tests 245
17.1 Transforming data to a normal distribution 246
17.2 The Mann-Whitney test - a non-parametric method 250
17.3 Dealing with ordinal data 255
17.4 Other non-parametric methods 257
17.5 Chapter summary 264
Appendix to chapter 17 264
PART 5: SOME CHALLENGES FROM THE REAL WORLD 267
18 Multiple testing 269
18.1 What is it and why is it a problem? 269
18.2 Where does multiple testing arise? 270
18.3 Methods to avoid false positives 272
18.4 The role of scientific journals 276
18.5 Chapter summary 277
19 Questionnaires 279
19.1 Is there anything special about questionnaires? 280
19.2 Types of questions 280
19.3 Designing a questionnaire 284
19.4 Sample sizes and return rates 285
19.5 Analysing the results 287
19.6 Confounded epidemiological data 288
19.7 Multiple testing with questionnaire data 293
19.8 Chapter summary 294
PART 6: CONCLUSIONS 297
20 Conclusions 299
20.1 Be clear about the purpose of the experiment 299
20.2 Keep the experimental design simple and therefore clear and powerful 300
20.3 Draw up a statistical analysis plan as part of the experimental design – it is not a last minute add-on 301
20.4 Explore your data visually before launching into statistical testing 302
20.5 Beware of multiple analyses 303
20.6 Interpret both significance and non-significance with care 304
Index 305