Starting out in Statistics

To form a strong grounding in human-related sciences it is essential for students to grasp the fundamental concepts of statistical analysis, rather than simply learning to use statistical software. Although the software is useful, it does not arm a student with the skills necessary to formulate the experimental design and analysis of a research project in later years of study or indeed, if working in research.

This textbook deftly covers a topic that many students find difficult. With an engaging and accessible style it provides the necessary background and tools for students to use statistics confidently and creatively in their studies and future career.

Key features:

• Up-to-date methodology, techniques and current examples relevant to the analysis of large data sets, putting statistics in context

• Strong emphasis on experimental design

• Clear illustrations throughout that support and clarify the text

• A companion website with explanations on how to apply learning to related software packages

This is an introductory book written for undergraduate biomedical and social science students with a focus on human health, interactions, and disease. It is also useful for graduate students in these areas, and for practitioners requiring a modern refresher.

Auteur

Patricia de Winter, Research Associate, University College London; Sessional Lecturer, Birkbeck College London; Translational Uro-Oncology, Division of Surgury & Interventional Science, University College London.

Peter M. B. Cahusac, Lecturer, University of Stirling, Department of Psychology, University of Stirling, Scotland.

Contenu
Introduction What's the Point of Statistics? xiii Basic Maths for Stats Revision xv

Statistical Software Packages xxiii

About the Companion Website xxv

1 Introducing Variables, Populations and Samples 'Variability is the Law of Life' 1

1.1 Aims 1

1.2 Biological data vary 1

1.3 Variables 3

1.4 Types of qualitative variables 4

1.4.1 Nominal variables 4

1.4.2 Multiple response variables 4

1.4.3 Preference variables 5

1.5 Types of quantitative variables 5

1.5.1 Discrete variables 5

1.5.2 Continuous variables 6

1.5.3 Ordinal variables a moot point 6

1.6 Samples and populations 6

1.7 Summary 10

Reference 10

2 Study Design and Sampling 'Design is Everything. Everything!' 11

2.1 Aims 11

2.2 Introduction 11

2.3 One sample 13

2.4 Related samples 13

2.5 Independent samples 14

2.6 Factorial designs 15

2.7 Observational study designs 17

2.7.1 Cross-sectional design 17

2.7.2 Case-control design 17

2.7.3 Longitudinal studies 18

2.7.4 Surveys 18

2.8 Sampling 19

2.9 Reliability and validity 20

2.10 Summary 21

References 23

3 Probability 'Probability ... So True in General' 25

3.1 Aims 25

3.2 What is probability? 25

3.3 Frequentist probability 26

3.4 Bayesian probability 31

3.5 The likelihood approach 35

3.6 Summary 36

References 37

4 Summarising Data 'Transforming Data into Information' 39

4.1 Aims 39

4.2 Why summarise? 39

4.3 Summarising data numerically descriptive statistics 41

4.3.1 Measures of central location 41

4.3.2 Measures of dispersion 47

4.4 Summarising data graphically 54

4.5 Graphs for summarising group data 55

4.5.1 The bar graph 55

4.5.2 The error plot 56

4.5.3 The box-and-whisker plot 57

4.5.4 Comparison of graphs for group data 58

4.5.5 A little discussion on error bars 59

4.6 Graphs for displaying relationships between variables 59

4.6.1 The scatter diagram or plot 60

4.6.2 The line graph 62

4.7 Displaying complex (multidimensional) data 63

4.8 Displaying proportions or percentages 64

4.8.1 The pie chart 64

4.8.2 Tabulation 64

4.9 Summary 66

References 66

5 Statistical Power '. . . Find out the Cause of this Effect' 67

5.1 Aims 67

5.2 Power 67

5.3 From doormats to aortic valves 70

5.4 More on the normal distribution 72

5.4.1 The central limit theorem 77

5.5 How is power useful? 79

5.5.1 Calculating the power 80

5.5.2 Calculating the sample size 82

5.6 The problem with p values 84

5.7 Confidence intervals and power 85

5.8 When to stop collecting data 87

5.9 Likelihood versus null hypothesis testing 88

5.10 Summary 91

References 92

6 Comparing Groups using t-Tests and ANOVA 'To Compare is not to Prove' 93

6.1 Aims 93

6.2 Are men taller than women? 94

6.3 The central limit theorem revisited 97

6.4 Student's t-test 98

6.4.1 Calculation of the pooled standard deviation 102

6.4.2 Calculation of the t statistic 103

6.4.3 Tables and tails 104

6.5 Assumptions of the t-test 107

6.6 Dependent t-test 109

6.7 What type of data can be tested using t-tests? 110

6.8 Data transformations 110

6.9 Proof is not the answer 111

6.10 The problem of multiple testing 111

6.11 Comparing multiple means the principles of analysis of variance 112 ...