Starting out in Statistics

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.

• Introduction – What’s the Point of Statistics? xiiiBasic Maths for Stats Revision xvStatistical Software Packages xxiiiAbout the Companion Website xxv1 Introducing Variables, Populations and Samples – ‘Variability is the Law of Life’ 11.1 Aims 11.2 Biological data vary 11.3 Variables 31.4 Types of qualitative variables 41.4.1 Nominal variables 41.4.2 Multiple response variables 41.4.3 Preference variables 51.5 Types of quantitative variables 51.5.1 Discrete variables 51.5.2 Continuous variables 61.5.3 Ordinal variables – a moot point 61.6 Samples and populations 61.7 Summary 10Reference 102 Study Design and Sampling – ‘Design is Everything. Everything!’ 112.1 Aims 112.2 Introduction 112.3 One sample 132.4 Related samples 132.5 Independent samples 142.6 Factorial designs 152.7 Observational study designs 172.7.1 Cross-sectional design 172.7.2 Case-control design 172.7.3 Longitudinal studies 182.7.4 Surveys 182.8 Sampling 192.9 Reliability and validity 202.10 Summary 21References 233 Probability – ‘Probability So True in General’ 253.1 Aims 253.2 What is probability? 253.3 Frequentist probability 263.4 Bayesian probability 313.5 The likelihood approach 353.6 Summary 36References 374 Summarising Data – ‘Transforming Data into Information’ 394.1 Aims 394.2 Why summarise? 394.3 Summarising data numerically – descriptive statistics 414.3.1 Measures of central location 414.3.2 Measures of dispersion 474.4 Summarising data graphically 544.5 Graphs for summarising group data 554.5.1 The bar graph 554.5.2 The error plot 564.5.3 The box-and-whisker plot 574.5.4 Comparison of graphs for group data 584.5.5 A little discussion on error bars 594.6 Graphs for displaying relationships between variables 594.6.1 The scatter diagram or plot 604.6.2 The line graph 624.7 Displaying complex (multidimensional) data 634.8 Displaying proportions or percentages 644.8.1 The pie chart 644.8.2 Tabulation 644.9 Summary 66References 665 Statistical Power – ‘. Find out the Cause of this Effect’ 675.1 Aims 675.2 Power 675.3 From doormats to aortic valves 705.4 More on the normal distribution 725.4.1 The central limit theorem 775.5 How is power useful? 795.5.1 Calculating the power 805.5.2 Calculating the sample size 825.6 The problem with p values 845.7 Confidence intervals and power 855.8 When to stop collecting data 875.9 Likelihood versus null hypothesis testing 885.10 Summary 91References 926 Comparing Groups using t-Tests and ANOVA – ‘To Compare is not to Prove’ 936.1 Aims 936.2 Are men taller than women? 946.3 The central limit theorem revisited 976.4 Student’s t-test 986.4.1 Calculation of the pooled standard deviation 1026.4.2 Calculation of the t statistic 1036.4.3 Tables and tails 1046.5 Assumptions of the t-test 1076.6 Dependent t-test 1096.7 What type of data can be tested using t-tests? 1106.8 Data transformations 1106.9 Proof is not the answer 1116.10 The problem of multiple testing 1116.11 Comparing multiple means – the principles of analysis of variance 1126.11.1 Tukey’s honest significant difference test 1206.11.2 Dunnett’s test 1216.11.3 Accounting for identifiable sources of error in one-way ANOVA: nested design 1236.12 Two-way ANOVA 1266.12.1 Accounting for identifiable sources of error using a two-way ANOVA: randomised complete block design 1306.12.2 Repeated measures ANOVA 1336.13 Summary 133References 1347 Relationships between Variables: Regression and Correlation – ‘In Relationships Concentrate only on what is most Significant and Important’ 1357.1 Aims 1357.2 Linear regression 1367.2.1 Partitioning the variation 1397.2.2 Calculating a linear regression 1417.2.3 Can weight be predicted by height? 1457.2.4 Ordinary least squares versus reduced major axis regression 1527.3 Correlation 1537.3.1 Correlation or linear regression? 1547.3.2 Covariance, the heart of correlation analysis 1547.3.3 Pearson’s product–moment correlation coefficient 1567.3.4 Calculating a correlation coefficient 1577.3.5 Interpreting the results 1597.3.6 Correlation between maternal BMI and infant birth weight 1607.3.7 What does this correlation tell us and what does it not? 1617.3.8 Pitfalls of Pearson’s correlation 1627.4 Multiple regression 1647.5 Summary 174References 1748 Analysis of Categorical Data – ‘If the Shoe Fits .’ 1758.1 Aims 1758.2 One-way chi-squared 1758.3 Two-way chi-squared 1798.4 The odds ratio 1868.5 Summary 191References 1929 Non-Parametric Tests – ‘An Alternative to other Alternatives’ 1939.1 Aims 1939.2 Introduction 1939.3 One sample sign test 1959.4 Non-parametric equivalents to parametric tests 1999.5 Two independent samples 1999.6 Paired samples 2039.7 Kruskal–Wallis one-way analysis of variance 2079.8 Friedman test for correlated samples 2119.9 Conclusion 2149.10 Summary 214References 21510 Resampling Statistics comes of Age – ‘There’s always a Third Way’ 21710.1 Aims 21710.2 The age of information 21710.3 Resampling 21810.3.1 Randomisation tests 21910.3.2 Bootstrapping 22210.3.3 Comparing two groups 22710.4 An introduction to controlling the false discovery rate 22910.5 Summary 231References 231Appendix A: Data Used for Statistical Analyses (Chapters 6, 7 and 10) 233Appendix B: Statistical Software Outputs (Chapters 6–9) 243Index 279