Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences

Dr Paul J. Mitchell is Senior Lecturer and Associate Professor in the Department of Pharmacy and Pharmacology, University of Bath, UK, and Adjunct Lecturer in the Department of Pharmacology and Therapeutics, National University of Ireland (NUI), Galway, Ireland. He has more than 45 years' experience in experimental pharmacology, experimental design, and statistical analysis. For the last 25 years Dr Mitchell has collaborated with colleagues to develop a coherent strategy to teach experimental design and statistical analysis to undergraduate and graduate students across subject areas.

Foreward 4

1 Introduction 6

2 So, what are data? 8

3 Numbers; counting and measuring, precision and accuracy 9

4 Data collection: Sampling and populations, different types of data, data distributions 12

5 Descriptive statistics: measures to describe and summarize data sets. 16

6 Testing for Normality and transforming skewed data sets 22

7 The Standard Normal Distribution 28

8 Non-Parametric Descriptive statistics 30

9 Summary of descriptive statistics; so, what values may I use to describe my data? 34

Decision Flowchart 1: Descriptive Statistics - Parametric v Non-parametric data 43

10 Introduction to Inferential statistics 44

11 Comparing 2 sets of data - Independent t-test 50

12 Comparing 2 sets of data - Paired t-test 55

13 Comparing 2 sets of data - Independent non-parametric data 58

14 Comparing 2 sets of data - Paired non-parametric data 62

15 Parametric 1-way Analysis of Variance 66

16 Repeated Measures Analysis of Variance 78

17 Complex Analysis of Variance models 86

18 Non-parametric ANOVA 102

Decision Flowchart 2: Inferential Statistics - Single and multiple pairwise comparisons 115

19 Correlation Analysis 116

20 Regression Analysis 126

21 Chi-Square Analysis 136

Decision Flowchart 3: Inferential Statistics -Tests of Association 145

22 Confidence Intervals 146

23 Permutation Test of Exact Inference 150

24 General Linear Model 152

Appendices Introduction to Appendices 155

A Data distribution: probability mass function and probability density functions

A.1 Binomial Distribution 156

A.2 Exponential Distribution 157

A.3 Normal Distribution 158

A.4 Chi-square Distribution 159

A.5 Student t-Distribution 160

A.6 F Distribution 161

B Standard Normal Probabilities

B.1 AUC values for z values below the mean (i.e. -z) 162

B.2 AUC values for z values above the mean (i.e. +z) 163

C Critical values of the t-distribution 164

D Critical values of the Mann-Whitney U statistic

D.1 Critical values for U; One-tailed test, p = 0.05 165

D.2 Critical values for U; One-tailed test, p = 0.01 166

D.3 Critical values for U; Two-tailed test, p = 0.05 167

D.4 Critical values for U; Two-tailed test, p = 0.01 168

E Critical values of the F distribution

E.1 Critical values of F, p = 0.05 169

E.2 Critical values of F, p = 0.01 170

E.3 Critical values of F, p = 0.001 171

F Critical values of the Chi-square distribution 172

G Critical z values for multiple non-parametric pairwise comparisons

G.1 Critical values of z according to the number of comparisons 173

G.2 Alternative critical values of z according to the number of comparisons when all groups have an equal number of subjects 173

H Critical values of correlation coefficients

H.1 Pearson Product Moment Correlation 174

H.2 Spearman Rank Correlation 174

H.3 Kendall's Rank Correlation (Kendall's tau) 175

Overall Decision Flowchart: Descriptive and Inferential Statistics 176

Index