Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences

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