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 

A practical guide to the use of basic principles of experimental design and statistical analysis in pharmacology Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences provides clear instructions on applying statistical analysis techniques to pharmacological data. Written by an experimental pharmacologist with decades of experience teaching statistics and designing preclinical experiments, this reader-friendly volume explains the variety of statistical tests that researchers require to analyze data and draw correct conclusions. Detailed, yet accessible, chapters explain how to determine the appropriate statistical tool for a particular type of data, run the statistical test, and analyze and interpret the results. By first introducing basic principles of experimental design and statistical analysis, the author then guides readers through descriptive and inferential statistics, analysis of variance, correlation and regression analysis, general linear modelling, and more. Lastly, throughout the textbook are numerous examples from molecular, cellular, in vitro, and in vivo pharmacology which highlight the importance of rigorous statistical analysis in real-world pharmacological and biomedical research. This textbook also: Describes the rigorous statistical approach needed for publication in scientific journalsCovers a wide range of statistical concepts and methods, such as standard normal distribution, data confidence intervals, and post hoc and a priori analysisDiscusses practical aspects of data collection, identification, and presentation Features images of the output from common statistical packages, including GraphPad Prism, Invivo Stat, MiniTab and SPSS Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences is an invaluable reference and guide for undergraduate and graduate students, post-doctoral researchers, and lecturers in pharmacology and allied subjects in the life sciences.