Experimental Design and Statistical Analysis for Pharmacologists will provide an invaluable teaching resource for students, lecturers and researchers in pharmacology. The book will guide the reader through the basic principles of experimental design and statistical analysis, data presentation, descriptive statistics and inferential statistics (including power analysis, analysis of 2 groups of data, analysis of more than 2 groups of data (Analysis of Variance, post hoc and a priori analysis), the relationship between 2 variables, confidence intervals and General Linear Modelling).
A large array of examples will be used throughout the book, describing the variety of experimental methods for which the statistical tests are appropriate; such experimental methods will include examples from molecular and cellular pharmacology, in vitro pharmacology, including isolated tissue techniques, and in vivo pharmacology. In addition, it is envisaged that each section will link directly to a dynamic and organic database that will provide further examples of data analysis coupled with descriptions of appropriate experimental design. This approach ties in with the eLearning platform proposed by the British Pharmacological Society (BPS) in support of the Core Curriculum for Pharmacology.
Foreword
Introduction
Experimental design
The important decision about statistical analysis
Statistical analysis
Why are statistical tests required? The eye-ball test!
So what are data?
Data handling and presentation
Text
Tables
Line charts and scatterplots
Bar charts
Numbers; counting and measuring
Precision
Accuracy
Coefficient of variation
% Accuracy
Errors in measurement
Blunder
Systematic Error
Random Error
Instrumental Error
Observer Error
Data collection
Sampling and populations
So why do we need statistics?
Descriptive statistics
Data summary
Data presentation
Data variation
Data distribution
Minimum, maximum, range
Mean
Arithmetic (data from a linear scale)
Geometric (data derived from a logarithmic scale, or nth root of the products of the values)
Harmonic (often used when rates are compared)
Medium
Mode
Unimodal, bimodal, multimodal
Variance
Standard deviation
Frequency distribution
Unimodal Distribution
Bimodal Distribution
Multimodal Distribution
Normal Distribution
Standard deviation
Standard normal distribution curve
Z scores
Non-normal Distribution
Central tendency
Skewness (Pearsonian Coefficient of skewness)
Kurtosis
Interquartile range
Coefficient of variation
Standard error of the mean
cf Standard Deviation
Which descriptive statistics should I report and why?
Inferential statistics
Overview
Experimental design
Power analysis calculations and sample size
Stages of hypothesis testing
Assumption of no effect : The Null Hypothesis. Threshold to accept or reject.
The Alternate Hypothesis
Types of variable: Independent and dependent variables.
1-tailed or 2-tailed testing
Experiments with two groups of data (incl. Excel spread sheet data)
Normal data
Assumptions of t-tests
t-tables
Degrees of Freedom
P values (what does p really mean?)
Type 1 and Type 2 Errors
Independent groups: Independent (Student’s) t-test
Paired groups: Paired t-test
Non-normal data
Ranking data: effect of outliers
Sign test
Independent groups: Wilcoxan rank sum test, Mann-Whitney U test
Paired groups: Wilcoxan signed-rank test
Multiple pair-wise comparisons and Type 1 Errors.
Experiments with more than 2 groups.
Overview of Analysis of Variance: Why is ANOVA important?
Assumptions of One-way ANOVA
Frequency distribution (Normality testing: Shapiro-Wilk test, Normal probability plot)
Homogeneity of variance (Levene’s test)
Type of measurement
Group size and type
One-way ANOVA: Experimental design (incl. Excel data spread sheet)
How does it work and what does the result mean?
Total variance
Within group variance
Between group variance
Degrees of Freedom
F ratio
Relationship between F ration and t-value.
How to report and interpret ANOVA data
Main effect of treatment
What next?
Post hoc analysis – variety of tests, why so many different tests?
All Mean comparisons
Control Mean comparisons
Why are repeated t-tests inappropriate?
Bonferroni correction
Holme correction.
A priori tests
Data transformation
Repeated Measures ANOVA
Experimental design (incl. Excel data spread sheet)
Concept of sphericity and adjusting for violations (Greenhouse-Geisser estimate, Huynh-Feldt correction)
Main effect of time
One-way ANOVA with Repeated Measures
Experimental design (incl. Excel data spread sheet)
Main effect of treatment and appropriate post hoc analysis
Main effect of time and appropriate post hoc analysis
Interaction between treatment and time, and appropriate post hoc analysis
Two-way ANOVA
Experimental design (incl. Excel data spread sheet)
Main effect of treatment 1 and appropriate post hoc analysis
Main effect of treatment 2 and appropriate post hoc analysis
Interaction between treatment 1 and treatment 2, and appropriate post hoc analysis
Two-way ANOVA with Repeated Measures
Experimental design (incl. Excel data spread sheet)
Main effect of treatment 1 and appropriate post hoc analysis
Main effect of treatment 2 and appropriate post hoc analysis
Main effect of Time and appropriate post hoc analysis
Interaction between treatment 1 and treatment 2, and appropriate post hoc analysis
Interaction between treatment 2 and time, and appropriate post hoc analysis
Interaction between treatment 1, treatment 2 and time, and appropriate post hoc analysis
Three-way ANOVA
Experimental design (incl. Excel data spread sheet)
Main effect of treatment 1 and appropriate post hoc analysis
Main effect of treatment 2 and appropriate post hoc analysis
Main effect of treatment 3 and appropriate post hoc analysis
Interaction between treatment 1 and treatment 2, and post hoc analysis
Interaction between treatment 1 and treatment 3, and post hoc analysis
Interaction between treatment 2 and treatment 3, and post hoc analysis
Interaction between treatment 1, treatment 2 and treatment 3, and post hoc analysis
What to do when standard post hoc tests are inappropriate.
Are all pair-wise comparisons necessary?
Non-parametric analysis of variance
One-way non-parametric ANOVA for Independent goups: Kruskal-Wallis ANOVA by ranks
Post hoc multiple comparisons: what test is appropriate?
MWUT with Bonferroni correction
All group comparisons for Independent groups
Control group comparisons for Independent groups
Repeated measures non-parametric ANOVA: Friedman ANOVA by ranks
Post hoc multiple comparisons: what test is appropriate?
Wilcoxan signed rank test with Bonferroni correction
All group comparisons for Paired data sets
Control group comparisons for Paired data sets
Relationship between 2 variables
Correlation
Variables
Normal data
Pearson’s Product Moment Correlation coefficient
Non-parametric data
Spearman’s Rank Correlation coefficient
Kendall’s tau
Application of Bonferroni/Holme correction
Regression
Independent and Dependent variables
Linear regression
Least squares method
Assumptions
Confidence limits
Regression sum of squares and residual sum of squares
Regression and ANOVA
Coefficient of determination
Confidence limits for slope
Confidence limits for intercept
Multiple regression
Non-linear regression
Chi-Squared test
When to use Chi-square analysis.
Purpose of Chi-Sq
Contingency tables
Null hypothesis
Explanation of Chi-Sq
Observed Frequencies
Expected Frequencies
a) Prescribed frequency data
b) Calculated Frequencies
Cell contribution to Chi-Sq
Calculation of Total Chi-Sq and degrees of freedom
Importance of differences between observed and expected frequencies
Calculation of Standardized residuals
Relationship between z-scores and probability values.
Patterning across columns and rows and effect on expected frequencies
Assumptions of Chi-Sq
Expected frequencies less than 5
Fisher’s Exact test
Special conditions of 2x2 contingency tables.
Yates’ correction
Risk and Relative Risk
Odds and Odds Ratio
Confidence Intervals
What are Confidence Intervals
Use and Misuse
Confidence Intervals and/or P values?; that is the question!
Sample size
Confidence Intervals and Power
Difference between calculated mean values
Single sample data
Unpaired two sample data
Paired two sample data
Non-normal data sets
Single sample data
Two sample data
Differences between calculated median values
Medians and quantiles
Unpaired two sample data
Paired two sample data
Differences between proportions
Single sample data
Unpaired two sample data
Paired two sample data
Regression and Confidence Intervals
Correlation and Confidence Intervals
General Linear Modelling
