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Experimental Design and Statistical Analysis for Pharmacologists

Experimental Design and Statistical Analysis for Pharmacologists

Paul J Mitchell

ISBN: 978-1-119-43766-6

Jul 2019

200 pages

$76.99

Product not available for purchase

Description

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