# Experimental Design and Statistical Analysis for Pharmacologists

ISBN: 978-1-119-43766-6

Jul 2019

200 pages

Select type: E-Book

\$95.00

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## 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