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## How to Visualize and Analyze Data

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Request a sales quote** **** **** **** **** **** **** **** **** **** **### Andrew P. King

### Robert Eckersley

- 1st Edition - May 18, 2019
- Authors: Andrew P. King, Robert Eckersley
- Language: English
- Paperback ISBN:9 7 8 - 0 - 0 8 - 1 0 2 9 3 9 - 8
- eBook ISBN:9 7 8 - 0 - 0 8 - 1 0 2 9 4 0 - 4

Statistics for Biomedical Engineers and Scientists: How to Analyze and Visualize Data provides an intuitive understanding of the concepts of basic statistics, with a focus on… Read more

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*Statistics for Biomedical Engineers and Scientists: How to Analyze and Visualize Data* provides an intuitive understanding of the concepts of basic statistics, with a focus on solving biomedical problems. Readers will learn how to understand the fundamental concepts of descriptive and inferential statistics, analyze data and choose an appropriate hypothesis test to answer a given question, compute numerical statistical measures and perform hypothesis tests ‘by hand’, and visualize data and perform statistical analysis using MATLAB. Practical activities and exercises are provided, making this an ideal resource for students in biomedical engineering and the biomedical sciences who are in a course on basic statistics.

- Presents a practical guide on how to visualize and analyze statistical data
- Provides numerous practical examples and exercises to illustrate the power of statistics in biomedical engineering applications
- Gives an intuitive understanding of statistical tests
- Covers practical skills by showing how to perform operations ‘by hand’ and by using MATLAB as a computational tool
- Includes an online resource with downloadable materials for students and teachers

Biomedical: engineers, biomedical sciences: students, researchers

**1 Descriptive Statistics I: Univariate Statistics**

1.1 Introduction

1.2 Types of Statistical Data

1.3 Univariate Data Visualisation

1.3.1 Dotplot

1.3.2 Histogram

1.3.3 Bar Chart

1.4 Measures of Central Tendency

1.4.1 Mean

1.4.2 Median

1.4.3 Mode

1.4.4 Calculating Measures of Central Tendency in MATLAB

1.4.5 Which Measure to Use?

1.5 Measures of Variation

1.5.1 Standard Deviation

1.5.2 Inter-Quartile Range

1.5.3 Calculating Measures of Variation in MATLAB

1.5.4 Which Measure of Variation to Use?

1.6 Visualising Measures of Variation

1.6.1 Visualising Mean and Standard Deviation

1.6.2 Visualising Median and IQR: the Box Plot

1.7 Summary

1.8 Further Resources

1.9 Exercises

2 Descriptive Statistics II: Bivariate Statistics

2.1 Introduction

2.2 Visualising Bivariate Statistics

2.2.1 Two Categorical Variables

2.2.2 Combining Categorical and Continuous Variables

2.2.3 Two Continuous Variables

2.2.4 General Comments on Choice of Visualisation

2.3 Pearson’s Correlation Coefficient

2.3.1 Example Use of Pearson’s Correlation Coefficient

2.3.2 p-values and Correlation Coefficient Values

2.4 Spearman’s Rank Correlation Coefficient

2.4.1 Example Use of Spearman’s Rank Correlation Coefficient

2.5 Which Measure of Correlation to Use?

2.6 Regression Analysis

2.6.1 Calculating the Equation of Best Fit Line Using MATLAB

2.6.2 Plotting the Best Fit Line

2.6.3 Using the Best Fit Line to Make Predictions

2.6.4 Fitting Non-linear Models

2.6.5 Fitting Higher Order Polynomials

2.7 Summary

2.8 Further Resources

2.9 Exercises

3 Descriptive Statistics III: ROC Analysis

3.1 Introduction

3.2 Notation

3.2.1 Sensitivity and Specificity

3.2.2 Positive and Negative Predictive Values

3.2.3 Example Calculation of Se, Sp, PPV and NPV

3.3 ROC Curves

3.4 Exercise

3.5 Recap on Scripts and Functions

3.6 Case Study: ROC Analysis

3.7 Summary

3.8 Further Resources

4 Inferential Statistics I: Basic Concepts

4.1 Introduction

4.2 Probability

4.2.1 Probabilities of Single Events

4.2.2 Probabilities of Multiple Events

4.3 Probability Distributions

4.3.1 Why the Normal Distribution is so Important: The

Central Limit Theorem

4.4 Standard Error of Mean

4.5 Confidence Intervals of Mean

4.6 Summary

4.7 Further Resources

4.8 Exercises

5 Inferential Statistics II: Parametric Hypothesis Testing

5.1 Introduction

5.2 Hypothesis Testing

5.2.1 Types of Data for Hypothesis Tests

5.3 The t-distribution and Student's t-test

5.4 One Sample Student’s t-test

5.5 Confidence Intervals for Small Samples

5.6 Two Sample Student’s t-test

5.6.1 Paired Data

5.6.2 Unpaired Data

5.6.3 Paired vs. Unpaired t-test

5.7 1-tailed vs. 2-tailed Tests

5.8 Summary

5.9 Further Resources

5.10 Exercises

6 Inferential Statistics III: Nonparametric Hypothesis Testing

6.1 Introduction

6.2 Sign Test

6.3 Wilcoxon Signed Rank Test

6.4 Mann-Whitney U test

6.5 Chi Square Hypothesis Test for Categorical Variables

6.6 Summary

6.7 Further Resources

6.8 Exercises

7 Inferential Statistics IV: Choosing a Hypothesis Test

7.1 Introduction

7.2 Visual Methods to Investigate Whether Sample Fits a Normal

Distribution

7.3 Numerical Methods to Investigate Whether Sample Fits a Normal Distribution

7.3.1 Probability Plot Correlation Coefficient

7.3.2 Comparing the Skews

7.3.3 Z-values

7.3.4 Shapiro-Wilk Test

7.3.5 Chi Square Test for Normality

7.4 So Should We Use a Parametric or Nonparametric Test?

7.5 Does it Matter if We Use the Wrong Test?

7.6 Summary

7.7 Further Resources

7.8 Exercises

8 Inferential Statistics V: Multiple Hypothesis Testing

8.1 Introduction

8.2 Bonferroni’s Correction

8.3 Analysis of Variance (ANOVA)

8.3.1 One Way ANOVA

8.3.2 Two Way ANOVA

8.4 Summary

8.5 Further Resources

8.6 Exercises

9 Experimental Design and Sample Size Calculations

9.1 Introduction

9.2 Experimental and Observational Studies

9.3 Random and Systematic Error (Bias)

9.4 Methods to Reduce Random and Systematic Errors

9.4.1 Blocking (Matching) Test and Control Subjects

9.4.2 Blinding

9.4.3 Multiple Measurement

9.4.4 Randomisation

9.5 Sample Size and Power Calculations

9.5.1 Illustration Power Calculation for Single Sample t-test

9.5.2 Illustration of a Sample Size Calculation

9.5.3 Power and Sample Size Calculations in MATLAB

9.6 Summary

9.7 Further Resources

9.8 Exercises

9.9 Experimental Design Case Studies

10 Statistical Shape Models

10.1 Introduction

10.2 SSMs and Dimensionality Reduction

10.3 Forming an SSM

10.3.1 Parameterise the Shape

10.3.2 Align the Centroids

10.3.3 Compute the Mean Shape Vector

10.3.4 Compute the Covariance Matrix

10.3.5 Compute the Eigenvectors and Eigenvalues

10.4 Producing New Shapes from an SSM

10.5 Biomedical Applications of SSMs

10.6 Summary

10.7 Further Resources

10.8 Exercises

11 Case Study on Descriptive and Inferential Statistics

11.1 Introduction

11.2 Data

11.3 Part A: Measuring Myocardium Thickness

11.4 Part B: Intra-observer Variability

11.5 Part C: Sample Analysis

11.6 Summary

11.7 Further Exercises

- No. of pages: 274
- Language: English
- Edition: 1
- Published: May 18, 2019
- Imprint: Academic Press
- Paperback ISBN: 9780081029398
- eBook ISBN: 9780081029404

AK

Dr King has over 20 years of experience of teaching computing courses at university level. He is currently a Reader in the Biomedical Engineering department at King's College London. With Paul Aljabar, he designed and developed the Computer Programming module for Biomedical Engineering students upon which this book was based. The module has been running since 2014 and Andrew still co-organises and teaches on it. Between 2001-2005, Andrew worked as an Assistant Professor in the Computer Science department at Mekelle University in Ethiopia, and was responsible for curriculum development, and design and delivery of a number of computing modules. Andrew's research interests focus mainly on the use of machine learning and artificial intelligence techniques to tackle problems in medical imaging, with a special focus on dynamic imaging data, i.e. moving organs (Google Scholar: https://goo.gl/ZZGrGr, group web site: http://kclmmag.org).

Affiliations and expertise

Reader in Medical Image Analysis, School of Biomedical Engineering and Imaging Science, King's College London.RE

Dr. Robert Eckersley is a Senior Lecturer in the School of Biomedical Engineering and Imaging Sciences at King’s College London. His research interests include all aspects of the physics and engineering of medical ultrasound imaging. He has a long standing interest in the development of microbubble contrast agents for quantitative functional imaging with ultrasound. He is currently PI on an EPSRC grant investigating the development of super-resolution strategies for ultrasound imaging and is an co-investigator on the Wellcome and EPSRC funded iFind project http://www.ifindproject.com.

Affiliations and expertise

Senior Lecturer, Division of Imaging Sciences and Biomedical Engineering, King's College, London, UKRead *Statistics for Biomedical Engineers and Scientists* on ScienceDirect