Statistics for biomedical engineers and scientists : how to visualize and analyze data / Andrew P. King, Robert J. Eckersley.

Format:

Book

Author/Creator:

King, Andrew P., author.

Eckersley, Robert J., author.

Language:

English

Subjects (All):

Biomedical engineering.

Statistics.

Medical Laboratory Personnel.

Biomedical Engineering.

Statistics as Topic.

Medical Subjects:

Medical Laboratory Personnel.

Biomedical Engineering.

Statistics as Topic.

Physical Description:

1 online resource (276 pages)

Edition:

First edition.

Place of Publication:

London, United Kingdom : Academic Press, an imprint of Elsevier, [2019]

System Details:

text file

Summary:

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

Contents:

Front Cover

Statistics for Biomedical Engineers and Scientists

Copyright

Dedication

Contents

About the Authors

Preface

Aims and Motivation

Learning Objectives

How to Use This Book

Instructors

Students and Researchers

Web Site Resources

Contents and Organization

Acknowledgments

1 Descriptive Statistics I: Univariate Statistics

1.1 Introduction

1.2 Types of Statistical Data

1.3 Univariate Data Visualization

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 Which Measure of Central Tendency to Use?

1.5 Measures of Variation

1.5.1 Standard Deviation

1.5.2 Interquartile Range

1.5.3 Which Measure of Variation to Use?

1.6 Visualizing Measures of Variation

1.6.1 Visualizing Mean and Standard Deviation

1.6.2 Visualizing Median and IQR: The Box Plot

1.7 Summary

1.8 Using MATLAB for Univariate Descriptive Statistics

1.8.1 Visualization of Univariate Data

1.8.2 Calculating Measures of Central Tendency

1.8.3 Calculating Measures of Variation

1.8.4 Visualizing Measures of Variation

1.9 Exercises

2 Descriptive Statistics II: Bivariate and Multivariate Statistics

2.1 Introduction

2.2 Visualizing 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 Which Variable Should Go on Which Axis?

2.2.5 General Comments on Choice of Visualization

2.3 Measures of Variation

2.3.1 Covariance

2.3.2 Covariance Matrix

2.4 Correlation

2.4.1 Pearson's Correlation Coef cient

2.4.2 Spearman's Rank Correlation Coef cient

2.4.3 Which Measure of Correlation to Use?

2.5 Regression Analysis

2.5.1 Using the Best-Fit Line to Make Predictions.

2.5.2 Fitting Nonlinear Models

2.5.3 Fitting Higher-Order Polynomials

2.6 Bland-Altman Analysis

2.6.1 The Bland-Altman Plot

2.7 Summary

2.8 Descriptive Bivariate and Multivariate Statistics Using MATLAB

2.8.1 Visualizing Bivariate Data

2.8.2 Covariance

2.8.3 Correlation

2.8.4 Calculating Best-Fit Lines

2.8.5 Bland-Altman Analysis

2.9 Further Resources

2.10 Exercises

3 Descriptive Statistics III: ROC Analysis

3.1 Introduction

3.2 Notation

3.2.1 Sensitivity and Speci city

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 Summary

3.5 Using MATLAB for ROC Analysis

3.6 Further Resources

3.7 Exercises

4 Inferential Statistics I: Basic Concepts

4.1 Introduction

4.2 Notation

4.3 Probability

4.3.1 Probabilities of Single Events

4.3.2 Probabilities of Multiple Events

4.4 Probability Distributions

4.4.1 The Normal Distribution

4.5 Why the Normal Distribution Is so Important: The Central Limit Theorem

4.6 Standard Error of the Mean

4.7 Con dence Intervals of the Mean

4.8 Summary

4.9 Probability Distributions and Measures of Reliability Using MATLAB

4.9.1 Probability Distributions

4.9.2 Standard Error of the Mean

4.9.3 Con dence Interval of the Mean

4.10 Further Resources

4.11 Exercises

5 Inferential Statistics II: Parametric Hypothesis Testing

5.1 Introduction

5.2 Hypothesis Testing

5.3 Types of Data for Hypothesis Tests

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

5.5 One-Sample Student's t-test

5.6 Con dence Intervals for Small Samples

5.7 Two Sample Student's t-test

5.7.1 Paired Data

5.7.2 Unpaired Data

5.7.3 Paired vs. Unpaired t-test

5.8 1-tailed vs. 2-tailed Tests

5.9 Hypothesis Testing with Larger Sample Sizes: The z-test.

5.10 Summary

5.11 Parametric Hypothesis Testing Using MATLAB

5.11.1 Student's t-test

5.11.2 z-test

5.11.3 The t-distribution

5.12 Further Resources

5.13 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 Test

6.5.1 One-Sample Chi-Square Test

6.5.2 Two-Sample Chi-Square Test for Independence

6.6 Summary

6.7 Nonparametric Hypothesis Testing Using MATLAB

6.7.1 Sign Test

6.7.2 Wilcoxon Signed-Rank Test

6.7.3 Mann-Whitney U Test

6.7.4 Chi-Square Test

6.8 Further Resources

6.9 Exercises

7 Inferential Statistics IV: Choosing a Hypothesis Test

7.1 Introduction

7.2 Visual Methods to Investigate Whether a Sample Fits a Normal Distribution

7.2.1 Histograms

7.2.2 Quantile-Quantile Plots

7.3 Numerical Methods to Investigate Whether a Sample Fits a Normal Distribution

7.3.1 Probability Plot Correlation Coef cient

7.3.2 Skew Values

7.3.3 z-values

7.3.4 Shapiro-Wilk Test

7.3.5 Chi-Square Test for Normality

7.4 Should We Use a Parametric or Nonparametric Test?

7.5 Does It Matter if We Use the Wrong Test?

7.6 Summary

7.7 Assessing Data Distributions Using MATLAB

7.7.1 Visual Methods

7.7.2 Numerical Methods

7.8 Further Resources

7.9 Exercises

8 Inferential Statistics V: Multiple and Multivariate Hypothesis Testing

8.1 Introduction

8.2 Multiple Hypothesis Testing

8.2.1 Bonferroni's Correction

8.2.2 Analysis of Variance (ANOVA)

ANOVA With Unequal Sample Sizes

8.3 Multivariate Hypothesis Testing

8.3.1 Hotelling's T2 Test

Two Sample Hotelling's T2 Test

8.3.2 Multivariate Analysis of Variance (MANOVA)

8.4 Which Test Should We Use?

8.5 Summary.

8.6 Multiple and Multivariate Hypothesis Testing Using MATLAB

8.6.1 Bonferroni's Correction

8.6.2 ANOVA

8.6.3 Hotelling's T2 Test

8.6.4 MANOVA

8.7 Further Resources

8.8 Exercises

9 Experimental Design and Sample Size Calculations

9.1 Introduction

9.2 Experimental and Observational Studies

9.2.1 Observational Studies

9.2.2 Experimental Studies

9.2.3 Showing Cause-and-Effect

9.3 Random and Systematic Error (Bias)

9.4 Reducing 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 Randomization

9.5 Sample Size and Power Calculations

9.5.1 Illustration of a Power Calculation for a Single Sample t-test

9.5.2 Illustration of a Sample Size Calculation

9.6 Summary

9.7 Power and Sample Size Calculations Using MATLAB

9.7.1 Sample Size Calculations

9.7.2 Power Calculations

9.8 Further Resources

9.9 Exercises

10 Statistical Shape Models

10.1 Introduction

10.2 SSMs and Dimensionality Reduction

10.3 Forming an SSM

10.3.1 Parameterize 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 Statistical Shape Modeling Using MATLAB

10.8 Further Resources

10.9 Exercises

11 MATLAB Case Study on Descriptive and Inferential Statistics

11.1 Introduction

11.2 Data

11.3 Part A: Measuring Myocardium Thickness

11.4 Part B: Intraobserver Variability

11.5 Part C: Sample Analysis

11.6 Summary

A Statistical Tables

References

Index

Back Cover.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9780081029404

0081029403

9780081029398

008102939X

OCLC:

1125343529