Statistics for Biomedical Engineers and Scientists: How to Visualize and Analyze Data

By Andrew P. King and Robert Eckersley

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

• Language: English
• Publisher: Academic Press
• Release date: May 18, 2019
• ISBN: 9780081029404

Andrew P. King

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).

Book preview

Chapter 1

Descriptive Statistics I: Univariate Statistics

Abstract

This chapter provides a general introduction to the field of statistics. The difference between descriptive and inferential statistics is outlined, and the four different types of statistical data are introduced: categorical, ranked, discrete, and continuous. The distinction between univariate, bivariate, and multivariate statistics is also made. The rest of the chapter focuses on univariate descriptive statistics. Visualization techniques are introduced such as the dotplot, histogram, and bar chart. Three different measures of central tendency are described (mean, median, and mode), and the situations in which each is applicable are made clear. Similarly, two measures of variation are introduced: the standard deviation (and variance) and the interquartile range. An overview is given of techniques for visualizing these measures of central tendency and variation: the errorbar plot and the box plot. An introduction is provided to the use of MATLAB for univariate descriptive statistics.

Keywords

statistics; descriptive; univariate; categorical; ranked; discrete; continuous; dotplot; histogram; mean; median; mode; standard deviation; variance; interquartile range; errorbar; box plot; MATLAB

Learning Objectives

At the end of this chapter you should be able to:

O1.AExplain the reasons for using statistics

O1.BIdentify different data types

O1.CDisplay univariate statistics in MATLAB

O1.DCalculate measures of central tendency (mean, median, mode) by hand and using MATLAB

O1.ECalculate measures of variation (standard deviation, interquartile range) by hand and using MATLAB

O1.FDecide which statistic and display method is most appropriate for your data

1.1 Introduction

We are living in a world in which more and more data are being recorded. As digital and computing advances are made, more data are generated, and more sophisticated machines are developed to allow us to record, track and measure data. Data are recorded in almost every discipline (e.g. economics, health, business, politics, science and engineering), and extremely important decisions are taken based upon analyzing these data. Statistics is the study of how to correctly manipulate data to best inform such decisions. In particular, it helps us to deal with uncertainty in measurements. Outside of the world of pure mathematics, data will always contain errors and variation. Statistics enables us to decide when conclusions can be formed, despite our data containing variation. It can be thought of as mathematics meets the real world.

Statistics can be defined as the science of collecting and analyzing data. It can be split into two main categories:

■  Descriptive Statistics

■  Inferential Statistics

The relationship between descriptive and inferential statistics is illustrated in Fig. 1.1. We will use an example problem to help our explanation and introduce a number of statistical terms in italics along the way. Imagine that we have been given the task of finding the average height of first-year undergraduate students in the whole country. Height would be termed the variable that we aim to measure. The population under consideration would be every first-year undergraduate student in the country. To measure and record data from every such student would be very time consuming and costly; therefore we decide just to measure a sample, e.g. the height of first-year undergraduate students at a specific college or in a specific class.

Figure 1.1 Overview of how descriptive statistics, inferential statistics, population and sample are related.

Once we have gathered all of the height values from our sample, we need a method to easily make sense of the data. This is the role of descriptive statistics, which provides methods to allow us to summarize and describe our sample data. More specifically, descriptive statistics helps us to analyze and understand our results, and to clearly present our results to