# Chapter 1: Introduction to quantitative literacy

Quantitative literacy can be defined as the ability to interpret and communicate numbers and mathematical information throughout everyday life. Whether you are a scientist or not, you will be continuously confronted with claims based on quantitative data, sometimes regarding medical treatments and diagnostics but also in relation to the environment, politics, economics, and other aspects of life. Therefore, everybody needs to be able to interpret quantitative information to make informed decisions.

Quantitative literacy is especially important for students of biomedicine. Modern biomedicine is evidence based, which means fundamentally it is underpinned by quantitative data. This is becoming increasingly important as recent technological advances have led to biomedicine (and biology in general) becoming more ‘data driven’ and hence a more quantitative and predictive science. Think about the advances in DNA sequencing driving personalised medicine and then imagine the sorts of skills that will be in demand to navigate this kind of data in the future.

It is normal for many students to initially find aspects of mathematics and quantitative literacy difficult and therefore a source of anxiety. This resource, *Foundations of Biomedical Science*, and the problems within, are designed to help reduce this anxiety by targeting the skills you will need for later stages of your studies and beyond. These skills will help you interpret quantitative data and understand basic mathematical concepts and be able to apply them to authentic biomedical problems. However, your overarching goal here should be to habitually question any quantitative data you come across and to use the skills you will learn in this resource to make informed judgements about its veracity.

### Why should you care about quantitative literacy?

Imagine the following scenario.

Before beginning a new job, you are sent for a mandatory health check. The health check is comprehensive and includes tests for some rare diseases. One of the diseases is found in 1 in 10,000 people but is incredibly deadly. Let’s call it Disease X.

In your follow-up appointment the doctor tells you that you have tested positive for Disease X.

This is bad news, right?

Perhaps.

But first we need to know how accurate the test is.

The doctor tells you that the test is 99% accurate.

Okay, so now this is really bad news, right?

Well, maybe. But what does she mean by ‘accurate’?

When we say a test is 99% accurate we mean this is the chance that if you have Disease X you will test positive, not that if you test positive there is a 99% chance that you have disease. You will learn later that using ‘accuracy’ to describe the effectiveness of a diagnostic test is a bad idea!

So, what are your chances of having Disease X?

Suppose 1 million people are tested for Disease X. Given that the prevalence is 1 in 10,000 people, then on average 100 out of the 1 million will have the disease. This means that out of the 1 million, 999,900 people do not have the disease. Since the test is only 99% accurate, 99 out of the 100 people with the disease will test positive, and 1 of the 100 with the disease will test negative but will still have the disease.

However, the accuracy of 99% also means that out of the 999,900 people that do not have the disease, 9,999 will test positive (1% of 999,900 = 0.01 x 999,900 = 9,999). Therefore, even though you tested positive you actually only have about a 1% chance (99 / (99 + 9,999) × 100) of actually having the disease.

Those odds suddenly look much better!

Having some quantitative skills will not just help with your grades – it will also provide you with some useful tools for questioning the truth and navigating life in general.