# How People Approach Numbers, Statistics, and Risks

DOI: 10.4018/978-1-4666-0152-9.ch009
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## Abstract

The previous chapter dealt with how people interpret graphics. This chapter examines how people interpret numbers, typically given as probabilities or risks (Figure 1). In a majority of HII situations, numbers are essential for gaining a full understanding of the situation. This chapter covers how people react to numbers. Since many people have a high literacy level but a low numeracy (number literacy), design teams must understand how people interact with and interpret numbers as it is essential to understanding how it affects the communication process.
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## Background

Numerical quantities focus on expected values, graphical summaries on unexpected values. —John Tukey

Figure 1.

HII model – Approaching numbers and statistics

This chapter looks at:

• Numeracy and Literacy: Explains the definitions of numeracy and literacy and how they affect understanding numerical data.

• Interpretation of Numbers: Discusses the basic issues involved in interpreting quantitative data.

• Causes of Misinterpreting Numbers: Most quantitative data is presented in the form of statistical data, but most people have trouble understanding it. Discusses how people interpret and misinterpret statistics.

• Risk Perception: Risk information can be presented in different ways and people’s interpretation of each way can change their perception of the risk.

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## Introduction

A significant portion of technical material relevant to HII contains numbers which must be effectively communicated to people. Without some level of experience or training, people are quite poor at comprehending how the numbers apply to their situation. Numbers typically get presented as an abstraction (3 of 10 drivers will have a major accident within 5 years), and people are not good at cognitively handling abstraction. Likewise, they are not good at dealing with big numbers (a 10 billion dollar government program) or in comprehending probabilities (a drug has a 15% chance of a side effect). In addition, people tend to see causal relationships within data where a relationship does not exist, leading to actions such as wearing lucky hats.

A large quantity of HII information contains data which describes statistics, probabilities, or risks. Examples include healthcare information containing effectiveness of treatment options, financial investment information, results of a study for constructing a new building in a city, or proposals for hiring new employees. Unfortunately, people have a difficult time fully comprehending information presented as a probability. Healthcare research has found that patients find it difficult to adequately comprehend risk information (Evans et al, 1994; Lerman, Kash, & Stefanek, 1994). For example, given a range of risks for heart disease, people consistently place themselves at the low end, but believe other people are at high risk. However, making informed decisions about lifestyle and treatment options requires that they understand and effectively use that risk information. An HII goal is to effectively communicate that numerical information.

Statistics and probability theory are mathematical models that describe the uncertainties in the world. Many risk experts promote quantitative probabilities because they believe that numbers are more precise and convey more information to the public than qualitative risk statements (Monahan & Steadman, 1996; Murphy & Winkler, 1971). How people perceive the results and interpret the uncertainties frequently differ from what the mathematical model itself predicts. This fact was vividly portrayed by Schlesinger in his testimony to the Senate Subcommittee on National Security and International Operations:

What happened in Vietnam is that we were simply drowned in statistics; we were drowned in information. A very small proportion of this information was adequately analyzed. We would have been “ much better off to have a much smaller take of information and to have done a better job of interpreting what that information meant (Schlesinger, 1970, p. 482).

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