# Using Visual Reasoning to Understand Numbers

Reading time: 3 min

Hunter Whitney’s book Data Insights: New Ways to Visualize and Make Sense of Data was recently published. It offers multidisciplinary perspectives and useful information about how visualizations can open your eyes to data. It paints the picture using a diverse blend of original illustrations and real-world examples, both classical and cutting-edge. Even under the best of circumstances, making sense of data and statistics can be hard for many of us. When the numbers involve the potentially life-altering probability of having a serious disease, their true meaning can be both profoundly important and utterly mystifying. Further complicating matters is the fact that it can be hard for many of us to track all the relevant comparisons that are included in the calculations of the final key numbers. A cascade of varying comparisons and re-calculations flows into the final results. Can visualizations make it easier for doctors and patients to better understand and trace exactly what is involved in order to have discussions that more closely reflect reality? For illustrative purposes, let’s say the probability of breast cancer is 1% for a woman at age 40 who participates in routine screening. If a woman has breast cancer, the probability is 80% that she will have a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she, too, will have a positive mammography.

## A Positive Result on a Medical Test

Example 1: A woman in this age group had a positive mammography on a routine screening. What is the probability that she has breast cancer? Patients and doctors alike can have a difficult time making sense of these words and numbers. The individual terms and figures themselves may be easy to grasp; it is when they are combined in various ways that their meanings can begin to unravel.  Additionally, physicians may not pay enough attention to the subtle nuances of the various questions that might be asked and the resulting answers. What is the best way to frame a response based on available information that will be most meaningful and relevant to the patient? To help determine the probability that Nancy actually has breast cancer, consider the data in the table below.

 Has Breast Cancer Doesn’t Have Breast Cancer Total Positive Mammogram (a) 8 (b) 95 103 Negative Mammogram (c) 2 (d) 895 897 Total 10 990 1000

Language, Numbers, Calculations How might the data in the table be represented in a more understandable form?

## A Negative Result on a Medical Test

Whether it’s positive or negative, a test result is not always definitive. Depending the unique history of the patient involved, gaining more understating of the nature of that uncertainty – even for a negative result – can still be very important. Example 2: What is the probability of breast cancer for a woman over 40 who tests negative? If a woman has a negative mammography, the probability that she has breast cancer is only 0.22%.

It can be very difficult for just about anybody to track the numbers and shifting comparisons that need to be factored into many kinds of risk calculations. By using simple forms of visual shorthand, doctors and patients alike, can get a clearer, more representative picture of what the risks truly are.