If you think numeracy is a branch of astrology dealing with numbers and divining the future, you’re wrong. Also known as quantitative literacy (QL) and quantitative reasoning (QR), numeracy refers to an individual’s ability to understand quantitative issues and analyze arguments supported by quantitative data.
In an effort to explain numeracy, we consulted with two faculty experts at CU Denver—Lucy Dwight, PhD, in the School of Public Affairs and Stephanie Santorico, PhD, in the Department of Mathematical and Statistical Sciences. Simply put, “It’s the basic ability to critically assess information that relies on numerical data,” said Dwight, who teaches quantitative methods. Santorico, a statistician, offers this definition: “It is being able to read quantitative summaries and critically reflect on what they mean.”
Numbers Don’t Lie—Or Do They?
Contrary to the popular expression, numbers can lie. Santorico points to a classic statistics book that breaks down all the ways numbers can lie: How to Lie with Statistics by Darrell Huff. “There is terror in numbers,” Huff famously said. His book seeks to break people’s blind acceptance of numerical truth.
Questioning statistics is something that Santorico also teaches to her students. “Don’t believe them on face value,” she said. “Think about how the data was collected, what was measured, and what was not measured.”
Dwight, a sociologist by training, primarily focuses on statistics and research methods. She argues that quantitative literacy is important for everyone. “We’re bombarded with data in our everyday living as citizens—election results, polling, information about vaccines,” she said. “Having an understanding of data is a really important skill, even for those who will never be statisticians. Just having that literacy is key.”
Correlation, Causation, Sharks, and Ice Cream
When analyzing data, consider everything. Who collected the data? What does the data measure? Who does the data represent? How is the data interpreted? Who funded the study?
Even when people using data don’t intend to lie, their findings can be inaccurate. “Historically, studies in human genetics have been done mostly on white populations and for a long time it was only men,” Santorico explained. “Who does the data represent?”
Dwight brings up other potential problems with numbers. “The known uncertainty of using a sample to represent a population, confirmation bias, the contingent nature of science,” she said. “Most of what we know is going through a process of revision. Any one study is likely not going to reveal truth.”
Statisticians, mathematicians, journalists, and comedians have all illustrated how numbers can be wrong using cartoons and graphs. Santorico provided some salient examples from the Spurious Correlations website. The website graphs data that correlate but have no causal relationship. For example, the number of ice cream cones sold correlates with the number of sharks attacks: when ice cream sales increase, shark attacks increase—but eating ice cream does not cause more shark attacks!
Statistics Don’t Lie—But Liars Use Statistics
The more problematic issue is when people use numbers to lie intentionally. Lying with numbers can happen in many different ways, but there are a few common tactics. One popular technique is often practiced by political pollsters—using a biased sample. “If you want to talk about election, you need a random sample,” Santorico said. “If you only poll people in Alabama, then it’s not reflective of the country.”
Using a very small sample is another way to lie with numbers. If you poll 10 dentists, nine of whom like a certain brand of toothpaste, you can say 90% of dentists recommend X toothpaste. Beware of percentages if the actual numbers behind those percentages are not provided.
Another deceptive technique is to change the way you present numbers. Santorico provided a simple example: “If you have a partial mutation, your risk of a heart attack is three times higher. As soon as you say that, most people think it’s really bad. If your risk is 1 out of a million, the risk for people with a partial mutation is 3 out of a million—not so bad.”
Numeracy is an important skill, especially in a network society. Numbers are everywhere—news, social media, website analytics, data mining, polls, and ads. “We’re teaching our students to be critical thinkers,” Santorico said. “They need to think about how the data was collected.”