How to use statistics in persuasive writing

Turn numbers into people and otherwise reframe the data

Which is more dangerous? A disease that kills 1,286 out of every 10,000 people it strikes? Or one that kills 12.86% of its victims?

The former is about 20% more dangerous, said a group of college students, according to an article in Money magazine. In fact, 1,286 out of 10,000 is just a different expression of 12.86%.

To make statistics more compelling, make them more emotional.

When writing about people, use whole numbers instead of percentages.

Here are four other things to consider when choosing a frame for your data:

1. Choose a positive frame.

Which steak tastes better?

75% lean	25% fat
Tastes great, more filling People would rather buy steak that’s 75% lean than steak that’s 25% fat — even though it’s the same piece of meat.

People in one study said they were more likely to buy the 75% lean steak rather than the 25% fat steak, even though they are the exact same steak (Johnson and Levin, 1985; Levin et al., 1985).

Call it the framing effect bias: People react differently to an option or idea based on how it is presented.

So frame your products and positively instead of negatively.

You might, for instance, express odds of survival after one month of surgery instead of odds of dying.

When I wrote a charitable giving annual report, my clients were devastated to learn that 25% of Kansas City households and 21% of local businesses contributed nothing to charity. I wrote:

Because it’s true. And it’s a better frame.

2. Tap the power of percentages.

How long would you be willing to walk to avoid a 25% Lyft or Uber fare increase? What about a 1.25x increase?

Some 38% of people were willing to walk to avoid the 1.25x fare, according to a survey by Irrational Labs and Common Cents Lab. But 44% were will to walk to avoid the 25% increase — even though these are exactly the same amount.

But wait! There’s more! People were more willing to walk 5 minutes to avoid a 25% increase vs. a 1.75x fare — even though 1.75 is 50 percentage points more than 25%.

So use absolute numbers for increases. But when offering discounts, stick with percentages.

3. Use absolute frequencies instead of percentages to express risk.

Percentages may misrepresent risk, according to two European researchers.

That’s because most people believe the quoted percentage refers to people like themselves — say, those who are considering a medical procedure. In fact, in health care, the percentages often refer to a much smaller group, such as people who die with or without a procedure.

Let’s say, for instance, that we tell women over 50 that a mammogram reduces their risk of dying from breast cancer by 25%. That number is misleading. It might actually represent an absolute risk reduction of only 1 in 1,000.

Instead, you might say, “Of 1,000 women who do not have mammograms, an average of four will die from breast cancer within 10 years. Of 1,000 women who do have mammograms, an average of three will die from breast cancer within 10 years.”

The percentage disguises the fact that relatively few women die from breast cancer and that mammograms don’t detect breast cancer in all women who have it.

Solution: Use absolute frequencies instead of relative percentages to communicate risk.

4. Use like forms.

Which is bigger: three-quarters, 80% or seven out of 10? How much bigger?

Don’t make readers perform mathematical backflips to follow the numbers in your copy. Don’t compare apples to watermelons.

When you compare numbers, put them all in the same form.

In this case: 75%, 80% and 70%.

How are you making sure your stats support your message instead of making your readers’ eyes glaze over?

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Sources: I.P. Levin and G.J. Gaeth, “How consumers are affected by the framing of attribute information before and after consuming the product,” Journal of Consumer Research, No. 15, 1988, pp. 374-378

Gerd Gigerenzer and Adrian Edwards, “Simple Tools for Understanding Risks: From Innumeracy to Insight,” British Medical Journal, vol. 327, no. 7417, Sept. 27, 2003, pp. 741-744

TJ Larkin & Sandar Larkin, “Communicating Risk in Health Care,” Larkin Page, #27, February 2006

Amos Tversky and Daniel Kahneman, “The Framing of Decisions and the Psychology of Choice,” Science, Vol. 211, 30, January 1981