Express it with frequencies video

Biogen-194255 december 2022

Statistical Information that can be easily understood

It will come as no surprise that individuals vary  in how comfortable they are when they have to face numbers. It will probably also not come as a surprise that statistical information is one of the domains in which we feel most uncomfortable.

According to a US study, one in five  adults did not know which of 1%, 5% or 10% risk is the highest.(1)

In a representative sample of US adults only one in four could correctly identify that 0.1 % was the same as 1 in 1 000.(2)

Risks and benefits of medical treatments are often explained by using statistical information. Therefore it is of  importance that we convey statistical information so that patients – and medical personnel – can assimilate it in a good way.

Given the difficulties we have with statistics, it is generally a good idea to also use words to describe risks, such as ”you are at a low risk  ….”, or “it is very likely that …” . However, the solution is not to replace numbers with words. People may feel more comfortable if they do not have to deal with numeric information, but when it comes to grasping probabilities, words are far less precise than numbers. People’s understanding of what a “low risk” means varies much more than their understanding of what 1 out of 10 000 does. The recommendation is to use both numeric information and a verbal description of it.(3)

One thing that has been shown to sometimes improve the understanding of risks is to use natural frequencies rather than percentages to communicate it.(4)

If a particular side effect happens in 3 out of 100 treated individuals, this is often more understandable than if we say that it happens to 3%. Individuals with low numeracy have been shown to be more worried about side effects when they are presented as frequencies compared to percentages.(5)

In some circumstances, frequencies will also help decision makers to better understand the context surrounding the decision to be made. This is because they sometimes make it easier to understand base rates – roughly how common something is in the group we are interested in.

A well known example comes from Gigerenzer and colleagues who have carefully investigated how both the general public and the medical community understand false positive tests.(6)

In the context of mammographies, we can imagine the base rate for breast cancer in women in their 40ies to be 1 % or 1 out of 100. Consider these two tasks:

  1. ” The probability of breast cancer is 1% for women at age forty who participate in routine screening. If a woman has breast cancer, the probability is 80% that she will get a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she will also get a positive mammography. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
  2. ”10 out of every 1,000 women at age forty who participate in routine screening have breast cancer. 8 of those 10 women with breast cancer would have shown up with a positive mammography. 95 out of the other 990 women without breast cancer will also get a positive mammography. Here is a new representative sample of women at age forty who got a positive mammography in routine screening. How many of these women do you expect to actually have breast cancer? __ out of ___”.

When you ask women from the relevant age groups or physicians administrating these tests about how likely it is that a woman with a positive mammogram will have breast cancer, answers differ depending on whether they received formulation 1 or 2 above.

In general, estimations are more correct when the numbers are given as frequencies. This is because they seem to give a better understanding of the fact that false positives will be quite common given the low base rate of breast cancer in this age group.


(Picture from Gigerenzer and Hoffrage 1995)(6)

One of the  advantages of using frequencies is that they draw attention to the base rate. If 10 women out of 1000 taking a mammogram have breast cancer we will also have 990 women without breast cancer taking the mammogram. And even if the risk of a falsely positive mammogram is low in itself, the size difference in numbers between the group with and the group without breast cancer will magnify the probability that a positive mammogram falsely positive.

1, Lipkus, I.M., Samsa, G., & Rimer, B.K. (2001). General performance on a numeracy scale among highly educated samples. Medical Decision Making, 21, 37–44.
2, Schwartz, L.M., Woloshin, S., Black, W.C., & Welch, H.G. (1997). The role of numeracy in understanding the benefit of screening mammography. Annals of Internal Medicine, 127, 966–972.
3, Fagerlin, Arbor, Peters (2009). Qualitative information. In Fischhoff, Brewer and Downs (eds). Communicating risks and benefits: An evidence-based user’s guide. FDA Us Department of Health and Human Services, Food and Drug Administration.
4, Hoffrage & Gigerenzer (1998) Using natural frequencies to improve diagnostic inferences. Academic Medicine, 73(5): 538-540.
5, Peters, Hart, Fraenkel (2010). Informing patients: The influence of numeracy, framing and format of side-effect information on risk perceptions. Medical Decision Making. 3: 432-436.
6, Gigerenzer & Hoffrage (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102 (4), 684-704.


Biogen-194057 december 2022
Senast uppdaterad: 2022-12-21