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How Good Are We With Numbers?

Numeracy in medical students
Numeracy in patients

Bandolier 103 featured a study that looked at literacy attainments in rheumatoid arthritis patients. Literacy is especially important because these patients often have complicated medication regimens. The study found that one patient in six would, at best, struggle with patient education material, and one in 20 could not read prescription labels. We now have some studies looking at numeracy, both in medical students and patients.

But first we need to have some understanding of what is numeracy. The dictionary definition is one of competence in mathematical skills to allow us to cope with everyday life, but also includes understanding mathematical terms from graphs, charts, or tables. Fortunately health numeracy has been provided with a set of definitions [1].

Various levels of health numeracy have been defined (Table 1). The four levels start at the most basic, with statistical numeracy being that degree of numeracy that we would expect from most doctors, and quite a lot of other health professionals.

Table 1: Some definitions of health numeracy

Concept Definition
Health numeracy The degree to which individuals have the capacity to access, process, interpret, communicate, and act on numerical, quantitative, graphical, biostatistical, and probabilistic health information needed to make effective health decisions
Basic numeracy Having sufficient skills to identify numbers, and to make sense of quantitative data requiring no manipulation of numbers. An example would be identifying the correct numbver of pills to be taken, data and time of appointments, using a phone book
Computational numeracy The ability to count, quantify, compute, and otherwise iuse simple manipulation of numbers, quantities, items, or visual elements in a health context so as to function in everyday situations. An example would be using nutritional labels correctly
Analytical numeracy This involves the ability to make sense of information, as well as higher functions like inference, estimation, proprtions, percentages, frequencies, and equivalent situations. Information may be from multiple sources, and an example would be deterimining whether an analytical result was within the normal range, or understanding graphs
Statistical numeracy An understanding of basic biostatistics involving probability statements, skills to compare different scales (Probability, proportion, percent), to critically analyse quantitative information like life expectancy or risk, and understanding concepts like randomisation and blinding. An example would be making choices between treatments based on standard outcomes of relative or absolute risk

Numeracy in medical students

One way of measuring numeracy is to ask a few simple maths questions, and see how many correct answers you get. It does not need to be an intensive examination, and one set of questions used in studies of medical students and patients is shown in Table 2 [2]. Most of us would expect to get the right answers to these three questions, on simple probability, and converting frequency to percentages and back again. The level is that of basic and computational numeracy in Table 1.

Table 2: Three simple questions to test numeracy

Correct answer
Imagine that we flip a coin 1000 times.
What is your best guess about how many times the coin would come up heads?
1000 x 0.5
In the lottery, the chance of winning a prize is 1%.
What is your best guess about how many people would win a prize if 1000 people each buy a single ticket to the lottery?
1/100 = X/1000
In the publishing sweepstake, the chances of winning a car is 1 in 1000.
What percent of tickets to the publishing sweepstake wins a car?
1/1000 = X/100

These questions were answered by 62 first-year medical students at the University of North Carolina at Chapel Hill medical school who attended a risk-communication seminar. Most students answered all three questions correctly, but 5% (1 in 20) answered only one or none correctly (Figure 1).

Figure 1: Numeracy as measured in medical students and patients

Students were also given information about treatment choices, with results presented in different ways (relative risk reduction, absolute risk reduction, number needed to treat, and a combination). Most students (90%) correctly stated which drug worked better (comparative answer), but only 61% could work out the quantitative answer. For both, there was a strong relationship with being able to answer the simple maths questions correctly (Figure 2).

Figure 2: Students' interpretation of quantitative information according to their correct answers to numeracy questions

Numeracy in patients

The same research group performed the same tests in 257 patients aged 50 to 80 years attending for health care at an internal medicine clinic [3]. The results for numeracy are in Figure 1, and show that most patients could answer only one (30%) or no (41%) numeracy questions correctly. It was also true that whatever way information was presented to them, only 40-60% were able to determine which of two treatments was better, but fewer than 20% (1 in 5) were able to work out the quantitative difference.


There is not a huge literature on numeracy, but it is likely to be important, and at least as important as literacy. For instance, a single observational study [4] showed that patients older than 50 years attending anticoagulation management units had significantly poorer control of INR when they had low numeracy skills, while low literacy made no difference.

But numeracy and literacy have to be taken together. A detailed paper too difficult to précis [5] asked professionals and public about ways of expressing results relating to prenatal diagnosis and chromosome abnormalities. There were huge differences in the way people responded to the same information. For instance, when asked which of 5% or 1 in 20 sounded bigger, 81% thought 1 in 20 sounded bigger. That paper is certainly worth a read for anyone teaching communication skills.

The bottom line, though, is that on limited information, we can identify that many patients and some professionals have problems with numbers. That puts even more heat on trying to explain those numbers in ways that people can understand.


  1. AL Golbeck et al. A definition and operational framework for health numeracy. American Journal of Preventive Medicine 2005 29: 375-376.
  2. SL Sheridan, M Pignone. Numeracy and the medical student's ability to interpret data. Effective Clinical Practice 2002 5: 35-40.
  3. SL Sheridan et al. A randomized comparison of patients' understanding of number needed to treat and other common risk reduction formats. Journal of General Internal Medicine 2003 18: 884-892.
  4. CA Estrada et al. Literacy and numeracy skills and anticoagulant control. American Journal of Medical Science 2004 328: 88-93.
  5. L Abramsky, O Fletcher. Interpreting information: what is said, what is heard – a questionnaire study of health professionals and members of the public. Prenatal Diagnosis 2002 22: 1188-1194.

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