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Too many digits: the presentation of numerical data
  1. T J Cole
  1. Correspondence to Professor T J Cole, Population, Policy and Practice Programme, UCL Institute of Child Health, London WC1N 1EH, UK; tim.cole{at}ucl.ac.uk

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Emperor Joseph II: My dear young man, don't take it too hard. Your work is ingenious. It's quality work. And there are simply too many notes, that's all. Just cut a few and it will be perfect.Mozart: Which few did you have in mind, Majesty?Emperor Joseph II: Well, there it is.

Quotation from the film Amadeus (1984)

As a statistical reviewer for Archives and BMJ I am interested in the presentation of numerical data.1 It concerns me that numbers are often reported to excessive precision, because too many digits can swamp the reader, overcomplicate the story and obscure the message.

A number's precision relates to its decimal places or significant figures (or as preferred here, significant digits). The number of decimal places is the number of digits to the right of the decimal point, while the number of significant digits is the number of all digits ignoring the decimal point, and ignoring all leading zeros and some trailing zeros (for a fuller definition see ‘significant figures’ on Wikipedia).

Ideally data should be rounded appropriately, not too much and not too little (one might call it Goldilocks rounding).2 The European Association of Science Editors guidelines include the useful rule of thumb: “numbers should be given in (sic) 2–3 effective digits”.3

Take as an example the odds ratio (OR) of 22.68 (95% CI 7.51 to 73.67) comparing beta mimetics with placebo for side effects requiring a change of medication.4 Its two decimal places and four significant digits are excessive when the effect size and confidence interval (CI) are so large. Reporting it rounded to two significant digits, as 23 (7.5 to 74), or even as 23 (8 to 70), with one …

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