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Be clear, be trustworthy

In some situations – for example when you are communicating research on COVID-19, or climate science – trust can be an issue. People may have strong prior beliefs about the subject and recent research has shown that people trust balanced information more.

You cannot expect to be trusted by your audience – instead you have to be trustworthy. But how do you do this? David Spiegelhalter and his colleagues from the Winton Centre for Risk and Evidence Communication developed Five rules for evidence communication:

This is part of our practical writing guide - find out more here!
  • Inform, not persuade
  • Balance, but not false balance
  • Disclose uncertainties
  • State evidence quality
  • Inoculate against misinformation

As David told us in March 2020:

"Trustworthiness has been characterised quite well by Onora O'Neill, a philosopher of Kant. She describes what she calls intelligent transparency. This involves making sure that information is accessible, which means repeating it again and again making sure it's available from many sources. The information has got to be comprehensible, people have to understand it and you should check that they are getting the right impression. And the information has to be useable — answer people's questions and concerns: you have got to listen."

"The final and crucial point, which people fall down on all the time, is that the information must be assessible: you shouldn't just have to take it on trust. Most people will take it on trust, but there are people out there who know a lot about what is going on, and these people should be able to check your working."

In January 2023, the Newton Gateway to Mathematics organised the event Communicating Mathematics for the Public, which gave a wealth of information about communicating important ideas clearly, accessibly and in a trustworthy way. You can watch many of the talks from the event online, but here are some particularly useful tips.

Statistics and uncertainty

Based on the talk by Mark Pont from the Office for Statistics Regulation.

Statistics aren't certain facts but are often presented as if they were. You want to be clear on the caveats but you don't want to undermine trust.

Always ask yourself, or the researchers you are working with: are there uncertainties involved in the mathematical or scientific research that should be highlighted to the reader?

Communicating uncertainty is hard, but it is very important to be honest about the limitations of any statistics or results. Here are some recommendations from Mark's talk, and from a very useful review on presenting uncertainty, produced by Full Fact in 2021:

  • Be transparent about the quality and limitations of the data.

  • Be specific about what exactly is uncertain – for example is the uncertainty due to insufficient data? The purpose of presenting uncertainty is to avoid your audience drawing misleading conclusions, not to make them think that nothing can be trusted.

  • Not every number needs to have the word "estimate" around it. Intersperse this occasionally, to clarify and give the narrative that these numbers are not absolute facts. Rounding numbers is also helpful as it avoids spurious accuracy.

  • Indicate uncertainty in existing data using numerical ranges in brackets, after the main value. For example, say "unemployment is estimated at 3.9% (between 3.7% and 4.1%)" at least when you introduce the figure.

  • In case of future predictions, use verbal expressions to indicate the general direction of travel, but supplement these with numerical probability ranges, and wherever possible access to underlying data. Do say, for instance, "global warming is likely (66% chance) to reach 1.5°C between 2030 and 2052 if it continues to increase at the current rate".

  • Take care when using large numbers and jargon. If jargon is necessary, remember to explain it. When using large numbers, remember that the difference between 1 million and 1 billion is clearer if the latter is expressed as 1,000 million.

Charts and visualisations

Based on the talk by Martin Ralphs from the Office for National Statistics.

  • Simple is (usually) better than complex. Charts should work on their own, without having to read the stuff around it. This is particularly useful if someone is likely to reuse your chart or graphic elsewhere.

  • One main message per visual: you only have 10-15 seconds to get the message across.

  • Have a good descriptive title that conveys your main message. If a statistical description is necessary it could sit beneath this main title, or be in the caption.

  • Try to bring uncertainty into any graphics: Uncertainty is your friend in statistics. Try to embrace it and embed it.

  • Accessibility really matters.


Based on the talk by Hannah Thomas from the Government Analysis Function.

Digital accessibility is all about making content published online easy to access and use for all users, regardless of impairment, medical condition or disability.

  • All non-text content should have a text alternative that serves the equivalent purpose. For example, what is the message of your chart? Answering this question will make your chart better. Include a fully descriptive text alternative directly under your chart, before information on sources, notes, etc.

  • Do not use colour alone to communicate a message. If you can't differentiate between the elements in your charts legend, you won't be able to differentiate between the categories of your data.

  • Use 3 to 1 contrast ratio for adjacent colour elements in visualisations.

Here is some guidance specifically on the use of colour and on accessibility more generally.

Useful resources

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This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics. The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

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