1.7

## The University of Sheffield

Skip to 0 minutes and 9 secondsHaving thought already about different kinds of big numbers, let's now think about another kind of number that might sound big or small, changes in things. If I say that there's half as much rice in my house today as there was yesterday, then how dramatic that is depends on how much rice we're talking about. If there's half as much because there wasn't that much to begin with and I ate some, that's different from if my house is used as a rice store that was targeted by rice thieves overnight. So what are some of the different ways that the media reports changes in things and differences between things?

Skip to 0 minutes and 45 secondsLet's go back to the earlier example of NATO members spending 2% of GDP on defence. This became a talking point in the UK in June 2015, when a research briefing published by the House of Commons Library projected that defence spending would fall to 1.87% of GDP by the 2015-16 financial year. It's possible to present these numbers in a number of different ways, depending on the story you want to tell. You could say that defence spending fell as a fraction of GDP by 0.13% between the financial years 2014-15 and 2015-16. This would reflect the percentage point change or absolute change. Alternatively, you could say that defence spending fell by 6.5% over the same period. This would reflect the relative change.

Skip to 1 minute and 43 secondsLooking forward to the figures projected for the future does something similar. If you look at fraction of GDP spent on defence, it looks flat. But if you look at projected spend, it's a different story. This is an increase in spending to the tune of £4.162 billion since 2014-15. And as a relative increase in money, not in fraction of GDP, it represents an increase of 12%. So changes can look very different according to how you report them. So, when we're comparing change over time, it's important to understand the difference between percentage increases and percentage point increases, and to read reports in the media carefully, as they often confuse the two. But not all comparisons involve a change over time.

Skip to 2 minutes and 32 secondsOthers concern risk factors. If you start a particular behaviour, how much does that increase your risk of particular outcomes.

Skip to 2 minutes and 41 secondsIn the case of the relationship between smoking and cancer, for example, the results are similarly striking regardless of how it's described. In other cases, though, the ways in which data represented by the media heavily influence how dramatic differences appear to be. Cancer Research UK draws attention to headlines that emerged in the UK press in 2012, which reported that having had several CT scans as a child could make you three times as likely to develop leukaemia or brain cancer as an adult. Three times as likely to develop leukaemia or brain cancer is equivalent to 200% increased chance of developing leukaemia or brain cancer.

Skip to 3 minutes and 23 secondsHowever, it's difficult to interpret how serious this is without knowing how many people develop leukaemia or brain cancer. In fact, the chances of developing these cancers are very small. 0.4 children out of every 10,000 children develop brain tumours, and 0.6 children out of every 10,000 develop leukaemia. So this increased risk can also be reported as one additional case of brain cancer and one additional case of leukaemia for every 10,000. Having addressed earlier how percentages only tell part of the story without the numbers they're referring to, this is even more strongly the case when we look at differences between percentages rather than absolute differences, or differences with a common baseline, as in the case of risk.

Skip to 4 minutes and 13 secondsMedia outlets often only tell part of the story and use this to their advantage, making big numbers seem smaller than they are and small numbers seem bigger than they are. In the next step, we'll go into more detail on each of these terms.

# Reporting change and risk

Another way that the media uses data is to report change and risk - how much has something increased or decreased? If you start a particular behaviour, how much does that increase your risk of a particular outcome?

As we saw earlier, when numbers are stripped of context, it can be difficult to tell whether they are as dramatic as they seem. This is even more strongly the case when we look at differences between percentages or differences without a common baseline, as in the case of risk.

In this video, Mark explains the difference between percentage increases and percentage point increases and between absolute and relative risk. Don’t worry if you don’t quite catch these concepts first time round, we’ll revisit them in the next step to make sure you’re following.

Which of these techniques do you encounter most frequently? Are any of them new to you?

### References

Rob Page (2015) Defence Expenditure - Nato 2% Target. House of Commons Library Research Briefing online [Accessed 3 Feb. 2016]

Sarah Williams (2013) Absolute versus relative risk - making sense of media stories. Cancer Research UK Science Blog online [Accessed 3 Feb. 2016]