Risk (Higher)
Risk is the probability of an unwanted event happening within a group, compared between groups using the absolute risk difference (the gap between two percentages) or the relative risk (how many times more likely one group is). Higher tier GCSE Statistics questions often require both measures and an explanation of why they can give very different impressions of how serious a change in risk really is.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find the risk for each group by dividing the number of people affected by the total number in that group, then convert to a percentage if needed.
- Find the absolute risk difference by subtracting the smaller risk from the larger risk, in percentage points.
- Find the relative risk by dividing the larger risk by the smaller risk.
- State the relative risk as 'X times as likely' and the absolute risk difference as 'X percentage points higher or lower'.
- Recognise that a large relative risk can come from a small absolute risk difference when both risks are small, so quote both figures when comparing.
- Interpret the risk in context, without claiming the factor being studied definitely causes the difference.
Worked example
A new medicine's side effect occurs in 2 out of 1000 patients who take it, compared with 1 out of 1000 patients who take a placebo. (a) Find the risk of the side effect for each group as a percentage. (b) Find the relative risk of the side effect for patients taking the medicine compared with the placebo. (c) Find the absolute risk difference. (d) Comment on the difference between your answers to (b) and (c).
- Medicine risk = 2/1000 = 0.002 = 0.2%.
- Placebo risk = 1/1000 = 0.001 = 0.1%.
- Relative risk = 0.2% divided by 0.1% = 2, so patients taking the medicine are 2 times as likely to have the side effect.
- Absolute risk difference = 0.2% - 0.1% = 0.1 percentage points.
- Final answer: the medicine doubles the relative risk (2 times as likely), but the absolute risk only increases by 0.1 percentage points, showing the actual increase in risk to any one patient is very small.
Practice questions
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Q1Out of 800 patients given Drug A, 16 experienced nausea. Find the risk of nausea as a percentage.Show answer
Answer: 2% (16/800 = 0.02).
Q2Out of 800 patients given a placebo, 8 experienced nausea. Find the risk of nausea as a percentage.Show answer
Answer: 1% (8/800 = 0.01).
Q3Using your answers to the previous two questions, find the relative risk of nausea for Drug A compared with the placebo.Show answer
Answer: 2 (2% divided by 1%).
Q4Using the same data, find the absolute risk difference between Drug A and the placebo.Show answer
Answer: 1 percentage point (2% - 1%).
Q5A condition affects 4 in 10000 people who take Treatment X and 2 in 10000 people who do not. State the relative risk, then explain why a headline saying 'Treatment X doubles your risk' could be misleading.Show answer
Answer: Relative risk = 2; misleading because the absolute risk only rises from 0.02% to 0.04%, an increase of just 0.02 percentage points, so the real extra risk to any individual is tiny.
Q6The risk of an event is 15% in Group 1 and 5% in Group 2. Find both the relative risk and the absolute risk difference for Group 1 compared with Group 2.Show answer
Answer: Relative risk = 3 (15% divided by 5%); absolute risk difference = 10 percentage points (15% - 5%).
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
In a study, 30 out of 600 workers in Factory A had a workplace injury last year, compared with 10 out of 500 workers in Factory B. (a) Find the risk of injury for each factory as a percentage. (b) Find the relative risk of injury for Factory A compared with Factory B.
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A screening test finds a condition in 6 out of 3000 people in Area A and 3 out of 3000 people in Area B. (a) Find the risk for each area as a percentage. (b) Find the relative risk of the condition for Area A compared with Area B. (c) Find the absolute risk difference between the two areas.
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A charity reports that 45 out of 900 people who took part in a fundraising run were injured, compared with 6 out of 600 people who did not run but volunteered at the event. (a) Find the risk of injury for each group as a percentage. (b) Find the relative risk of injury for runners compared with volunteers. (c) Find the absolute risk difference. (d) Explain why the relative risk alone could give a misleading impression of the danger of running in this event.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the risk (higher) worksheet pack - 17 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 19 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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