Risk & Bias (Edexcel GCSE Statistics)

Relative & Absolute Risks

How do I calculate the absolute risk of an event happening?

• You can use collected data to estimate the probability that an event will occur

  • If the event is something negative or undesirable

    • then the estimated probability is known as the risk (or absolute risk) of the event occurring

  • 

    • This is just the experimental probability of the 'risky' event occurring

    • So risk will always be a number between zero and one

  • e.g. an area in a particular town has flooded in 8 years out of the past 50 years

    • the risk of the town flooding in a given year is

• Insurance companies use risk to decide how much to charge for insurance

  • Higher risk means higher cost for the insurance

How do I calculate relative risk?

• Relative risk measure how many times more likely an event is to occur for one group, compared with another group

  • 

    • This is not a probability

    • So relative risk does not have to be between zero and one

  • e.g. the risk of having an accident is 0.025 for people who have taken a driving safety course, and 0.09 for people who have not taken the course

    • the relative risk of having an accident for people who haven't taken the course compared with people who have taken the course is

    • i.e. a person who hasn't taken the course is 3.6 times more likely to have an accident than someone who has taken the course

• Note that relative risk doesn't tell you how likely an event is in the first place

  • It only compares risk between two groups

    • e.g. relative risk may tell us that members of group A are 50 times more likely to develop a disease than members of group B

    • But if the risk for members of B is very small, then the risk for members of group A may also be small (just not as small)

Identifying Possible Bias

• Estimated probabilities from data can help to identify bias

  • For example, whether or not a dice is fair

    • i.e. whether it has an equal probability of landing on each side

  • If a dice (or spinner, coin, etc.) is not fair, then it is called biased

• Compare the expected number of times an event would occur (e.g. if the dice was fair)

  • with the actual number of times the event occurs

    • A large difference between the two suggests bias

    • A small difference may just be due to randomness

• Remember that an estimated probability tends to get closer and closer to the exact probability as the number of trials increases

  • So a larger number of trials gives a more reliable result than a smaller number of trials

• In addition to considering basic probabilities

  • you may be asked to compare experimental results to the expected results for a binomial distribution

  • See the 'Binomial Distribution' revision note for how to calculate binomial distribution probabilities