Communicating Uncertainty Quick Quiz Answer Key

Quick Quiz Answer Key

1) Read the following summary of some research in which you must communicate the degree of uncertainty in your results.

a) Decide whether you can simplify the three numbers without affecting their accuracy too much, to make this easier for people to interpret, and then make these simplifications if you think it is possible to do so (1 mark for each decision, 3 marks total).

Simplifications, where possible, appear in bold font below:

We have assessed the risk of a serious volcanic eruption affecting people living in the nearest town and believe there is approximately a 1 in 150,000 chance that such an eruption will occur in the next week, approximately a 1 in 100 chance in the next 10 years and a 1 in 12 chance that it will happen in the next 50 years.

b) Read the following descriptions of the risk facing town residents, and rank these in order from best to worst, remembering the importance of avoiding framing bias (4 marks):

BEST = D: There is an absolutely tiny chance that the volcano will erupt in the next week. [This is accurate – there is a chance, but is it incredibly small]

SECOND-BEST = B: It is a bit more likely that the volcano will erupt by 2065 than by 2025. [It is more likely, but more than a bit]

SECOND-WORST = C: It is very unlikely that the volcano will erupt in the next 50 years. [This is potentially misleading – what does ‘very unlikely’ mean? 1 in 12 is not ‘very unlikely’ to most people; perhaps ‘unlikely’ would acceptable]

WORST = A: Realistically, there is no chance that the volcano will erupt in the next week. [This is wrong; there is a chance]

2) Read the three short descriptions below that all deal with scientific uncertainty in some way. Try to suggest what the potential problems are with each one and then re-write them to remove these problems (3 marks).

Problems and re-written versions appear in bold font below:

i) If the pest outbreak spreads to the city, there is a 1.3% chance that all the maple trees will die. Scientists think there is approximately a 14% chance that it will reach the city.

Problem: Two sets of probabilities should be combined into one, because on their own they imply a greater likelihood than in reality.

Example re-write: There is only around a 1 in 500 chance that all the maple trees will die, because there is a 14% chance the pest outbreak will reach the city and only a 1.3% chance that it will kill all the trees if it does.

[Note: 0.14 x 0.013 = 0.00182, = ~ 0.2%, or 1 in 500]

ii) Statistics show that cyclists involved in traffic accidents have a 45% chance of missing at least two weeks of work to recover from injuries. Car drivers have only a 15% chance, but on average they are involved in six times as many accidents.

Problem: The sentence suggests that you are more likely to miss work due to a cycling injury than a car injury, due to the framing bias of mentioning this first and not assessing the true risk based on the frequency of the accidents involving each commuter.

Example re-write: Car drivers are twice as likely to miss at least two weeks of work than cyclists due to traffic accidents; although cyclists involved in accidents are three times as likely to miss work for such a period, they are six times less likely to be involved in these accidents in the first place.

iii) Every single one of our 150 test subjects improved their performance in biology exams following our instructional course, so there is no chance that you would pay for it and not see an improved result at the end of term.

Problem: All 150 subjects improved their performance but that does not mean that every person on the planet would! This is just a wrap-up from a relatively small sample size.

Example re-write: All 150 of our test subjects improved their performance in biology exams following our instructional course, so there is an exceptionally good chance that you would pay for it and see an improved result at the end of term.