There are many things in the world around us that we don't understand or would like to predict. Scientists face uncertainty everyday and they design experiments to test their theories. As they progress with their research, they aim to decrease the uncertainty and increase their confidence in the results.

Present the class with the puzzle. If they take it as homework they are likely to find the correct answer on the internet (this may be acceptable to you).

Discuss the implications of this type of misunderstanding (known as a Type 1 error) which might include:

  • The costs of treating everyone who has a positive result eg supplying drugs for every person who has tested positive.
  • The implications of treatment if the treatment may be harmful itself eg a 30% chance of serious side effects or death.
  • How might it affect the person's life eg if they tested positive for HIV?

An extension activity: Use the internet to look up some of the different types of home testing kits that are available for different diseases (eg HIV). What information is available about their accuracy - does it say what the probability of false positives or negatives are?

 

Curriculum links

Science
Data, evidence, theories and explanations 1a. how scientific data can be collected and analysed
1b. how interpretation of data, using creative thought, provides evidence to test ideas and develop theories
Applications and implications of science 4b. to consider how and why decisions about science and technology are made, including those that raise ethical issues, and about the social, economic and environmental effects of such decisions
4c. how uncertainties in scientific knowledge and scientific ideas change over time and about the role of the scientific community in validating these changes.

 


Scottish Curriculum for Excellence

Science general - experiences and outcomes express opinions and make decisions on social, moral, ethical, economic and environmental issues based upon sound understanding
develop as a scientifically-literate citizen with a lifelong interest in the sciences
SCN 4-20a. Topical Science: I have researched new developments in science and can explain how their current or future applications might impact on modern life
SCN 4-20b. Having selected scientific themes of topical interest, I can critically analyse the issues, and use relevant information to develop an informed argument
Environmental Science National 4 & 5 Potentially relevant to modules: Sustainability (environmental, economic and social impacts, and identifying possible solutions)
Science National 4 Potentially relevant to modules: Human Health (scientific analysis of health claims and consider moral and ethical issues), Science at Work (risk and safety)





Presenting probability

Norovirus_250The way that probability is presented can influence the way we think about a problem. When it comes to probability our intuition is often wrong. Try this puzzle...

A test to detect a disease has a false positive rate of 5% (this means 5% of the results will be positive even though these people do not actually have the disease).

If you test positive for the disease what are the chances of you actually having the disease?

Some further information to take into account:

  • In the population as a whole, 1 in 1000 people have the disease
  • There are no false negative results with the test (when a person who actually has the disease gets a negative result)
  • Everyone is tested (it doesn't depend on showing any symptoms of the disease)

Why it is important that healthcare professionals are aware of this?

Try and work it out then click here for the answer.

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer

Most people intuitively think the answer is 95%...but it is not. The answer is actually 2%. To work out why think of it like this:

If 1000 people are tested then only 1 person will actually have the disease.

The test has a 5% false positive rate, so in 1000 people 50 of them will test positive (5% of 1000) even though they do not have the disease (false positives).

In total if 1000 people are tested, 51 of them will have a positive result but only 1 of them has the disease. If you are one of these 51 people with a positive result then your chances of having the disease are really only 1 out of 51 which equals (almost) 2%.

Understanding these types of error rates is important for the healthcare profession because of:

  • The costs of treating everyone who has a positive result eg supplying drugs for every person who has tested positive.
  • The implications of treatment if the treatment may be harmful itself eg a 30% chance of serious side effects or death.
  • How might it affect the person's life eg if they tested positive for HIV.

An audio clip talking about predictions and behaviours can be heard on the website: Mervyn King, Governor of the Bank of England, on uncertainty in macroeconomic policy making.