The test is positive: But what are the odds it's wrong?

• In court, the jury is told that DNA found at the crime scene is very likely to have come from the suspect.  How good is this as evidence?
• A couple have two children, both of whom die of cot death.  Is this such an unlikely coincidence that there must be some other explanation?  Is it more likely that in fact the mother killed her children?
• People in the UK and many other countries are routinely tested for certain cancers, including bowel, breast, prostate and cervical cancers.  But does a positive test mean you definitely have cancer?

It's tempting to think that a scientific test will give a definite result which you can trust absolutely - so a positive test means it is your DNA or you do have the disease, a negative test means it isn't you, and you're not ill.

It's tempting to think that if there is a match between a suspect's DNA and that found at the crime scene, then the suspect must be guilty.    It's also tempting to think that if the probability of an event, such as cot death, occurring is very small, then the probability of it occurring twice in the same family is so unlikely that some other explanation should be sought.

In the video clips in this pack, Professor Philip Dawid looks at assumptions like these.  Whether evidence is used in a court of law or in a diagnostic test, or in a variety of other everyday situations, we need to understand how probability and statistics can help us to evaluate that evidence.  This topic is designed to help students become informed citizens, who can understand that unless we ask the right questions, we won't do the right things with the numbers.

The resources which accompany the video clips complement them by providing problems for students to work on, so helping them to explore the principles which Philip Dawid discusses.  Some are intended to be direct follow-up to the video clips, while others extend and/or provide alternative approaches to the topic.

Answers and additional notes are also provided.

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Suggested route:

Any resource can be used on its own, although we would strongly recommend that students watch the preceding video(s) so that they understand the context of the resources.

• Download all videos (zip file, 56MB)
• Download all pdf files

Type of Resource	Resource Name	Notes
	Answers and notes	Teachers: Start here! Additional notes on answers and areas for further discussion
	The test is positive: Introduction	Introductory video clip (4 min 51 secs): you have to ask the right question to get the right answer
	Do spots mean measles?	The probability of having spots if you have measles versus the probability that, if you have spots, you have measles
	Evaluating Headlines	Media headlines are intended to catch our attention, but what else do we need to know if we are to evaluate the information they give?
	Misuse of probability	Video clip (4 mins 30 secs): what can go wrong if numbers are used in a naive way without thinking through the logic of the questions asked
	Rare events	Presentation - the pitfalls of the 'naive' approach to combining probabilities
	How believable are test results?	Worksheet - using alternative means (contingency table and tree diagrams) to analyse what test results really mean
	How strong is DNA evidence?	Presentation - what does it mean to say that two specimens of DNA are a match?  This presentation is intended to help students understand the next video clip more fully.
	Matching criminals	Activity: Discover why matches between two unrelated people aren't that uncommon through this activity on our sister website, Plus
	The case of Denis John Adams	Video clip (4 mins 16 secs): does a DNA match mean the suspect must be guilty?
	Interpreting the evidence	Video clip (4 mins 20 secs): analysing the numerical data
	R v Denis John Adams	Follow-up worksheet
	Interpreting evidence	Worksheet: use of contingency tables and tree diagrams to analyse conditional probabilities
	Additional evidence	Video clip (2 mins 59 secs): what have we overlooked?