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1. TWO WAY TABLES

2. Task One – Data Collection

3. What is the probability that… • A student has an Ipod? • A student has been to the SI? • A student does not have an Ipod? • A student has not been to SI? • A student has an Ipod and has been to the SI? • A student has an Ipod or has been to SI) • A student does not have an Ipod or has not been to the SI?

4. Same same but different?? • If we know they have an Ipod, what is the probability they have been to South Island? • If we know they have been to the South Island what is the probability they have an Ipod?

5. Example Two

6. What is the probability that… • A student is blonde? • A student spent less than 2 hours watching TV last night? • A student is blonder and spent more than 2 hours watching TV last night? • A blonde student spent less than 2 hours watching TV last night? • A student who was watching TV for more than 2 hours last night is blonde?

7. Example 3

8. Questions? • Write your own set of at least 5 questions you could answer using the previous two-way table.

9. Fill in the gaps 110 130 295 595

10. Design your own two way table Write 5 probability questions to go with your table

11. Medical diagnosis • A patient has a test to see if they have or do not have a particular disease • The test gives a result – either positive or negative

12. Two Way Table for testing

13. Definitions • False Positive • A healthy person is told they have the disease • False Negative • A person with the disease is told they don’t have it

14. Further definitions • Sensitivity • Probability that a person who has the disease gets a positive result • Closer it is to 1 the better the test is at determining if a person has the disease • Specificity • Probability that a person who does not have the disease gets negative result • Closer it is to 1 the better the test is at determining if a person does not have the disease

15. Real Life example 1 – Lead Levels

16. Questions • Calculate the probability of a false positive • Calculate the probability of a false negative • Calculate the specificity and sensitivity of this test • How effective is this test?

17. Example 2

18. Questions • Calculate the probability of a false positive • Calculate the probability of a false negative • Calculate the specificity and sensitivity of this test • How effective is this test?

19. Real Life example 3 – HIV Testing

20. Questions • Calculate the probability of a false positive • Calculate the probability of a false negative • Calculate the specificity and sensitivity of this test • How effective is this test?

21. Design your own 3 way table Write 5 probability questions to go with your table

22. Thinking flexibly • What other contexts do you think two way tables would be useful in?