2. Task One – Data Collection Has an Ipod TOTALS YesNo Has been to the South Island Yes No TOTALS

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. Task Two Blonde TOTALS YesNo Hours watching TV last night Less than 1 hrs 1 – 2 hours More than 2 hours TOTALS

6. What is the probability that…  A student is blonde?  A student spent less than 2 hours watching TV last night?  A student is blonde 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. Task Three Did Homework TOTALS YesNo Has correct equipment for class All No Book No calculator No book or calculator TOTALS

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 Sex TOTALS MaleFemale Eat breakfast on a regular basis Yes 190300 No 165 TOTALS 320275 110 130 295 595

10. Questions  A female student chosen at random has breakfast regularly?  A male student chosen at random does not have breakfast regularly?  A student has breakfast regularly?  A student who has breakfast regularly is female?  A student who does not have breakfast regularly is male?  A student selected at random is female.

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 Test Result PositiveNegative Actual Status Positive Negative False Negative False Positive Correct

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 Test Result TOTALS PositiveNegative Actual Status Positive 493685 Negative 1418 14752893 TOTALS 146715112978 False Negative =  False Positive =  Sensitivity =  Specificity = 

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 Test Result TOTALS Has Disease Healthy Actual Status Has Disease 3928 Healthy 24576 TOTALS

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 Test Result TOTALS PositiveNegative Actual Status Positive 3982 Negative 49899102 TOTALS

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 2 way table with three options per side TOTALS 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?