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TWO WAY

This guide explores the use of two-way tables for calculating probabilities related to students' ownership of iPods and their experiences in the South Island, alongside medical testing scenarios. Key questions address probabilities of having an iPod, watching TV, and the effectiveness of diagnostic tests, including sensitivity and specificity in detecting diseases. Practical examples and exercises encourage learners to create their own two-way tables and formulate relevant probability questions, enhancing comprehension of data collection and analysis in real-life contexts.

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TWO WAY

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Presentation Transcript

  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?

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