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## TWO WAY

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**TWO WAY**TABLES**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?**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?**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?**Questions?**• Write your own set of at least 5 questions you could answer using the previous two-way table.**Fill in the gaps**110 130 295 595**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.**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**Two Way Table for testing**False Negative Correct False Positive Correct**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**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**=**= = = Real Life example 1 – Lead Levels False Positive False Negative Sensitivity Specificity**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?**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?**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?**Design your own 2 way table with three options per side**Write 5 probability questions to go with your table**Thinking flexibly**• What other contexts do you think two way tables would be useful in?