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

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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?

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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?

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Example Two Blonde TOTALS YesNo Hours watching TV last night Less than 2 hours 2 or more hours TOTALS

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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?

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Example 3 Did Homework TOTALS MaleFemale Has correct equipment for class Yes No TOTALS

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

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

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

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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

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Two Way Table for testing Test Result PositiveNegative Actual Status Positive Correct False Negative Negative False Positive Correct

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Definitions False Positive A healthy person is told they have the disease False Negative A person with the disease is told they dont have it

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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

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Real Life example 1 – Lead Levels Test Result TOTALS Elevated levels Normal levels Actual Status Elevated levels 493685 Normal levels 141814752893 TOTALS 146715112978

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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?

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Example 2 Test Result TOTALS Has Disease Healthy Actual Status Has Disease 3928 Healthy 24576 TOTALS

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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?

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Real Life example 3 – HIV Testing Test Result TOTALS PositiveNegative Actual Status Positive 3982 Negative 49899102 TOTALS

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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?

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

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

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