Two Way Tables & Data Collection

WARMUP– Data Collection Has an Ipod TOTALS Yes No Has taken drivers ed 5 9 12 20

What is the probability that… A student has an Ipod A student has taken drivers ed? A student does not have an Ipod? A student has not taken drivers ed? A student has an Ipod and has taken drivers ed? A student has an Ipod or has taken drivers ed. A student does not have an Ipod or has not taken drivers ed?

Same or different?? If we know they have an Ipod, what is the probability they have a permit? If we know they have a permit, what is the probability they have an Ipod?

Hours watching TV last night Example 1 Blonde TOTALS Yes No Hours watching TV last night Less than 2 hours 8 2 or more hours 4 9 11 20

What is the probability that… A student is blonde? A student spent less than 2 hours watching TV last night? A student is blond 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?

Example 2 Did Homework TOTALS Male Female Rode the Bus Yes No

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

Eat breakfast on a regular basis Fill in the gaps Sex TOTALS Male Female Eat breakfast on a regular basis Yes 190 300 No 165 320 275 110 130 295 595

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

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 Test Result Positive Negative Actual Status Correct False Negative False Positive

Definitions False Positive False Negative 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 Specificity 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 Test Result TOTALS Elevated levels Normal levels Actual Status 49 36 85 Normal levels 1418 1475 2893 1467 1511 2978

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?

Example 2 392 8 24 576 Test Result TOTALS Actual Status Has Disease Healthy Actual Status 392 8 24 576

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?

Real Life Example 3 – HIV Testing Test Result TOTALS Positive Negative Actual Status 398 2 498 99102

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

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