1. Two Way Tables
&
Data Collection

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

3. 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?

4. 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?

5. 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

6. 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?

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

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

9. 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

10. Design your own two way table
TOTALS
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
Test Result
Positive
Negative
Actual Status
Correct
False Negative
False Positive

13. 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

14. 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

15. 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

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

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
Positive
Negative
Actual Status
398 2
498
99102

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
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?