task one – data collection has an ipod totals yesno has been to the south island yes no totals
TRANSCRIPT
Task One – Data Collection
Has an Ipod TO
TA
LSYes No
Has been to the South
Island
Yes
No
TOTALS
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?
Example Two
Blonde TO
TA
LSYes No
Hours watching TV
last night
Less than 2 hours
2 or more hours
TOTALS
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?
Example 3
Did Homework TO
TA
LSMale Female
Has correct equipment for
class
Yes
No
TOTALS
Questions?
Write your own set of at least 5 questions you could answer using the previous two-way table.
Fill in the gaps
Sex TO
TA
LSMale Female
Eat breakfast on a regular
basis
Yes 190 300No 165
TOTALS 320 275
110
130 295
595
Design your own two way tableT
OT
AL
S
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
Positive CorrectFalse
Negative
NegativeFalse
PositiveCorrect
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
Test Result TO
TA
LSElevated
levelsNormallevels
Actual Status
Elevated levels 49 36 85
Normal levels 1418 1475 2893
TOTALS 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
Test Result TO
TA
LSHas
DiseaseHealthy
Actual Status
Has Disease 392 8
Healthy 24 576
TOTALS
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 TO
TA
LSPositive Negative
Actual Status
Positive 398 2
Negative 498 99102
TOTALS
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 tableT
OT
AL
S
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?