two way

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?

Task Two

Blonde TO

TA

LSYes No

Hours watching TV last night

Less than 1 hrs

1 – 2 hours

More than 2 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 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?

Task Three

Did Homework TO

TA

LSYes No

Has correct

equipment for class

All

No Book

No calculator

No book or calculator

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

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

Test Result

Positive Negative

Actual Status

Positive

Negative

False Negative

False Positive

Correct

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

Test Result TO

TA

LSPositive Negative

Actual Status

Positive 49 36 85

Negative 1418 1475 2893

TOTALS 1467 1511 2978

False Negative

=

False Positive

=

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?

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 2 way table with three options per side

TO

TA

LS

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?