TWO WAY

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TWO WAY
TABLES
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Task One Data Collection
Has an Ipod Has an Ipod TOTALS
Yes No TOTALS
Has been to the South Island Yes
Has been to the South Island No
TOTALS 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 Blonde TOTALS
Yes No TOTALS
Hours watching TV last night Less than 2 hours
Hours watching TV last night 2 or more hours
TOTALS 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 Did Homework TOTALS
Male Female TOTALS
Has correct equipment for class Yes
Has correct equipment for class No
TOTALS 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 Sex TOTALS
Male Female TOTALS
Eat breakfast on a regular basis Yes 190 300
Eat breakfast on a regular basis No 165
TOTALS TOTALS 320 275
110
130
295
595
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Design your own two way table
TOTALS
TOTALS


TOTALS 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 Test Result
Positive Negative
Actual Status Positive Correct False Negative
Actual Status 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 Test Result TOTALS
Elevated levels Normal levels TOTALS
Actual Status Elevated levels 49 36 85
Actual Status Normal levels 1418 1475 2893
TOTALS TOTALS 1467 1511 2978
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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 Test Result TOTALS
Has Disease Healthy TOTALS
Actual Status Has Disease 392 8
Actual Status Healthy 24 576
TOTALS 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 Test Result TOTALS
Positive Negative TOTALS
Actual Status Positive 398 2
Actual Status Negative 498 99102
TOTALS 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
TOTALS



TOTALS 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?