ECON 2300 LEC

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ECON 2300 LEC 14
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Outline

• Test of Independence
• Expected Frequency
• Test statistic
• Examples

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Test of Independence

• Finds out if variables are independent of each
  other
• Contingency table is used to test independence -
  Contingency table test
• Procedure
• State the null and alternate hypothesis
• Ho The column variable is independent of the
  
• row variable
• Ha The column variable is not independent of
  
• the row variable

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Test of Independence

• Select a random sample and record the observed
  frequencies for each cell of the contingency
  table
• Compute the expected frequency of each cell
• Compute the value of the test statistic
• Rejection rule
• p-value approach Reject Ho if p-valuelta
• Critical value approach Reject Ho if
• where
• a Level of significance,
• dof (n-1)(m-1)

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Expected frequencies for contingency table

• Assumption Variables are independent

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Test Statistic
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Example

• Albers manufactures and distributes three types
  of beer light, regular and dark. In an analysis
  of the market segments for the three beers, the
  firms market research group raised the question
  of whether preferences for the three beers differ
  among male and female beer drinkers.
• Ho Beer preference is independent of the
  
• gender of the beer drinker
• Ha Beer preference is not independent of
  
• the gender of the beer drinker

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Example
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Example
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Example

• p-value0.0468ltalpha Reject Ho