Chi Square: A nonparametric hypothesis test

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Chi SquareA nonparametric hypothesis test

• Unit 12
• Homework
• Ch 16 1, 3, 7, 9, 13, 15, 17 (pp.500-503)

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Finals Schedule

• Section 1 (2 pm)
• 11 am, Thursday, Dec 14
• Section 2 (3 pm)
• 2 pm, Thursday, Dec 14

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Parametric vs. Nonparametric Tests

• Parametric hypothesis test
• about population parameter (m or s2)
• z, t, F tests
• interval/ratio data
• Nonparametric tests
• do not test a specific parameter
• nominal ordinal data
• frequency data

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Chi-square (C2)

• Nonparametric tests
• same 4 steps as parametric tests
• Chi-square test for goodness of fit
• single variable
• Chi-square test for independence
• two variables
• Same formula for both
• degrees of freedom different
• fe calculated differently

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Assumptions Restrictions

• Independence of observations
• any score may be counted in only 1 category
• Size of expected frequencies
• If fe lt 5 for any cell cannot use C2
• More likely to make Type I error
• Solution use larger sample

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C2 Test for Goodness of Fit

• Test about proportions (p) in distribution
• 2 different forms of H0
• No preference
• category proportions are equal
• No difference
• from comparison population
• e.g., student population
• 55 female and 45 male?
• H1 the proportions are different

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Null Hypotheses C2
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Sample Data ?2

• Frequency
• Expected frequency (fe)
• fe pn
• Observed frequency (fo)
• S fo n
• Degrees of freedomGoodness of fit
• C-1
• C number of cells (categories)
• C2cv from table B.7, page A-34

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Chi-square (C2)
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Example

• Classess favorite Coke or Pepsi?
• H0 ?
• ?2cv
• ? .05
• df

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Coke or Pepsi?
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C2 Test for Independence

• 2 variables
• are they related or independent
• H0 also 2 forms
• no relationship between variables
• distribution of 1 variable is the same for the
  categories of other
• Same formula as Goodness of Fit
• different df

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C2 Test for Independence

• Differences from Goodness of Fit
• df (R-1)(C-1)
• R rows
• C columns
• Expected frequency for each cell

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Example

• Does watching violent TV programs cause children
  to be more aggressive on the playground?
• Data frequency data
• Violent program yes or no
• Aggressive yes or no

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C2 Test for Independence
Aggressive
Yes
No
Violent TV
Yes
No