Nonparametric Tests: Chi Square ? 2

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Nonparametric TestsChi Square ? 2

• Lesson 16

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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 (C 2)

• 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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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.5, page 364

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Chi-square (C2)
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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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SPSS No Preference

• Data in 1 column
• Analyze
• Nonparametric
• Legacy Dialogs
• Chi square
• Dialogue box
• Test Variable List
• Expected Values ? All categories Equal
• Options ? Descriptives (frequencies)

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SPSS No Difference

• Same menus as No Preference
• But must specify proportions or frequencies
• Dialogue box
• Expected Values ? Values
• Specify Add vales one at time
• In same order as defined values for variable in
  variable view

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Effect Size 1 Variable

• N total sample size across all categories
• df categories 1
• zero no difference
• 1 large difference

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C2 Test for Independence

• 2 variables
• are they related or independent
• H0
• distribution of 1 variable is the same for the
  categories of other
• no difference
• 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
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SPSS Test for Independence

• Two variables
• Two-Way Contingency Table Analysis
• Data 1 column for each variable
• Analyze
• Descriptives
• Crosstabs
• Dialogue Box
• Variables ? Rows or Columns
• Statistics ? Chi Square, Phi

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Effect Size (?) 2 Variables

• N total sample size across all categories
• Phi values 0-1
• Interpret similar to Pearsons r
• Small .1 medium .3, large .5