Tests For Multinomials

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Tests For Multinomials
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The Multinomial Situation

• Have k qualitative choices
• Hypothesize
• H0 p1, p2, pk are the true proportions
• H1 At least one of these proportions is
  incorrect
• Determine the expected number of observations for
  each choice if H0 were true e1, e2 ,,, ek
• e1 np1 e2 np2 . ek npk
• All eis should be ? 5 for the ?2 test to be
  valid
• Observe the actual number of observations f1,
  f2,,fk

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The ?2 Test

• Determine the ?2 statistic by ?2 ?((fi-ei)2/ei)
• If the ?2 statistic gt ?2?, k-1
• -- Accept H1 -- the proportions differ from the
  hyp. values

In EXCEL CHITEST(actual values, expected
values) gives the p-value for the ?2 test
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Example

• You hypothesize that of the cars driven by
  students to campus
• 26 are white, 16 are blue, 18 are red, 40 are
  some other color
• Take a sample of 163 cars
• 46 white, 33 blue, 34 were red, 50 other
• Can we conclude the true proportions are
  different from the hypothesized values?

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Set-Up columns for Hypothesized
Proportions Actual Observations Expected
Observations
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Find the total of observations
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Find Expected if hypothesized proportions are
true.
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Get p-value for the ?2 test