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Tests For Multinomials

Tests For Multinomials. The Multinomial Situation. Have k qualitative choices Hypothesize: H 0 : p 1 , p 2 , … p k are the true proportions H 1 : At least one of these proportions is incorrect

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Tests For Multinomials

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  1. Tests For Multinomials

  2. 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 ei’s should be  5 for the 2 test to be valid • Observe the actual number of observations: f1, f2,…,fk

  3. The 2 Test • Determine the 2 statistic by 2 = ((fi-ei)2/ei) • If the2 statistic > 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

  4. 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?

  5. Set-Up columns for: Hypothesized Proportions Actual Observations Expected Observations

  6. SUM(D3:D6) Find the total # of observations

  7. =C3*$D$7 Drag down to E6 Find Expected # if hypothesized proportions are true.

  8. =CHITEST(D3:D6,E3:E6) Get p-value for the 2 test

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