Chapter9.4 lecture notes

# Chapter9.4 lecture notes - 9.4 ANALYSIS OF r x c table Two...

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• PresidentHackerCaribou10582
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9.4 ANALYSIS OF r x c table. Two variables: A with r categories placed in r rows. B with c categories placed in c columns. B 1 B 2 ………… B j ……… B c Total A 1 π 11 π 12 ………… π 1j ……… π 1c π 1+ A 2 π 21 π 22 ………… π 2j …………. π 2c π 2+ . . . . ………… ………… . . . . . . A i . . π i1 . . π i2 …………. ………… ………… π ij …….. ……….. ……….. π ic . . π i+ . . A r π r1 π r2 …………. π rj…………… π rc π r+ Total π +1 π +2 …………. π +j ……… π +c 1.0 Notation : π ij = P(A i B j ) for i=1,2…..r and j=1,2….. c π i+ = P(A i ) π +j = P(B j ) o ij = observed number of A i B j in sample. R i = total row i C j = total for column j ij e ˆ = estimated expected frequency for A i B j = (R i x C j )/n Null Hypothesis:
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Unformatted text preview: A, B independent H : P(A i ∩ B j ) = π ij = π i+ π +j = P(A i )P(B j ) j=1,2,3…c ; i=1,2…r H 1 : 0 ≤ π ij ≤ 1 Test statistic = X 2 = ∑∑ = =-r i c j ij ij ij e e o 1 1 2 ˆ ) ˆ ( Reject if X 2 > 2 α χ ν = (r-1 ) (c-1) P value = P( 2 > X 2 ) Example: Relationship between majors and Undergraduate degree for individuals in an MBA program. MBA Major Undergrad Major Accounting Finance Marketing Total BA 31 13 16 60 BE 8 16 7 31 BBA 12 10 17 39 Other 10 5 7 22 61 44 47 159 Chi - square = 14.7 Df = 6 P=0.023 Critical value for P=0.05 = 12.59....
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• Fall '03
• Mendell
• Null hypothesis, Statistical hypothesis testing, Bachelor's degree

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