011+Categorical+data

# It is called contingency table and presents

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Unformatted text preview: n the two-way table. The data are summarized in the two-way table. It is called contingency table and presents multinomial count data classiﬁed on two scales, or dimensions of classiﬁcation. Below we present a view of contingency table 1 1 n11 2 n21 . . . . . . r nr1 Total C1 2 n12 n22 . . . nr2 C2 · · · c Total · · · n1c R1 · · · n2c R2 . . . ... . . . · · · nrc Rr · · · Cc n And corresponding table for probabilities is 3 A. Zhensykbaev Categorical data analysis 1 2 1 p11 p12 2 p21 p22 . . . . . . . . . r pr1 pr2 Total P C1 P C2 ··· c Total · · · p1c P R1 · · · p2c P R2 . . . . ... . . · · · prc P Rr · · · P Cc n such that nij is the number of observations in (i, j )-s cell and pij its probability. Last column (row) represents the marginal probability: c P Ri = r pij = pi1 + pi2 + · · · + pic , P Cj = j =1 pij = p1j + p2j + · · · + pcj . i=1 We want to know whether the two classiﬁcations are dependent. Recall two events A and B are independent iﬀ P (A ∩ B ) = P (A) · P (B ). Thus, we test the null hypothesis H0 of independence two classiﬁcations. Alternative hypothe...
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## This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.

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