Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables
Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let pij= Pr(X = i, Y = j). This paper introduces a family of tests based on φ–divergence measures for testing H0: pij = pji...
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| Published in | Australian & New Zealand journal of statistics Vol. 45; no. 1; pp. 115 - 123 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK and Boston, USA
Blackwell Publishing Ltd
01.03.2003
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1369-1473 1467-842X |
| DOI | 10.1111/1467-842X.00265 |
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| Abstract | Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let pij= Pr(X = i, Y = j). This paper introduces a family of tests based on φ–divergence measures for testing H0: pij = pji against H1: pij ≥ pji (I≥ j); and for testing H1 against H2: pij unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test. |
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| AbstractList | Let X and Y denote two ordinal response variables, each having
I
levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let
pij
= Pr
(X = i, Y = j)
. This paper introduces a family of tests based on
φ
–divergence measures for testing
H
0
: pij = pji
against
H1: pij ≥ pji (I≥ j)
; and for testing
H1
against
H2: pij
unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test. Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of classifications. Let pij= Pr(X = i, Y = j). This paper introduces a family of tests based on φ–divergence measures for testing H0: pij = pji against H1: pij ≥ pji (I≥ j); and for testing H1 against H2: pij unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test. |
| Author | Pardo, J.A. Menéndez, M.L. Pardo, L. |
| Author_xml | – sequence: 1 givenname: M.L. surname: Menéndez fullname: Menéndez, M.L. organization: ETSAM Technical University of Madrid – sequence: 2 givenname: J.A. surname: Pardo fullname: Pardo, J.A. organization: Complutense University of Madrid – sequence: 3 givenname: L. surname: Pardo fullname: Pardo, L. organization: Complutense University of Madrid |
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| Snippet | Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of... Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I 2 possible combinations of... |
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| StartPage | 115 |
| SubjectTerms | chi-bar squared distribution contingency table φ-divergence measure |
| Title | Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables |
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