Decomposing Chi-Square

Gudmund R. Iversen
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Gudmund R. Iversen: Swarthmore College

Sociological Methods & Research, 1979, vol. 8, issue 2, 143-157

Abstract: According to the statistical properties of the chi-square distribution, a variable which is distributed according to the chi-square distribution with p degrees of freedom can be written as the sum ofp chi-square variables, each with one degree of freedom. This means that a contingency table which gives rise to a chi-square with p degrees of freedom can be decomposed into as many as p smaller tables. The magnitudes of the chi-squares for these smaller tables will often give a better understanding of the relationship between the two variables than was possible to obtain from the overall chi-square for the original table. This paper gives explicit rules for how to decompose a table into smaller tables, and the rules are illustrated with an example from a content analysis of value orientations in different maga zines.

Date: 1979
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:8:y:1979:i:2:p:143-157

DOI: 10.1177/004912417900800202

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