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Decomposing Chi-Square

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  • Gudmund R. Iversen

    (Swarthmore College)

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.

Suggested Citation

  • Gudmund R. Iversen, 1979. "Decomposing Chi-Square," Sociological Methods & Research, , vol. 8(2), pages 143-157, November.
    • Handle: RePEc:sae:somere:v:8:y:1979:i:2:p:143-157
    DOI: 10.1177/004912417900800202
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