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Correspondence analysis of aggregate data: the \(2\times 2\) table. (English) Zbl 1140.62048
Summary: The issue of how much information the marginal frequencies of a single \(2\times 2\) table provide for the estimation of the cell frequencies is a topic that has received much attention since it was first made popular in the statistical literature by R. A. Fisher [The logic of inductive inference (with discussions). J. R.. Stat. Soc., n. Ser. A 98, 39–82 (1935; Zbl 0011.03205)]. The general consensus is this marginal information provides no useful information for making individual (cell) inferences.
This paper will provide a graphical investigation of the problem. In particular we will demonstrate the applicability of correspondence analysis on a single \(2\times 2\) table where the joint cell frequencies are not available, but where only the marginal information is known. To complement this approach an aggregate association index is proposed to determine, based only on the availability of the aggregate data, whether there is any possibility of there existing a significant association between the two dichotomous variables arising from the table.

MSC:
62H17 Contingency tables
62H25 Factor analysis and principal components; correspondence analysis
05C90 Applications of graph theory
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