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A Visual Basic Program for Estimating Missing Cell Frequencies in Chi Square Tests for Association

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by Richard G. Graf, Edward F. Alf, Jr., Steve Williams, and Ifeanyi Okolo
.

**Abstract:**
It is usually easy to calculate the chi square test for association in a table with r rows and c columns; but if the
frequency data are missing for one or more cells in the table, the analysis can be complicated. One class of such tables arises
in the analysis of transaction flows (Savage & Deutsch, 1960), such as the analysis of export/import data, emigration data, or
psychological interaction data, where the diagonal entries in the table are missing. Goodman (1968) presents an excellent
summary of methods for analyzing contingency tables with missing elements, including missing diagonals. Wagner (1970)
develops a maximum likelihood solution for estimating expected cell frequencies when the diagonal elements are missing. We
offer a slightly different solution to this problem. Each missing cell frequency is replaced with the value that would be
expected if the null hypothesis of no association between rows and columns were true. In this way, the missing cells make no
contribution to the resulting chi square. Further, replacing the missing values with their expectations yields the same
maximum likelihood solution given by Wagner (1970). A computer program for performing the analysis can be downloaded
from http://www.sci.sdsu.edu/misschi.
**Key Words: **
Chi Square, Missing Cells

**Authors:**

Richard Graf,
rgraf@sunstroke.sdsu.edu

Edward Alf, Jr.,

Steve Williams,

Ifeanyi Okolo

**Editor:**
Hector F. Coronel-Brizio,
hector@dino.coacade.uv.mx

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