A two-way table with r rows and c columns contains
sample counts. Let
denote the number of observations in the
ith row and the jth column,
,
. The
general form of the data table giving the sample counts is as follows:
In this table
are the column totals and
are the row
totals. Thus,
If the total sample size is n, then
For most
tables, a better understanding of the
information contained in the table is obtained by examining the
column proportions/ which are defined as the jth column proportion
. The resulting entries in each column form the
conditional distribution/ of the row variable given that value of
the column variable. Note that the sum of the entries in each column
should be 1 (making exception only for round off error). Tables
giving entries as proportions of row totals are also useful. Which
description to use depends upon the particular set of data being
analyzed and what questions are of interest.