Page 233 - Intermediate Statistics for Dummies

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Part IV: Building Strong Connections with Chi-Square Tests
Just to save you a little time, if you have the total number in a group and how
many of those individuals fall into one of the categories of the two-way table,
you can determine the number falling into the remaining category by sub-
tracting the total number in the group minus the number in the given cate-
gory. You can complete this process for each remaining group in the table.
Making marginal totals
One of the most important aspects of a two-way table is to have easy access
to all the pertinent totals. Because every two-way table is made up of rows
and columns, you can imagine that the totals for each row and the totals for
each column are important. Also, the grand total is important to know.
If you take a single row and add up all the cell counts in the cells of that row,
you get what is called a marginal row total for that row. Where does this mar-
ginal row total go on the table? You guessed it — out in the margin at the end
of that row. You can find the marginal row totals for every row in the table
and put them into the margins at the end of the rows. This group of marginal
row totals for each row represents what statisticians call the marginal distrib-
ution for the row variable. The marginal row totals should add up to the grand
total, which is the total number of individuals in the study. (The individuals
may be people, cities, dogs, companies, and so on, depending on the scenario
of the problem at hand.)
Similarly, if you take a single column and add up all the cell counts in the
cells of that column, you get the marginal column total for that column. This
number goes in the margin at the bottom of the column. Follow this pattern
for each column in the table, and you have the marginal distribution for the
column variable. Again, the sum of all the marginal column totals equals the
grand total. The grand total is always located in the lower-right corner of the
two-way table.
The marginal row total, marginal column totals, and the grand total for the
cell-phone example are shown in Table 13-3.
Table 13-3 Marginal and Grand Totals for the Cell Phone Data
Personal Personal Marginal
Calls: Yes Calls: No Row Totals
Males 325 183 (508 – 325) 508
Females 427 81 (508 – 427) 508
Marginal Column Totals 752 264 1,016 (Grand Total)