Basic Statistics

160 CATEGORICAL DATA: ANALYSIS OF TWO-WAY FREQUENCY TABLES

Table 11.9
Chi-square

Association Between Health Status and Affording Medical Care: Cells

Afford Medical Care

Health Status Almost Never Not Often Often Always Total

Excellent 2.30 .24 .56 1.23 4.34

Good 2.01 so .67 .13 3.31

Fair 3.88 1.37 .5 1 .67 6.43

Poor 12.57 .95 .09 3.02 16.63

Total 20.77 3.07 1.82 5.05 30.71

that association. This can be a particular problem for tables with numerous rows
and columns. One way this can be done is to compare the observed and expected
frequencies in Table 11 3. For example, if we look at the results for the respondents
who rated their health as poor, we see that we have higher observed values than
expected if there was no association for those who almost never, not often, or often
could afford medical care and observed frequencies lower than expected values for
those who were always able to afford the medical care they needed. At the other
extreme, the respondents who rated their health as excellent had lower observed values
than expected for having problems affording medical care. This type of comparison
of observed and expected values can provide some insight into the results. It is easier
to do when we have considerable knowledge about the variables being studied. It
is often easier when the results are from treatment groups (tables with two or more
treatment groups) than for survey data from a single sample. With different treatment
groups, we can compare the observed and expected values by examining the treatment
groups one at a time.
Another method of interpreting the results is to see what contributes most to the
numerical size of the computed chi-square. Many statistical programs print out the
individual terms,

(observed - expected)2

expected

for each cell. This option may be called cells chi-square or components of chi-square.
Table 1 1.9 gives the cells chi-square for the data given in Table 1 1.8.
From Table 1 1.9 it can be seen that the major contribution to the overall chi-square
comes from those who reported their health status as poor and almost never could
afford the health care they should have. In general, the responses falling in the first
column or last row make the largest contribution to the computed chi-square. Another
method of interpreting the results in larger tables is to present bar graphs as mentioned
at the end of Section 1 1.1.1.