![]() Chapter Contents |
![]() Previous |
![]() Next |
Table Analysis |
You may have noticed that the preceding statistical output also included a test called Fisher's Exact test. When the sample size for the test of association of a table does not meet the usual guidelines (generally 20-25 total observations for a 2 × 2 table, with 80 percent of the table cells having counts greater than 5), an exact test may be a useful strategy.
The following data illustrate where an exact test may be appropriate. A marketing research firm took a sample of members at a health club and asked them a series of questions. They were interested in gathering information that could help their clients decide on audiences to target for new magazines. One of the questions was what activity the member considered his or her primary activity at the club. Another question was whether the member was considering making a major diet change. The researchers were interested in what types of sports magazines in which to place ads for a new food and nutrition magazine.
Figure 9.9 displays the data table containing these data. Note that the data are in frequency form, with the variable count containing the frequencies of the profile contained in each row of the table. The variable activity contains the type of activity, which can be aerobics, yoga, weightlifting, team sports such as volleyball and basketball leagues, and cross-training. The variable DietChange indicates whether the member was contemplating a change in diet.
![]() |
Figure 9.10 displays the resulting dialog.
![]() |
Note that the Tables dialog specifications (see Figure 9.5) made in the previous analysis remain in effect. Therefore, both frequencies and row percentages are produced for this analysis.
Click OK in the Table Analysis dialog to perform the analysis.
![]() |
Figure 9.12 contains the table of chi-square statistics computed
for this table. The Pearson chi-square statistic has a value of
11.4993 and an associated p-value of 0.0215 with 4 degrees of
freedom. If you were doing strict hypothesis testing, you would reject
the hypothesis of no association at the = 0.05 level of
significance. However, if you look at Figure 9.11, you see that
three table cells have a count of less than 5, which violates one of
the sample size guidelines for the asymptotic tests. Thus, you may
want to compute the exact test for these data.
![]() |
![]() |
Figure 9.13 displays the resulting dialog. Notice the warning that exact test computations may take an excessive amount of time. This would not be the case with very small cell counts, but it is an issue for other tables.
![]() |
The exact test computes a p-value of 0.0139; thus, this test also results in the rejection of the hypothesis of no association in this table. There is some kind of association between the rows of the table and the columns of the table; type of primary activity made a difference in whether members were considering diet changes. Not only does degree of association seem to vary, but so does the direction. The market research company may end up suggesting that sports and fitness magazines be targeted in different ways for the new food and diet magazine ad campaign.
![]() Chapter Contents |
![]() Previous |
![]() Next |
![]() Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.