Database Reference
In-Depth Information
FIGURE 4.7
Crosstabs: Statistics dialog box; SPSS.
The main, and crucial, difference between the result we got in Excel and the result
obtained in SPSS is the availability of the Fisher's exact test (see solid arrow in
Figure 4.8
)
in addition to the regular chi-square result displayed (see dashed arrow in
Figure 4.8
).
And you can note that the chi-square
p
-value is the same 0.006 (here, rounded to three
digits) as we obtained doing the analysis in Excel. This, of course, is not a surprise!
SIDEBAR: FISHER'S EXACT TEST
Fisher's exact test was developed by Fisher (duh!), since it was noticed that the chi-square test of
independence did not perform as accurately as desired for a 2×2 table. Thus, we use Fisher's exact
test only when we have a 2×2 table. As a matter of fact, if you have more than two columns being
compared, the Fisher exact test will not even appear as part of the SPSS output. The primary reason
why Fisher's exact test is superior to the chi-square test when we have a 2×2 table is that the chi-
square is a continuous probability distribution, while the observed frequencies (number of passes
and fails that comprise our data) are, of course, integers. This “discrepancy,” or “disconnect,” is
immaterial when we have more than two quantities being compared, but is just material enough to
be noticed by Fisher and lead to his developing Fisher's exact test for the two comparison case. In
Figure 4.8
, the
p
-value for the chi-square is 0.006, while for the Fisher exact test it is 0.020. This is
a small difference (0.014) and leads to the same answer—reject H0—and the same conclusion that
the pass/fail rates are different for task 1 between Novix and Behemoth.
We mention this only because Excel does not provide the result for Fisher's exact test (theoreti-
cally, a shortcoming of Excel, but
C'est la vie
); in the vast, vast majority of time, the chi-square test
of independence and Fisher's exact test yield the same conclusion, as they do here.
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