The Journal of Finance
significant ratio on an individual basis. In fact, based on the statistical significance
measure, it would not have appeared at all. However, because of its
unique relationship to other variables in the model, the Sales/Total assets ratio
ranks second in its contribution to the overall discriminating ability of the
model.
To test the individual discriminating ability of the variables, an " F " test is
performed. This test relates the difference between the average values of the
ratios in each group to the variability (or spread) of values of the ratios within
each group. Variable means one financial statement prior to bankruptcy and
the resulting "F" statistics are presented in Table 1.
TABLE 1
VARIABLE MEANS AND TEST OF SIGNIFICANCE
Bankrupt Non-Bankrupt
Variable Group Mean Group Mean F Ratio
X4
X5
n=33
- 6.1%
-62.6%
-.-31.8%
40.1%;
150.0%
el.
^1,6
^1,6
^1,6
0 (.001)
0 (.01 )
0 (.05 )
n = 33
41.4%
35.5%
15.3%
247.7%
190.0%
= 12.00
= 7.00
= 4.00
32.60*
58.86*
26.56*
33.26*
2.84
Significant at the .001 level.
Variables Xi through X4 are all significant at the .001 level, indicating extremely
significant differences in these variables between groups. Variable Xs
does not show a significant difference between groups and the reason for its
inclusion in the variable profile is not apparent as yet. On a strictly univariate
level, all of the ratios indicate higher values for the non-bankrupt firms. Also,
the discriminant coefficients of equation (I) display positive signs, which is
what one would expect. Therefore, the greater a firm's bankruptcy potential,
the lower its discriminant score.
One useful technique in arriving at the final variable profile is to determine
the relative contribution of each variable to the total discriminating power of
the function, and the interaction between them. The relevant statistic is observed
as a scaled vector which is computed by multiplying corresponding elements
by the square roots of the diagonal elements of the variance-co-variance
matrix.^^ Since the actual variable measurement units are not all comparable to
each other, simple observation of the discriminant coefficients is misleading.
The adjusted coefficients shown in Table 2 enable us to evaluate each variable's
contribution on a relative basis.