Observation Oriented Modeling
- How is it possible to obtain a c-value less than
zero? I tested a model and the c-value was reported as : "Model
c-value :< 0.00"
Version 2 of OOM clarifies this potential source of confusion. Chance
values are now printed out in a format in which they are never reported as
0.00 or "< 0.00." If a randomization test fails to meet or exceed the PCC
index, then the c-value is reported as a note. For instance, for 1000 trials,
the note will appear as: "less than ( 1 /
1000); that is, < 0.001".
Here's the answer to this question for Version 1:
The c-value is in fact not less than zero. The c-value can also not, in
principle, be exactly equal to zero. With more decimal precision the "< 0.00"
text would be replaced with a value other than zero. For instance, consider
setting the randomization test to 1000 trials. Further, suppose the results
showed that not 1 in 1000 trials was the observed Percent Correct
Classification (PCC) index equaled or exceeded by the randomized versions of
the observations. In such an example, the c-value would be some value less
than 1 in 1000, or less than .001 (1 / 1000). With only two decimals of
precision, the result appears as "< 0.00", but with three decimals of
precision it appears as "< 0.001." When OOM encounters at least
one PCC value from randomized observations, then the inequality is removed
from the output; e.g., "Model c-value :
0.02." The c-value is never reported
as "Model c-value = 0.00"
because the observed pattern of results and
computed PCC index is a single event or ordered pattern out of many more
possible patterns. The observed pattern may be one of a trillion
possible patterns and may thus rarely show up when the observations are
randomized, but the c-value is still not exactly equal to zero.