For each statistical
property there is a class standard deviation of this property.
Here the class standard deviation of the 
distance to the empirical class invariant measure
as defined above is studied.
In figure 6, for each class the class standard deviation of
the distance is computed.
The contribution of each class to a distribution is weighted by
the number of rules in the class. The curves are then normalized so
that the total bin height is 1.
Error bars give 
1 standard deviation over the bin.
Orders of approximation 0-2 are shown.
Increasing dash length corresponds to increasing order of approximation.
These results suggest that variability of statistical
properties among rules in a class is small, and becomes smaller as the
order of approximation is increased.
Some of the variability
may be due to variability in the empirical
measurement of rule invariant statistical properties.
Figure:
Distribution of the class standard deviation of the
distance of the invariant measures of rules in a class to the
empirical class invariant measure.
The contribution of each class to a distribution is weighted by
the number of rules in the class. The curves are then normalized so
that the total bin height is 1.
Error bars give 1 standard deviation over the bin.
Orders of approximation 0-2 are shown.
Increasing dash length corresponds to increasing order of approximation.
The class standard deviation of the distance will be small if rules within a class have similar properties, regardless of how well or poorly the Markov approximation serves to predict these shared properties. It has been demonstrated above that as the order of approximation increases, so does the typically accuracy of predictions. The results presented in this subsection suggest that as the order of approximation increases, so does the tightness with which the properties of rules in a class cluster about their predicted value.