In the same way that we can introduce additional quantities into the
adjustment, so too can we determine the effects of withdrawing
quantities from the adjustment. We might do this for various
reasons,
but here particularly for the purpose of investigating the
rather peculiar nature of the specifications over 
and its
observed value 
.
When we remove 
from the adjustment at this stage, it as though
we are left with a simple adjustment of 
by . In
addition, we also learn about the partial adjustment of by
. Some of the results of this partial adjustment are worth
further consideration as follows. The resolutions for the adjustment by
and for the partial adjustment removing are:
showing - as we suspected - that alone is not a good source of
information: its effect is at best to reduce uncertainty by less than
5%; and that most of the information is contained wholly in :
when we remove we also remove nearly all of our
capability to reduce uncertainty in .
The evaluated adjusted expectations for the adjustment by
solely are
representing fairly large changes
( 
standard deviations) from the
initial values of 4.16 and 6.25 respectively. Although these are fairly
large changes, they correspond to only small reductions in uncertainty
about 
and 
. Informally it is as though the prior and
posterior distributions for and are quite flat, so
that large changes in expectation can correspond to small changes in
uncertainty.
Figure 3: Sizes for the adjustments and
The sizes of the adjustments are shown in figure 3 and
display two remarkable features. Firstly, the size ratio for the simple
adjustment by is more than five times as large as expected;
and secondly the size ratio for the partial adjustment after adjusting
by additionally is very much smaller than expected. The former
feature is more or less expected, given the sizes for the similar
adjustment shown in figure 2. The latter feature may be
interpreted as showing that a partial adjustment by in
addition to is expected to enable changes in expectation that
simply don't materialise.
Comparing figure 3 with figure 2, we see a size
ratio of 
for the simple
adjustment, and a size ratio of 
for
the partial adjustment by 
. Thus, the size ratio for the
simple adjustment is larger than the size ratio for the
adjustment where has been extracted. This might suggest that
although we have identified (with its observation )
above as having some peculiar features, this is also true of the portion
of that is common to .