Biology Reference
In-Depth Information
formed observations to obtain and . It is easy to see that
(
) /
2
2
05
.
05
.
1
˜
1
2
XN
~
,
and
(
) /
n
05
.
05
.
2
1
(
) /
2
2
(
) /
2
2
0
.
5
0 5
.
1
˜
1
2
1
2
YN
~
,
.
(
) /
(
) /
m
05
.
05
.
2
1
2
1
To study the difference between the two populations, now we
superimpose, that is translate, so that it matches in the
sense that is minimized. It can be seen
that the best translation in this case is no translation at all,
and that the difference between two populations is given by:
. As the sample sizes converge to infinity, this quantity
˜
˜
)(
˜
˜
)}
rXYXY
T
{(
converges to
2.
Edge superimposition analysis:
We can conduct similar
calculations where instead of translating the observations so
that least squares criterion is satisfied, we translate them so
that the first component (landmark 1) is matched. Such calcu-
lations lead to the difference in two populations which
converges to It leads us to the conclusion
that treatment 2 is effective only in reducing the systolic
blood pressure and has no effect on the diastolic blood pres-
sure. Had we decided to match the second component
(landmark 2), we would have come to the conclusion that
treatment 2 only affects the systolic blood pressure and not
the diastolic blood pressure.
It should be obvious from the above example, that the choice of the
side conditions has a significant impact on the scientific conclusions
and that even an infinite amount of data cannot tell us which side con-
dition is “correct.” One may argue that the choice of the side condition
is similar to the choice of the “Normal” distribution model. The differ-
ence between choosing a particular model such as the Normal
distribution in the above example and choosing a side condition is that
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