Biology Reference
In-Depth Information
Actual BG Scale
1.1
3.9
6.25
10
33.3
−
0.9
0
0.9
− √
10
√
10
Transformed BG Scale
FIGURE 5-6.
Transformation of the BG scale that uses the function f (BG ) from Eq. (5-4).
(a) Find the target range and the whole range of BG values in the U.S.
system.
(b) Find the values of
that will transform the target and whole
ranges into intervals centered at 0 for the U.S. system.
a
and
b
(c) Find the value of
g
that will scale the whole BG range to be
1
p
to
1
p
.
between
It is now time to test the transformation to determine its validity. We
again consider Figure 5-4, which presents the distribution of 186 BG
readings from the SMBG device of a subject with T1DM. As evident
from the graph, the distribution is substantially skewed. In fact, when
we calculate the basic statistics for the data, we find that the mean is
6.7 mmol/L and the standard deviation is 3.6. In applying statistical
tests, it is standard practice to assume that 95% of the data lies within
two standard deviations of the mean. For this data, x
¼
6
:
7, SD
¼
3.6, so
x
0.5 to 13.6 mmol/L. Now
about 2.5% (or four readings from the total 186 readings of this data)
should lie below
2
ð
SD
Þ¼
6
:
7
7
:
2 gives the range
0.5 mmol/L, which cannot happen.
We expect this skewed distribution will appear nearly normal in the
transformed BG measurement scale, and Figure 5-7 confirms this. It
presents the histogram of the same data over the transformed
symmetrized scale. Notice how symmetric the data now appear. If we
find the mean x and the SD of the data in this scale, we find
x
1.02. So x
¼
0
:
13 mmol
=
L and SD
¼
2
ð
SD
Þ¼
0
:
13
2
:
4, which
gives the range
2.17 to 1.91 mmol/L. Now four readings fall below
2.17 and three above 1.91. This is nearly an exact fit with a normal
distribution.
