Biology Reference
In-Depth Information
E
XERCISE
6-4
Compare the quantities in Eq. (6-2) with the low blood glucose index
and high blood glucose index measures defined in Chapter 5. What are
the differences? What are the similarities?
E
XERCISE
6-5
Find R
1
and R
2
for the following time series: 666.7, 666.7, 659.3, 666.7,
689.7, 652.2, 666.7, 681.8, 666.7, and 645.2.
Definition. The SA of the data set x
1
, x
2
,
...
, x
n
is defined by the ratio:
R
2
R
1
;
SA
¼
(6-3)
where R
1
and R
2
are the quantities defined by Eq. (6-2).
In Figure 6-7, we present two examples of data sets—one approximately
symmetric (panel A) and one positively skewed (panel B). The graph of
the weighing function (x
m)
2
is given by a solid black line. As
anticipated, the SA for the skewed distribution is higher compared with
the SA for the approximately symmetric distribution (3.5 vs 1.1). Notice
that for the data set with an approximately symmetric histogram, the SA
is close to 1. We leave it as an exercise to verify that the SA measure, as
defined by the Eq. (6-3), satisfies conditions 1 through 4 at the beginning
of this section.
E
XERCISE
6-6
Verify that the measure SA defined by Eq. (6-3) satisfies conditions
1 through 4 listed at the beginning of this section.
Figure 6-8 contains the histograms of the distributions of RRIs
depicted in Figure 6-3. The histograms present the distribution of the
RRI lengths with regard to their deviation from the median value
m. Note that we used a logarithmic vertical scale. As expected, the
distribution of RRIs in the period of health is approximately symmetric
[Figure 6-8(A)], while the HR abnormalities observed before sepsis cause
marked asymmetry of the histograms in panels B and C. The positive
(right) skewness of the histograms is caused by a reduction in the
number of shorter-than-median RRIs. The skewness of the distribution
increased from 0.82 in panel A to 1.92 in panel B and to 1.55 in panel C.
This change, however, is not consistent with the worsening medical
