Clinical Biochemistry of Domestic Animals (Sixth Edition) - UMK ...

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Chapter | 1 Concepts of Normality in Clinical Biochemistry
of parameters that provide information on the spread of
the distribution. The shape of the distribution is very
important. Some distributions are symmetric about their
center, whereas other distributions are asymmetric, being
skewed (having a heavier tail) either to the right or to
the left.
68.26%
N (m, s 2 )
II . REFERENCE INTERVAL
DETERMINATION AND USE
One task of clinicians is determining whether an animal
that enters the clinic has blood and urine analyte values
that are in the normal interval. The conventional method
of establishing normalcy for a particular analyte is based
on the assumption that the distribution of the analyte in the
population of normal animals is the “ normal ” or Gaussian
distribution. To avoid confusion resulting from the use of
a single word having two different meanings, the “ normal
” distribution henceforth is referred to as the Gaussian
distribution.
A . Gaussian Distribution
Understanding the conventional method for establishing
normalcy requires an understanding of the properties of
the Gaussian distribution. Theoretically, a Gaussian distribution
is defined by the equation
y
1
2πσ
x μ 2 2σ2
e ( ) /
where x is any value that a given measurement can
assume, y is the relative frequency of x , μ is the center
of the distribution, σ is the standard deviation of the
distribution, π is the constant 3.1416, and e is the constant
2.7183.
Theoretically, x can take on any value from to .
Figure 1-1 gives an example of a Gaussian distribution
and demonstrates that the distribution is symmetric around
μ and is bell shaped. Figure 1-1 also shows that 68% of
the distribution is accounted for by measurements of x that
have a value within 1 standard deviation of the mean, and
95% of the distribution includes those values of x that are
within 2 standard deviations of the mean. Nearly all of the
distribution (97.75%) is contained by the bound of 3 standard
deviations of the mean.
Most analytes cannot take on negative values and so,
strictly speaking, cannot have Gaussian distributions.
However, the distribution of many analyte values is approximated
well by the Gaussian distribution because virtually
all the values that can be assumed by the analyte are within
4 standard deviations of the mean and, for this range of
13.59% 13.59%
m2s m1s m
FIGURE 1-1 The Gaussian distribution.
m1s
values, the frequency distribution is Gaussian. Figure 1-2 ,
adapted from the printout of MINITAB, Release 14.13, 1
gives an example of the distribution of glucose values given
in Table 1-1 for a sample of 168 dogs from a presumably
healthy population.
[To produce this figure, place the glucose values for
the 168 dogs in one column of a MINITAB worksheet and
give the following commands:
Stat (from the main menu) → Basic Statistics
→ Graphical Summary
In the Graphical Summary dialog box, select the column
of the worksheet containing the glucose values and place it
in the Variables: box. Hit OK .
Though not perfectly Gaussian, the distribution is reasonably
well approximated by the Gaussian distribution.
Support for this claim is that the distribution has the characteristic
bell shape and appears to be symmetric about
the mean. Also, the mean [estimated to be 96.4 mg/dl
(5.34mmol/liter)] of this distribution is nearly equal to the
median [estimated to be 95.0mg/dl (5.27mmol/liter)], which
is characteristic of the Gaussian distribution. The estimates
of the skewness and kurtosis coefficients are close to zero,
also characteristic of a Gaussian distribution ( Daniel, 2005 ;
Schork and Remington, 2000 ; Snedecor and Cochran,
1989 ).
B . Evaluating Probabilities Using
a Gaussian Distribution
m2s
All Gaussian distributions can be standardized to the reference
Gaussian distribution, which is called the standard
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