Biomedical Engineering Reference
In-Depth Information
9 Statistics and Data Analysis
9.1 Statistical Equations
Some equations frequently used in evaluation of experimental data
are given in this chapter. Their theoretical background and math-
ematical derivations can be found in cited literature.
9.1.1 Mean and Related Functions
The arithmetic mean m of a population of values x with n members
is given by:
i
n
x
i
=
1
=
m
n
Degree of freedom of mean F is:
=
F
n−1
Standard deviation (s or SD) of mean
1
quantifies variability:
−
n
x
2
i
n
i
n
i
n
i
(x
i
−m)
2
(x
i
−m)
2
x
2
/n
=
=
=
=
=
1
=
1
=
1
1
s
n−1
F
n−1
Standard error of mean (SEM):
s
√
n
The standard deviation quantifies how much the values vary from
one another, whereas SEM quantifies how precisely you know the
true mean. If you want to show the variability of biological values,
use SD. For characterizing of the precision of an in vitro experiment,
SEM is the best expression.
The coefficient of variation cv (relative variability) is calculated
=
SEM
by
SD
m
=
cv
1
has the same dimension as the respective mean
