Biomedical Engineering Reference
In-Depth Information
The absolute error of mean
1
EM is calculated from formula
t
SD
√
n
·
=
EM
(for calculation of t see Sect. 9.1.3).
If the observed data follow a bell-shaped Gaussian (normal)
distribution, the confidence interval CI of mean is defined by
=
±
CI
1−P
m
x
EM
N: number of data x
i
; P: probability of significant deviation of
a value from data within interval confidence; t: - borders of the
(1 − P)th part of the area of the Gaussian distribution for a given F.
Mostly the 0.95 confidence interval of mean is given, i.e., you
can be 95% sure that your randomly selected sample of a population
is included in the population mean.
TocalculateEMandCIatagivenFwithdistinctprobabilityP
take t from Table 9.1.
9.1.2 Correlation: Linear Regression
Assuming that the variable y depends on the variable x by a linear
function
=
y
a+b
·
x,
it is often observed that the measured y values randomly deviate
from (theoretical) values calculated from the equation. Because
the true y values are unknown, it is possible to fit the observed
values by the method of least squares. Calculation of the regression
coefficients a and b by this method gives a regression line. The
correlation coefficient r serves as a measure for the goodness of fit
2
.
i
n
(x
i
−m
x
)
·
(y
i
−m
y
)
=
1
=
b
i
n
(x
i
−m
x
)
2
=
1
i
i
n
n
y
i
−b
·
x
=
=
1
1
=
=
a
m
y
−b
·
m
x
n
i
n
(x
i
−m
x
)
·
(y
i
−m
y
)
1
n−1
·
=
1
=
r
s
x
·
s
y
2
1
≥|
r
|≥
0.8, very well correlation; 0.8
≥|
r
|≥
0.6, medium correla-
tion;
|
r
|
<
0.6, bad or no correlation
