Biomedical Engineering Reference
In-Depth Information
pecially when a low correlation coefficient r is obtained. If there is
Comparison of
different fits
no linear correlation, a non-linear regression calculation of a hy-
perbola or sigmoid function should be selected. To support the de-
cision for another hypothetical model, some computer programs
offer a comparison of the different fits.
9.1.3 The
-test (Student's Test)
t
During an experiment one has a set of data which seems to be
formed from two groups. Is it wise to calculate a single mean of all
data because difference between means of subpopulations results
fromsimplefluctuations,orhavewetoformtwosubpopulations
with significantly different means? The hypothesis that all data are
parts of a sole population is the so-called null hypothesis. The
Null hypothesis
rejection of the null hypothesis leads to establishing a significant
difference between both groups of data. The
t
-test is used to decide
this question.
Student's test compares the means of both groups and is re-
stricted to two sets of data, which should come from a normal
distribution. The
t
-test works well if the variances of both groups
are not very different and the number of data in each data set is
similar.
If the null hypothesis is true, the calculated
t
-value is smaller
or equal to that obtained from Table 9.1 for the respective degree
of freedom and a chosen probability P, i.e., there is a significant
difference between the both means if t
calculated
>
t
1−P(Table)
.
For example, if the calculated
t
-value of group A (n
=
9) and B
=
=
=
(n
10) with F
F
A
+F
B
17, is 2.70, the groups are significantly
=
=
different at P
0.01.
The probability for a significant difference is (1−P)
0.02, but they are not different at P
=
·
100
98%.
n
A
·
n
B
n
A
+n
b
s
D
=
t
(m
A
−m
B
)
·
=
or,ifn
A
n
B
n
2
(m
A
−m
B
)
s
D
=
t
·
The standard deviation s
D
of the difference of the both means is
calculated by the equation
(x
Ai
−m
A
)
2
+
(x
Bi
−m
B
)
F
=
s
D
with
=
F
n
A
+n
B
−2
