Graphics Reference
In-Depth Information
Table 2.6
Average rankings
of the algorithms (Friedman)
Algorithm
Ranking
MLP-CG-C
2.5
RBFN-C
3.3333
SONN-C
1
LVQ-C
3.1667
Computing the Friedman and Iman-Davenport statistics as in Eqs. (
2.3
) and (
2.4
)
the respective values are:
•
Friedman statistic
(distributed according to chi-squared with 3 degrees of free-
dom): 12.2.
p
-value computed by Friedman Test:
0.006729
.
•
Iman and Davenport statistic
(distributed according to F-distribution with 3 and 15
degrees of freedom): 10.517241.
p
-value computed by Iman and Daveport Test:
0.000561296469
.
In our case, both Friedman's and ImanDavenport's tests indicate that significant
differences in the results are found in the three validations used in this study. Due to
these results, a post-hoc statistical analysis is required. In this analysis, we choose
the best performing method, SONN, as the control method for comparison with the
rest of algorithms.
Post-hoc comparision
We will first present the results obtained for Bonferroni-Dunn's, Holm's and
Hochberg's post-hoc tests with no adjustment of the
p
-values. Table
2.7
summa-
rizes the unadjusted
p
-values for each algorithm when compared to SONN.
By computing Bonferroni-Dunn's CD as in
2.5
those hypotheses that have an
unadjusted p-value
016667 are rejected. By using the
z
value indicated for
Holm's and Hochberg's procedures, we can observe that they reject those hypotheses
that have an unadjusted p-value
≤
0
.
05. The reader may notice that Bonferroni-
Dunn's is not able to reject the null-hypothesis for SONN versus MLP, while Holm's
and Hochberg's are able to reject all null-hypothesis due to their higher statistical
power.
The reader may usually refer directly to the adjusted
p
-values for the post-hoc
methods, as they make searching for critical differences unnecessary and improve
≤
0
.
Table 2.7
Post Hoc comparison table for
α
=
0
.
05 (Friedman)
i
Algorithm
z
=
(
R
0
−
R
i
)/
SE
p
Holm Hochberg
3
RBFN-C
3.130495
0.001745
0.016667
2
LVQ-C
2.906888
0.00365
0.025
1
MLP-CG-C
2.012461
0.044171
0.05
