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Adjusted p-values for the Friedman Aligned test (DE-Exp is the control method).

Table 14 Adjusted p-values for the Friedman Aligned test (DE-Exp is the control method).

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Average error obtained in the 25 benchmark functions.
Average error obtained in the 25 benchmark functions.
Nonparametric statistical procedures considered in this tutorial. Table 2
Nonparametric statistical procedures considered in this tutorial. Table 2
Associated post-hoc procedures. Table 3
Associated post-hoc procedures. Table 3
ritical values for the two-tailed sign test at w = 0.05 anda = 0.1. An algorithm is significantly better than another if it performs better on at least the cases presented ach row. Table 5 Table 4
ritical values for the two-tailed sign test at w = 0.05 anda = 0.1. An algorithm is significantly better than another if it performs better on at least the cases presented ach row. Table 5 Table 4
xample of Sign test for pairwise comparisons. SaDE shows a significant improvement over PSO, CHC, and SSGA, with a level of significance a = 0.05, and over SS-Arit, with level of significance a = 0.1. 3. Pairwise comparisons populations? It is anonparametric procedure employed in hypoth- esis testing situations, involving a design with two samples. This is analogous to the paired t-test in nonparametric statistical proce- dures; therefore, it is a pairwise test that aims to detect significant differences between two sample means, that is, the behavior of two algorithms.
xample of Sign test for pairwise comparisons. SaDE shows a significant improvement over PSO, CHC, and SSGA, with a level of significance a = 0.05, and over SS-Arit, with level of significance a = 0.1. 3. Pairwise comparisons populations? It is anonparametric procedure employed in hypoth- esis testing situations, involving a design with two samples. This is analogous to the paired t-test in nonparametric statistical proce- dures; therefore, it is a pairwise test that aims to detect significant differences between two sample means, that is, the behavior of two algorithms.
Therefore, a pairwise comparison test, such as Wilcoxon’s test, should not be used to conduct various comparisons involving a set of algorithms, because the FWER is not controlled. In pairwise analysis, if we try to extract a conclusion involving more than one pairwise comparison, we will obtain an accumu: lated error coming from its combination. In statistical terms, we are losing the control on the Family-Wise Error Rate (FWER), definec as the probability of making one or more false discoveries amons all the hypotheses when performing multiple pairwise tests. The true statistical significance for combining pairwise comparisons i: given by
Therefore, a pairwise comparison test, such as Wilcoxon’s test, should not be used to conduct various comparisons involving a set of algorithms, because the FWER is not controlled. In pairwise analysis, if we try to extract a conclusion involving more than one pairwise comparison, we will obtain an accumu: lated error coming from its combination. In statistical terms, we are losing the control on the Family-Wise Error Rate (FWER), definec as the probability of making one or more false discoveries amons all the hypotheses when performing multiple pairwise tests. The true statistical significance for combining pairwise comparisons i: given by
Wilcoxon signed ranks test results. SADE shows an improvement over PSO, CHC, and SSGA, with a level of significance a = 0.01, over IPOP-CMA-ES and SS-Arit, wit a = 0.05, and over SS-BLX, with a = 0.1.
Wilcoxon signed ranks test results. SADE shows an improvement over PSO, CHC, and SSGA, with a level of significance a = 0.01, over IPOP-CMA-ES and SS-Arit, wit a = 0.05, and over SS-BLX, with a = 0.1.
Friedman ranks (Example 4). Table 8 Friedman Aligned ranks (Example 4). Error rates achieved (Example 4). Table 7
Friedman ranks (Example 4). Table 8 Friedman Aligned ranks (Example 4). Error rates achieved (Example 4). Table 7
Ranks achieved by the Friedman, Friedman Aligned, and Quade tests in the main case of study. DE-Exp achieves the best rank in the three procedures. The statistics computed and related p-values are also shown.
Ranks achieved by the Friedman, Friedman Aligned, and Quade tests in the main case of study. DE-Exp achieves the best rank in the three procedures. The statistics computed and related p-values are also shown.
Friedman Aligned z-values and p-values (Example 6).
Friedman Aligned z-values and p-values (Example 6).
Ranks obtained in Example 6.
Ranks obtained in Example 6.
Quade z-values and p-values (Example 6).
Quade z-values and p-values (Example 6).
Friedman z-values and p-values (Example 6).
Friedman z-values and p-values (Example 6).
Adjusted p-values for the Friedman test (DE-Exp is the control method).
Adjusted p-values for the Friedman test (DE-Exp is the control method).
Adjusted p-values for the Quade test (DE-Exp is the control method).
Adjusted p-values for the Quade test (DE-Exp is the control method).
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Evolutionary algorithmsSwarm IntelligenceEvolutionary AlgorithmParameter Optimization
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