# Significance of Single-Interval Discrete Attributes: Case Study on Two-Level Discretisation
## 6 Discussion of Obtained Results
The maxima were close for both equal frequency and equal width algorithms, for both F-writers and M-writers and all learners. The provided bin numbers that were found accompanying the maxima indicate that, in the majority of cases, second level discretisation was advantageous. For some of the inducers, that was true for either the training or test sets, but for others, that was true also for both types of sets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Inducer**} \\ \cline{2-6}  & **NB** & **BNet** & **J48** & **kNN** & **RndF** \\ \hline Statistics & \multicolumn{5}{c}{F-writers, equal frequency binning (duf)} \\ \hline Avg & 93.39 & 89.42 & 87.00 & 86.83 & 92.45 \\ St.dev. & 01.34 & 02.33 & 02.56 & 01.75 & 02.37 \\ Min & 91.18 & 85.63 & 81.74 & 83.89 & 87.02 \\ Max & 95.77 & 92.85 & 91.18 & 89.17 & 95.84 \\ \(i\)-\(T_{Max}\) & 07 & 04 & 02 & 06 & 07 \\ \hline \multicolumn{6}{c}{F-writers, equal width binning (duw)} \\ \hline Avg & 90.65 & 89.76 & 86.68 & 85.91 & 90.94 \\ St.dev. & 01.60 & 02.26 & 03.39 & 01.81 & 02.83 \\ Min & 87.02 & 86.95 & 80.42 & 82.78 & 86.32 \\ Max & 92.22 & 93.41 & 90.97 & 88.68 & 94.59 \\ \(i\)-\(T_{Max}\) & 06 & 07 & 08 & 09 & 09 \\ \hline \multicolumn{6}{c}{M-writers, equal frequency binning (duf)} \\ \hline Avg & 79.48 & 79.27 & 77.11 & 74.22 & 81.61 \\ St.dev. & 02.30 & 02.43 & 03.75 & 02.97 & 02.69 \\ Min & 75.35 & 75.77 & 69.31 & 68.47 & 75.97 \\ Max & 81.60 & 81.74 & 80.91 & 77.85 & 84.38 \\ \(i\)-\(T_{Max}\) & 04 & 04 & 10 & 07 & 04 \\ \hline \multicolumn{6}{c}{M-writers, equal width binning (duw)} \\ \hline Avg & 79.44 & 79.37 & 75.59 & 72.74 & 80.35 \\ St.dev. & 02.54 & 02.81 & 02.21 & 02.36 & 03.98 \\ Min & 73.82 & 73.96 & 71.95 & 69.52 & 73.68 \\ Max & 82.22 & 82.92 & 79.24 & 77.22 & 85.14 \\ \(i\)-\(T_{Max}\) & 06 & 04 & 04 & 06 & 09 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistics of performance [%] for the inducers working on the datasets discretised by unsupervised algorithms (duf and duw). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Inducer**} \\ \cline{2-6}
**Dataset** & **NB** & **BNet** & **J48** & **kNN** & **RndF** \\ \hline F-writers & duf07 & duw07 & dsK & duf06 & duf07 \\  & 95.77 & 93.41 & 93.40 & 89.17 & 95.84 \\ M-writers & duw06 & duw04 & duf10 & dsF & duw09 \\  & 82.22 & 82.92 & 80.91 & 83.54 & 85.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The best performance [%] and the corresponding discretisation method for the standard approaches applied to the data. Table 10 includes the summarising characteristics for processing involving the Kononenko algorithm combined with unsupervised methods. Overall, the standard deviation for this group of discretisation approaches was rather lower than for the Fayyad and Irani methods used for the first level of discretisation. Yet still, J48 stood out from the other classifiers as the one with the lowest values of this characteristics. When the Kononenko-based two-level discretisation was compared with the Fayyad and Irani employed on the first level, it was observed that for most classifiers, the former was slightly better than the latter, in particular for the female writer dataset. The values of calculated averages, minima, and maxima were typically higher, while the standard deviation was smaller. In addition, for these variants of the data, in most cases additional transformations of 1-bin variables in sets resulted in enhanced predictions. All the detailed results from the substantial experiments performed, given in the previous section in the tables and charts and supported with summaries and characteristics included in this section, illustrate the advantages of employing the two-level approach to