## 4 Study Results
### Individual Investors' Profiles  
The dataset from the survey is a two-dimensional table with observations (people) and their features. Previous analysis has focused on clustering of observations to obtain groups of features. The following approach is the opposite; it involves clustering of features to obtain groups of observations that constitute investors' profiles. The data were numeric; thus, the k-means algorithm is sufficient, and extensions as k-modes for qualitative data or k-prototypes for mixed data are unnecessary. We also considered using Self-Organising Maps to detect clusters [42], but the results were not straightforward in interpretation. We ran pre- and post- clustering diagnostics to validate the results. In the pre-clustering analysis, we considered an optimal number of clusters using the silhouette statistic, the gap statistic, inertia and a dendrogram. In the post-clustering analysis, we examined the significance of differences in group means using a pairwise \(t\)-test with the Bonferroni \(p\)-value correction, using tabular and visual inspection tools. We also calculated the ratio  
Figure 5: Clustering of variables: (**a**) dendrogram in hierarchical clustering; (**b**) PCA-reduced dimensions of k-means clustering; (**c**) silhouette statistic; (**d**) feature importance. Note: K-means output (**b**) was PCA-reduced for 2D visualisation purposes; labels of x and y axes show the variance around the first and second principal components. Feature importance (**d**) is measured through misclassification rate; the higher the misclassification rate, the more important given feature. of average values inside and outside the cluster, which shows whether values within the cluster are significantly higher or lower than those in the rest of the sample. In the pre-clustering phase, the silhouette statistic recommended two clusters only, the gap statistic recommended a single cluster, inertia advised 14 clusters, while the dendrogram separated four visible groups. As in the previous section, we used results from the dendrogram, which performed the best with this dataset regarding sample size and inherited clusterability. A number of clusters are visible as vertical groupings (Figure 6). Distinctive division of observations into four clusters was possible at the height of ca. 8. The second feasible partitioning at height = 6.5 generated nine groups, which for 104 observations was too many. Partitioning below height = 6 are almost random and drive the system to singletons. In the post-clustering phase, each of the four obtained clusters conducted for each of the 12 variables involved a test for equality of means inside and outside the cluster. We examined the significance of the differences between inside- and outside-cluster values to determine the significant and important disparities only (Table 6). This helped us to find the significant drivers of each cluster and to validate the quality of partitioning. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Cluster\_1** & **Cluster\_2** & **Cluster\_3** & **Cluster\_4** \\ \hline experience & 0.675 & 0.797 & 0.736 & 1.902 \\ age & 0.000 & 0.000 & 0.706 & 1.414 \\ gender & 0.000 & 0.000 & 0.000 & 0.000 \\ investment & 1.129 & 0.552 & 1.192 & 1.106 \\ Iran\_economy & 0.793 & 0.000 & 0.000 & 0.000 \\ b\_confirmation & 1.206 & 0.000 & 0.000 & 0.845 \\ b\_loss & 1.490 & 1.229 & 0.597 & 0.000 \\ b\_gambler & 1.259 & 0.831 & 0.848 & 0.000 \\ b\_availability & 1.363 & 0.845 & 0.762 & 0.000 \\ b\_hot\_hand & 1.304 & 0.675 & 0.839 & 1.200 \\ b\_bandwagon & 1.438 & 0.000 & 0.758 & 0.000 \\ b\_durning & 0.000 & 0.000 & 0.000 & 1.170 \\ \hline \hline \end{tabular} Note: Non-zero values were reported in cases showing significant differences between the cluster and the rest of the observations. Values in tables are a ratio of average values within the cluster to average values outside the cluster.  
\end{table} 
Table 6: Predominant investors’ profiles. Figure 6: Hierarchical clustering with the dendrogram.