## 4 Study Results
### Direction and Strength of Biases  
The previous section revealed the patters of biases based on individual characteristics such as gender, age, and experience, but examined them separately. The analysis below goes further by discussing the behaviour of fallacies in groups (clusters). By grouping the biases together and comparing them with each other, one can measure which biases are crucial to explaining the variability within our data. For this purpose, we first implemented the Principal Component Analysis (PCA) method to reduce the dimensions of our independent variables and to then extract the variables that contribute the most to the dispersion of our individual investors. This analysis is oriented towards discovering whether any cognitive biases or investors' features overlap in terms of informational content. PCA analysis, based on eigenvectors, finds the synthetic variables--the axes of highest variability of data. The first and second eigenvectors are typically analysed and plotted, while their explanatory power results from the percentage of variance explained. The contribution of the variable to the following principal components is to make a ranking of their importance. The second method applied here, clustering of observations, allows for explicit groups of similar factors to be obtained. Unsupervised learning algorithms, such as k-means, require setting a priori the number of clusters; this parameter is crucial for the final grouping. There are many criteria for selecting the most appropriate number of clusters [41], while \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Years of Experience on the Stock Market**} \\ \cline{2-7}  & **\textless{3**}** & **3–5** & **5–10** & **\textgreater{10**}** & **Statistics** & \(p\)**-Value** \\ \hline Confirmation & 4.065 & 3.603 & 3.469 & 3.550 & 7.124 & 0.201 \\ \hline Loss aversion & 3.417 \({}^{\text{a}}\) & 2.790 \({}^{\text{b}}\) & 3.394 \({}^{\text{ab}}\) & 3.090 \({}^{\text{ab}}\) & 15.744 & 0.025 \({}^{\text{*}}\) \\ \hline Gambler’s & 3.394 & 3.502 & 3.380 & 3.613 & 10.107 & 0.087 \\ \hline Availability & 2.910 \({}^{\text{a}}\) & 2.858 \({}^{\text{a}}\) & 2.928 \({}^{\text{b}}\) & 2.932 \({}^{\text{ab}}\) & 12.524 & 0.047 \({}^{\text{*}}\) \\ \hline Hot hand’s & 2.932 & 3.109 & 3.239 & 3.459 & 11.334 & 0.072 \\ \hline Bandwagon & 2.936 \({}^{\text{a}}\) & 3.147 \({}^{\text{a}}\) & 2.622 \({}^{\text{b}}\) & 3.005 \({}^{\text{a}}\) & 16.226 & 0.020 \({}^{\text{*}}\) \\ \hline Dunning-Kruger & 3.228 \({}^{\text{ab}}\) & 3.035 \({}^{\text{a}}\) & 3.774 \({}^{\text{ab}}\) & 3.776 \({}^{\text{b}}\) & 11.823 & 0.044 \({}^{\text{*}}\) \\ \hline \hline \end{tabular} Note: letters in superscripts indicate significantly different groups.  
\end{table} 
Table 4: Fallacies based on years of experience on the stock market. their recommendations are often very diverse, as shown in practice. Each dataset requires individual treatment due to differing degrees of clusterability. An efficient approach is to inspect the hierarchical clustering, for which the dendrogram presents all available partitioning (from separation of all observations into individual [bottom] clusters called singletons to collection of all data into a single [top] cluster). Vertical lines illustrate the number of clusters at a given height (on the y axis) and support the clustering decision with regard to clusterability. To assure the robustness of division into groups, the dendrogram clusters are compared with k-means clusters. The following two measures of quality were applied: silhouette statistic, which examines whether the centroids of an object's own cluster are closer than centroids of the second-closest cluster (fine partitioning if all individual silhouette values are non-negative); and variable importance, which checks for each variable the degree to which partitioning changes when the examined variable is shuffled (a variable is important when, due to mixing of its values, the misclassification rate on the x-axis is high).