## 3 Results
### Results of the Pairwise Comparison with Forced-Choice
#### 3.2.1 Results of the Wireframe Buttons  
The observed frequencies of the winners and losers of the wireframe button versions (Buttons BW) in the pair comparison are shown in Table 6. In Table 6, the sum of the wins in the last column shows that the fourth version (V4) was preferred in most pairwise comparisons (115 out of a total of 400). This is followed in order by the third version (V3; 114 out of 400), the fifth version (V5; 91 out of 400) and the second version (V2; 75 out of 400). The first version (V1) shows the fewest gains (5 out of 400).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Buttons Blue** & **V1** & **V2** & **V3** & **V4** & **V5** & **Wins** \\ \hline V1 & & 10 & 4 & 9 & 12 & 35 \\ V2 & 22 & & 11 & 19 & 23 & 75 \\ V3 & 28 & 21 & & 13 & 17 & 79 \\ V4 & 23 & 13 & 19 & & 18 & 73 \\ V5 & 20 & 9 & 15 & 14 & & 58 \\ \hline Losses & 93 & 53 & 49 & 55 & 70 & 320 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The observed frequencies of the wins and losses of the different blue buttons.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **V1*** & **V2** & **V3** & **V4** & **V5** \\ \hline estimate & 0 & 1.0696 & 1.1834 & 1.0234 & 0.6302 \\ rank & 5 & 2 & 1 & 3 & 4 \\ \hline \hline \end{tabular} \({}^{*}\)V1 acts as the reference object.  
\end{table}
Table 5: The estimators for the item parameters and the ranks assigned to the blue buttons.  
After the frequencies were presented, the simple Bradley-Terry model was estimated. The estimators for the parameters of the items and the ranks assigned to the button versions are shown in Table 7.  
The parameter for the first button version (V1) was also set to zero in this case and thus functions again as a reference object. Based on the coefficient estimators (see Table 8), the study participants most frequently preferred the fourth button version (V4). In second place was the third button version (V3), followed by the fifth (V5) and the second (V2) button version. In last place, the most angular and therefore first button version (V1) can be found. For visualization, a graphical representation of the coefficient estimators is shown with the gray line in Figure 7. The first button version (V1) represents the reference object.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Buttons BW** & **V1** & **V2** & **V3** & **V4** & **V5** & **Wins** \\ \hline V1 & & 1 & 0 & 0 & 4 & 5 \\ V2 & 39 & & 9 & 10 & 17 & 75 \\ V3 & 40 & 31 & & 23 & 20 & 114 \\ V4 & 40 & 30 & 17 & & 28 & 115 \\ V5 & 36 & 23 & 20 & 12 & & 91 \\ \hline Losses & 155 & 85 & 46 & 45 & 69 & 400 \\ \hline \end{tabular}
\end{table}
Table 6: The observed frequencies of the wins and losses of the different wireframe buttons.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Buttons Blue** & **V1** & **V2** & **V3** & **V4** & **V5** & **Wins** \\ \hline V1 & & 0 & 3 & 3 & 9 & 15 \\ V2 & 40 & & 12 & 19 & 19 & 90 \\ V3 & 37 & 28 & & 23 & 24 & 112 \\ V4 & 37 & 21 & 17 & & 26 & 101 \\ V5 & 31 & 21 & 16 & 14 & & 82 \\ \hline Losses & 145 & 70 & 48 & 59 & 78 & 400 \\ \hline \end{tabular}
\end{table}
Table 7: The estimators for the item parameters and the ranks assigned to the wireframe buttons.  
Figure 7: Graphical representation of the coefficient estimators of the BT model for the data resulting from the pairwise comparison of the wireframe buttons and the blue buttons. The gray line refers to the wireframe buttons and the blue line to the blue buttons.