## 4 Results
### Results of Analyses of Effects of Two Factors
#### 4.2.6 Analysis of the Pair Contrast Ratio and the Device Used  
The last pair to be examined is the contrast ratio and the device used. For the contrast ratio, the authors used the same groups as before, \"NO_C\" and \"INC_C\". After creating the pairings, the \"NO_C, desktop display\" comprised 1183 tests, \"NO_C, Gear VR\" comprised 293 tests, \"INC_C, desktop display\" comprised 977 tests, and \"INC_C, Gear VR\" comprised 256 tests, as can be seen from Table 14. The results of the logistic regression analysis are presented in Table 25.  
The point of reference was \"NO_C, Desktop display\". According to the results, the Gear VR does not present a significant improvement with the \"NO_C\" contrast. However, with the \"INC_C\"  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Camera Rotation and Device Used** & **Estimate** & **Standard Error** & \(z\)**Value** & **Pr (\textgreater{}|z|)** \\ \hline Intercept & 0.63039 & 0.01778 & 35.465 & \textless{}2\times 10^{-16}\) \\ INC\_R & 0.11682 & 0.02500 & 4.673 & \(2.97\times 10^{-6}\) \\ Gear VR & \(-0.04388\) & 0.05049 & \(-0.869\) & \(0.3847\) \\ INC\_R and Gear VR & 0.13070 & 0.06115 & 2.137 & \(0.0326\) \\ \hline \hline \end{tabular}
\end{table}
Table 23: Logistic regression analysis results of the interactions between camera rotation and the device used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Resid.** & **Df Resid.** & **Dev** & **Df** & **Deviance** & **Pr (\textgreater{}Chi)** \\ \hline
1 & 2706 & 10,113 & - & - & - \\
2 & 2705 & 10,108 & 1 & 4.5511 & 0.0329 \\ \hline \hline \end{tabular}
\end{table}
Table 24: Comparison of the variables camera rotation and device used by ANOVA.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Camera Rotation and Device Used** & **Estimate** & **Standard Error** & \(z\)**Value** & **Pr (\textgreater{}|z|)** \\ \hline Intercept & 0.65115 & 0.01679 & 38.786 & \textless{}2\times 10^{-16}\) \\ NO\_C, Gear VR & 0.03204 & 0.03780 & 0.848 & 0.396699 \\ INC\_C, Desktop display & 0.08647 & 0.02514 & 3.440 & 0.000583 \\ INC\_C, Gear VR & 0.21296 & 0.04108 & 5.184 & \(2.18\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 25: Logistic regression analysis results of the additive model with variable contrast ratio and device used, allowing interaction.  
contrast, the results are significantly better. Moreover, if we compare \"INC_C, Desktop display\" and \"INC_C, Gear VR\", although the differences between the average rates are large (see Table 14), this difference is not significant (\(p\)-value = 0.06332). This is due to the relatively small number of tests (256 tests).  
Although the difference between the average rates of \"NO_C, Desktop display\" and \"INC_C, Desktop display\" provides a significant difference because the numbers of the samples is higher, the authors suspect that if they had more tests with Gear VR, the difference would become significant. Performing the logistic regression analysis for the additive model containing the variables contrast ratio and device used and applying the available data set, the same phenomenon can be realized (Table 26).  
Table 26 indicates that the contrast ratio has a significant effect (\(p\)-value = 0.000583), but aside from the described influence, the influence of the device is not significant (\(p\)-value = 0.396699) and interaction has not been detected (\(p\)-value = 0.094199). Table 27 shows the results of their interactions.  
Due to \(p\)-value = 0.09403, the authors concluded that the model that takes the interactions into account does not provide a significantly better probability in contrast to the additive model.