## 4 Results and Analysis
### Results and Analysis of Experiments
#### 4.2.2 Users' Previous Emotions and Their Effects in Real Environments  
The initial emotions of participants were happiness and surprise with 75.56% and 22.22% in the CAIR and 73.33% and 23.33% in the CPIR, respectively. The percentages of emotions after they were exposed to IF or CF three times in the CPIR and the CAIR are shown in Figure 6. Clearly, when users encounter CF, the percentages of negative emotions, such as sadness, anger, and disgust, are larger.  
[PERSON]'s exact test was employed to analyze the effects of users' previous emotions, i.e., RQ3, in real environments, and the results show significant differences. \(\chi^{2}\) = 85.123, \(p\) < 0.001, and the [PERSON]'s V coefficient is 0.357 for the second repeated interaction error, and \(\chi^{2}\) = 111.454, \(p\) < 0.001, and the [PERSON]'s V coefficient is 0.452 for the third time. The magnitude of the effect size is medium, and it grows with the number of times of interaction errors. Statistical differences exist for user emotions after they encounter interaction errors. For example, in the case of the second repeated interaction errors, when the previous emotion is happiness, the adjusted residuals are 2.7 in happiness and \(-2.2\) in anger, respectively, and this means participants tend to be happy after the error. When the previous emotion is surprise, the corresponding adjusted residuals are 3.4 in surprise and \(-2.7\) in disgust, respectively, and this means participants tend to be surprised after the error. In addition, when the previous emotions are negative, the adjusted residuals are larger than 2 in the negative emotions of the users' emotions after they encounter interaction errors. For example, for the three repeated interaction errors, when the previous emotion is disgust, the adjusted residual is 5.6 in disgust. The cases of IF and CF and the cases of the CAIR and the CPIR were considered, respectively. The corresponding results are shown in Table 7. It indicates that the previous emotions in these four cases also show significant differences.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(n\)* & \multicolumn{3}{c}{**CAIR**} & \multicolumn{3}{c}{**CPIR**} \\  & \(\chi^{2}\) & \(p\) & **Cramer’s V** & \(\chi^{2}\) & \(p\) & **Cramer’s V** \\ \hline
1 & 10.649 & 0.033 & 0.346 & 6.535 & 0.163 & 0.338 \\
2 & 9.131 & 0.081 & 0.321 & 6.431 & 0.168 & 0.33 \\
3 & 4.098 & 0.547 & 0.214 & 5.924 & 0.315 & 0.325 \\ \hline \end{tabular}  
* \(n\) is the number of times that error is repeated.  
\end{table}
Table 6: The results in the case of repeated errors for the effects of feedback in CAIR and CPIR, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \multirow{2}{*}{\(n\)*} & \multicolumn{3}{c}{**IF**} & \multicolumn{3}{c}{**CF**} & \multicolumn{3}{c}{**CAIR**} & \multicolumn{3}{c}{**CPIR**} \\  & \(\chi^{2}\) & \(p\) & **Cramer’s V** & \(\chi^{2}\) & \(p\) & **Cramer’s V** & \(\chi^{2}\) & \(p\) & **Cramer’s V** \\ \hline
2 & 38.926 & \textless{}0.001 & 0.452 & 44.692 & \textless{}0.001 & 0.410 & 56.187 & \textless{}0.001 & 0.371 & 28.703 & 0.002 & 0.378 \\
3 & 55.631 & \textless{}0.001 & 0.435 & 62.827 & \textless{}0.001 & 0.54 & 78.449 & \textless{}0.001 & 0.475 & 43.814 & \textless{}0.001 & 0.484 \\ \hline \end{tabular}  
* \(n\) is the number of times that error is repeated.  
\end{table}
Table 7: The results in the case of repeated errors for the effects of previous emotions in IF, CF, CAIR and CPIR, respectively.  
Figure 6: **(a)** The percentages of emotions after interaction errors in CPIR. **(b)** The percentages of emotions after interaction errors in CAIR.  
Then, for RQ4, using log-linear model analysis, no interaction effects between feedback, contexts, and previous emotions are shown, as all \(p\)-values are larger than 0.05 in the step summary of the model.