## 5 Implementation and User Scenario
### Technical Validation and Experimental Results
#### 5.4.3 Evaluation Criteria and Metrics  
To assess the performance and effectiveness of the proposed system, we used a diverse set of metrics that capture both behavioral and perceptual aspects of user experience across static and dynamically adapted UI models. All metrics were computed using structured  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Platform Name** & **Description** & **Platform** & **User Type** &
\begin{tabular}{c} **Interaction** \\ **Complexity** \\ \end{tabular} \\ \hline E-commerce Web & Online shopping platform & Reactjs & Consumers & High \\ Mobile App & Mobile Shopping app & Flutter & App Users & Medium \\ VR Store & VR shopping experience & WebVR & VR Users & Very High \\ Smartwatch UI & Minimal shopping interface & Watch-OS & Go Users & Low \\ Automotive UI & In-car shopping dashboard & In-car OS & Drivers & Medium \\ \hline \hline \end{tabular}
\end{table}
Table 5: UI Dynamic Adaptation Testing dataset.  
logs generated during simulation runs, and performance comparisons were conducted based on relative percentage changes.  
1. **Conversion Rate (\(CR\)):** Conversion rate measures the percentage of users who successfully complete a target task (e.g., purchase, sign-up): \[CR=\frac{N_{c}}{N_{u}},\] (15) where  
* \(N_{c}\): Number of successful conversions (e.g., purchases)
* \(N_{u}\): Number of unique users  
A relative improvement of over **20%** in CR was used as a threshold to evaluate the effectiveness of UI adaptations.  
2. **Click-Through Rate (\(CT\)):** CTR reflects user interest and engagement by quantifying how often users click on actionable elements: \[CTR=\frac{N_{clicks}}{N_{impression}}\times 100,\] (16) where  
* \(N_{clicks}\): Number of user's clicks on actionable elements.
* \(N_{impression}\): Number of times elements were shown.  
CTR serves both as a standalone indicator and a component of the overall engagement score (defined in Section 5.4.2).  
3. **Session Duration (\(SD\)):** Session duration measures the average length of time users remain actively engaged with the interface:  
\[SD=\frac{\sum_{i=1}^{S}t_{i}}{S}\times 100, \tag{17}\]  
where  
* \(t_{i}\): Duration of session \(i\).
* \(S\): Number of sessions.  
Longer session durations may indicate higher content relevance or user interest but are balanced against task completion time to avoid usability concerns.  
4. **Task Completion Time (\(TCT\)):** This metric captures the average time users take to complete predefined tasks. Faster completion is considered indicative of a more efficient and user-friendly interface:  
\[TCT=\frac{T_{static}-T_{adaptive}}{T_{static}}\times 100. \tag{18}\]  
* \(T_{static},T_{adaptive}\): Average task completion times under static and adaptive conditions. A reduction of **15% or more** was set as a performance improvement threshold.  
5. **User Satisfaction (\(US\)):** User satisfaction is derived from direct feedback collected via Likert-scale surveys (see Section 5.4.2). Users rate their experience across key aspects such as ease of navigation, content relevance, and visual appeal. Satisfaction is calculated as an average rating per user across dimensions:  
\[US_{u}=\frac{1}{N}\times\sum_{i=1}^{N}R_{u,i}, \tag{19}\]where  
* \(R_{u,i}\): rating of user \(u\) for UX aspect \(i\).
* N: number of UX aspects evaluated.
* 6. **Navigation Efficiency (_NU_):** As described earlier, navigation efficiency evaluates the directness of user paths during task execution: \[NU=\frac{L_{optimal}}{L_{actual}},\] (20) where
* \(L_{optimal}\): Optimal number of steps to complete the task.
* \(L_{actual}\): Observed number of steps.  
Higher values indicate smoother and more intuitive user engagement.