## 3 Methods
### The Data Analysis Methods  
Based on the user data collected from the surveys, this study analyzes the participants' experiences with different gesture types in TV and XR environments using Python (v.3.13) for data processing. The methodology encompasses several analytical procedures as follows. The participants' responses in the UEQ-S from the survey were processed using the UEQ-S data analysis tool [69]. This tool provides statistics and comparative outcomes, enabling a clear understanding of the users' hedonic and pragmatic perceptions acrossdifferent experimental conditions. Based on this setting, we conducted internal consistency analyses ([PERSON]'s \(\alpha\)) for two distinct dimensions that the UEQ-S contained: pragmatic and hedonic quality. For both dimensions, the [PERSON]'s \(\alpha\) values exceeded 0.7 across all gesture types, indicating acceptable reliability. Additionally, we referred to the benchmark data provided by Team UEQ to comparatively interpret the score levels for each gesture type across the environments.  
To clarify the results of the UEQ-S, statistical analyses were performed. All analyses began with a Shapiro-Wilk test to check for normality, followed by the application of either parametric or non-parametric tests depending on whether the within-subject data met the assumptions for normality (see \"Phase #3: Analysis\" in Figure 2). When post hoc tests were conducted, Bonferroni correction was applied to adjust the \(p\)-values and enhance the accuracy of the results. Furthermore, we aimed to examine whether the participants' preferences for gesture types differed between the TV and XR environments. To this end, we conducted both quantitative and qualitative analyses using the UEQ-S scores and the rank order data, in which the participants ranked their preferences for three gesture types in each environment.  
To examine the relationship between the gesture execution time (GET) for each gesture type (see Section 3.4.1) and the user experience measured through the UEQ-S scores further, an additional correlation analysis was conducted. After testing for normality, an appropriate correlation method--either Pearson's or Spearman's--was applied to assessing the relationship between the two variables. In addition, Ordinary Least Squares (OLS) regression was performed to more clearly identify potential linear associations between gesture efficiency and user satisfaction. All statistical analyses were executed using the Python (v.3.13)-based SciPy (v.1.15.2) and Statsmodels (v.0.14.04) libraries, facilitating a comprehensive evaluation of the differences in the user experience metrics across the various gesture types and environments.  
For the interview analysis, an open-coding process was applied to the documents containing the recorded interview contents. Open-coding refers to a process where the research team repeatedly reviews the qualitative data to identify the implicit categories embedded within the interview data. After this, the dispersed open-coded categories are analytically organized to identify and group the core messages from both individual participants and the collective feedback. Via this process, participant comments that represent key messages are selected.