## 5 Analysis of Results
### Detailed Analysis  
Figure 8 illustrates the responses for question Q1_1 to Q1_14 regarding the usability of 3D sketching tools in IVR: the Likert scale ranges from value 1 for strongly disagree to value 5 for strongly agree, with the neutral grade at value 3. Figure 9 illustrates the results obtained on the second survey on participants' experiment through the ephemeral architectural spaces at the Faculty of Fine Arts. The distribution of responses are displayed as a boxplot with whiskers. We can see that for the first survey about 3D sketching skills, the range of responses is much more distributed than for the survey about the sensations elicited by the designed space. It is common in practice to treat Likert scale data as if it is continuous, especially when aggregated across many participants. This simplification is widely used in survey research and applying the t-test can still yield meaningful insights. Based on these data, we can analyze whether the responses significantly differ from a neutral stance using statistical tests with a one-sample t-test. In a one-sample t-test, the null hypothesis (H0)  
Figure 8: Survey 1: Opinion on the Use of 3D Sketching Tools. For each box plot, the red circle is the mean answer. The box extends from the first quartile to the third quartile of the data, with a red line at the median. Figure 9: Survey 2: Beliefs about the Virtual Tour: distribution of responses. For each box plot, the red circle is the mean answer. The box extends from the first quartile to the third quartile of the data, with a red line at the median. states that \"_The sample mean is not significantly different from the population mean\"_. The alternative hypothesis is that \"_The average response is significantly different from neutral\"_. The neutral stance value is 3: we test if the mean response is significantly different from the neutral value (3). The \(p\)-value is the probability of obtaining a t-statistic as extreme as the one calculated. In Table 1, for each question the \(p\)-values were below the significance threshold of 0.05, making the result statistically significant, except for Q1_2 (\(p\)-value = 0.061) and Q1_4 (\(p\)-value = 0.107). When the \(p\)-value is above the commonly used significance threshold of 0.05, it means the result is not statistically significant: we can conclude that the average response for Q1_2 and Q1_4 is not significantly different from neutral. The average response for each of the other questions is significantly different from neutral, likely higher (agreement) or lower (disagreement). On the second survey, \"Beliefs about the Virtual Tour,\" for each question, the \(p\)-value was below the significance threshold of 0.05 (see Table 2). Since the \(p\)-values are much smaller than 0.05, we can reject the null hypothesis, meaning the responses are significantly different from the neutral value (3). Specifically, for questions Q2_1 to Q2_7, the strong positive t-statistic suggests that responses are significantly skewed towards agreement (4-5 range). For question Q2_8, the responses are significantly skewed toward disagreement because most of the participants did not have experience with VR. Researchers frequently use t-tests to evaluate survey responses aggregated in this way, especially when comparing a sample mean to a hypothesized value. It is a pragmatic choice widely seen in applied fields like psychology, education, and usability studies. Since Likert scales are ordinal, non-parametric statistical methods are often more appropriate for analysis. Assuming the distances between responses are equal, some researchers treat Likert scale data as interval data for parametric tests. One can argue that our data are not normal, but using a non-parametric test such as the Wilcoxon Signed-Rank test gives a similar result: it is a non-parametric test used to evaluate whether the median of a sample differs significantly from a specified value (in this case, 3).