## 5 Validation
### Experiment A: Evaluating the Improvement in the Hit Rate Using the Haptic Tuning Fork
#### 5.1.3 Results  
We checked the normality of the data using Kolmogorov-Smirnov and we applied the Student's t-test for paired samples. Results for the haptic scale with three notes were not statistically significant, whether using or not the haptic tuning fork. Actually, the hit rate was in both cases close to 100%.  
In the case of the scale of 5 haptic notes, the hit rate mean difference with and without haptic tuning fork, 10.3%, showed statistical significance at the 95 level (\(p\)-value \(<\) 0.05), favouring the use of the haptic tuning fork, see Figure 2(a). For the scale of 7 stimuli, the hit rate mean difference is 22.08%, which was also statistically significant (\(p\)-value \(<\) 0.001), see Figure 2(b). Details about the transmitted information can be found in the Supplementary Materials.  
Figure 4 shows the interaction effect of the number of notes in the frequency-based scale and the use of the haptic tuning fork on the hit rate and on the percentage accumulated error. A two-way ANalysis Of VAriance (ANOVA) followed by a post hoc analysis using the Tukey test showed these interaction effects were significant (\(p\)-value \(<\) 0.05). The use of the haptic tuning fork is particularly important when the haptic scale has a higher number of notes, increasing participants' hit rate, and decreasing the accumulated error, see Figure 4.  
Figure 3: Hit rate results for Experiment A.  
The accumulated error was calculated by adding the difference between the reported notes and the number identifying the real notes. The mean difference in the accumulated error, \(-1.55\), is also statistically significant for the 5-note scale (\(p\)-value \(<0.05\)) and for the 7-not scale \(-4.73\) (\(p\)-value \(<0.001\)). When users made a mistake in telling the haptic note being displayed, mistakes were closer to the right answer when using the haptic tuning fork.  
All subjects affirmed that, if they had to perform data analysis using the haptic channel, they would prefer to count with a haptic tuning fork to serve them as a haptic reference. Users were asked if they felt that the haptic tuning fork increased their level of confidence with a 5-point Likert scale, where 5 represents \"Extremely\", 4 represents \"Very\", 3 represents \"Moderately\", 2 represents \"Slightly\" and 1 represents \"Not at all\". 27.3% indicated that the haptic tuning fork extremely increased their confidence level, by answering 5; 63.6% answered 4; and 9.1% answered 3, indicating that the use of the haptic tuning fork moderately increased their level of confidence (median \"Very\", mode \"Very\"), see Figure 4(a). Regarding the usefulness of the haptic tuning fork, depending on the number of notes of the scale used, for the 3-note scale, most of the subjects reported that the haptic tuning fork was \"Slightly\" useful (median and mode \"Slightly\"); for the 5-note scale, most of the subjects reported that it was \"Very\" or \"Extremely\" useful (median \"Very\", mode \"Extremely\"); whereas for the 7-note scale, most of the subjects reported that the haptic tuning fork was \"Extremely\" useful (median and mode \"Extremely\"). These results are shown in Figure 4(b).  
Figure 4: Interaction effect charts for Experiment A.  
Figure 5: Subjective results for Experiment A.  
Experiment B: Evaluation of the Improvement in the Hit Rate When Users Discriminate Frequencies and Shapes Using the Haptic Tuning Fork  
The previous experiment demonstrated that the use of the haptic tuning fork helps to identify the notes for the frequency sinusoidal scales of 5 and 7 notes, respectively. This experiment wants to evaluate if using a haptic tuning fork for the shape helps to recognise both the perceived shape and frequency of the target stimuli.