3.3.1. Selection Time

In the process of the experimental data analysis, we set the target level (3 × 3, 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8) and the target region (A, B, C, and D) as independent variables. In this way, we performed repeated measurements ANOVAs (α = 0.05) on the time and accuracy of the target selection. The target selection time was defined as beginning from when the user clicked the Start button or pressed the left Ctrl button to when the user pressed the left Ctrl button again.

There was a main effect on the average time of the different regions (F2.058, 22.634 = 11.460, *p* < 0.001), see Figure 5a. The post hoc tests showed that there were no significant differences among the regions (*p* > 0.05) except for between regions B and C (*p* = 0.035) and regions B and D (*p* < 0.001). Region B had the fastest completion time, and region D had the slowest completion time.

**Figure 5.** The average time of Experiment 1. The error bars represent a 95% confidence interval: (**a**) average selection time with different regions; (**b**) average selection time with different target size levels; and (**c**) average selection time for different target size levels and different regions (A, B, C, and D).

There was a main effect for the average time of the different levels of target size (F2.321, 25.531 = 20.714, *p* < 0.001), see Figure 5b. The post hoc tests showed that the shortest time was for the 3 × 3 level, and the longest was for the 7 × 7 level. There were no significant differences between the 3 × 3, 4 × 4, and 5 × 5 levels (*p* > 0.119). There were no significant differences between the 6 × 6, 7 × 7, and 8 × 8 levels (*p* > 0.05).

Further analysis of the level of target size × target region on selection time showed there was no significant interaction (F4.272, 46.992 = 1.601, *p* = 0.187), see Figure 5c. When the users selected a target in the 3 × 3 level, the shortest selection time was needed on average, while the 7 × 7 level had the longest time.

#### 3.3.2. Selection Error Rate

The percentage of trials in which subjects made erroneous selections was defined as the selection error rate.

As shown in Figure 6a, there was a main effect on the average error rate of the different regions (F3, 33 = 4.240, *p* = 0.012). Post hoc tests showed no significant differences among all the regions (*p* > 0.052), except between regions B and D (*p* = 0.033). Region D had the lowest completion error rate, and region C had the highest completion error rate.

**Figure 6.** The error rate of Experiment 1. The error bars represent a 95% confidence interval: (**a**) average error rate with different regions; (**b**) average error rate with different target size levels; and (**c**) average error rate for different target size levels under different regions (A, B, C, and D).

As shown in Figure 6b, different target sizes had no significant effect on the average error rate (F2.402,26.419 = 2.617, *p* = 0.083). The post hoc tests showed no significant differences among all the target size levels (*p* > 0.157). The 3 × 3 level had the lowest error rate, and the 8 × 8 level had the highest. The higher the target size level, the higher the error rate when selecting the target. The largest increase in the error rate for adjacent levels was from the 5 × 5 to the 6 × 6 level. Thus, a target size of 5 × 5 (60.8 mm length and 48 mm width) provided a threshold for the most selections without a noticeable change in error rate.

Further analysis of what effect target size level × target region had on selection error rate showed there was no significant interaction (F4.256, 46.816 = 1.665, *p* = 0.171), see Figure 6c. The 3 × 3 target size level had the lowest selection error rate. The second-lowest selection error rate was the 4 × 4 level. The 8 × 8 level produced the highest error rate. The participants had the lowest error rate (0%) when the target region was D (bottom-right corner) and the highest error rate (3.54%) when the target region was C (bottom-left corner).

In previous literature [19], the author studied pointing at virtual buttons. The space is divided into 5 different sizes according to the angle, that is, the number of buttons. The experimental results show that the error rates are 0, 3.6%, 2.2%, 16.0%, 3.2%, respectively. As shown in Figure 6a, the error rates of our results are 0.31%, 0.83%, 1.39%, 2.78%, 2.22%, 3.06%, and the overall error rate is better. We also divided the regions, discussed the situation of each region, and the comprehensive situation of region and size. The literature only considers the error rate and not the task completion time. We comprehensively analyze the error rate and time and give suggestions for designing interactive technologies based on spatial regions, which are more convincing. Next, we studied the division of spatial regions in the absence of vision and give suggestions for designing interactive technologies based on spatial regions in the absence of vision.

#### *3.4. Comparative Experiment 1*

The participants in Experiment 1 were the same as in the pilot study, so they were trained and familiar with the experiment. To eliminate this influence, we invited 12 external participants who didn't know the experiment in advance. The experiment process was the same as experiment 1.

#### 3.4.1. Selection Time

There was a main effect on the average time of the different regions (F2.058, 22.634 = 11.168, *p* < 0.001), see Figure 7a. The post hoc tests showed that there were no significant differences among the regions (*p* > 0.05) except for between regions B and C (*p* = 0.023) and regions B and D (*p* = 0.002). Region B had the fastest completion time, and region D had the slowest completion time.

**Figure 7.** The average time of comparative Experiment 1. The error bars represent a 95% confidence interval: (**a**) average selection time with different regions; (**b**) average selection time with different target size levels; and (**c**) average selection time for different target size levels and different regions (A, B, C, and D).

There was a primary effect regarding the average time of the different levels of target size (F2.321, 25.531 = 20.870, *p* < 0.001), see Figure 7b. The post hoc tests showed that the shortest time was for the 3 × 3 level, and the longest was for the 7 × 7 level. There were no significant differences among the 3 × 3, 4 × 4, and 5 × 5 levels (*p* > 0.37). There were no significant differences among the 6 × 6, 7 × 7, and 8 × 8 levels (*p* > 0.05).

Further analysis of the level of target size × target region on selection time showed there was no significant interaction (F4.272, 46.992 = 1.635, *p* = 0.178), see Figure 7c. When the users selected a target in the 3 × 3 level, the shortest selection time was needed on average, while the 7 × 7 level had the longest time.

## 3.4.2. Selection Error Rate

As shown in Figure 8a, there was a primary effect on the average error rate of the different regions (F3, 33 = 3.996, *p* = 0.016). Post hoc tests showed no significant differences among all the regions (*p* > 0.063). Region D had the lowest completion error rate, and region C had the highest completion error rate.

As shown in Figure 8b, there was no significant effect for the average error rate of the different target sizes (F2.109, 23.199 = 2.184, *p* = 0.133). The post hoc tests showed no significant differences among all the target size levels (*p* > 0.122). The 3 × 3 level had the lowest error rate, and the 8 × 8 level had the highest.

Further analysis of target size level × target region on selection error rate showed there was no significant interaction (F4.9, 53.903 = 1.628, *p* = 0.17), see Figure 8c.

**Figure 8.** The error rate of comparative Experiment 1. The error bars represent a 95% confidence interval: (**a**) average error rate with different regions; (**b**) average error rate with different target size levels; and (**c**) average error rate for different target size levels under different regions (A, B, C, and D).

Compared with Experiment 1, the error rate of this experiment was slightly higher, and the average time was slightly longer, caused by the fact that new participants were not familiar with the experiment. The results showed that the regions (and levels) with the highest or lowest error rates were the same as Experiment 1. The regions (and levels) with the fastest or slowest average time were the same as Experiment 1, as shown in Figures 7 and 8.

#### **4. Experiment 2: Non-Visual Scenario**

To test the accuracy when the users performed the task with an eyes-free scenario, we set voice guidance for a visually impaired individual. The position of the users' hand mapping to the current block was shown on the experiment screen in real time, and the target block turned from green to red while the current block overlapped it.

## *4.1. Participants & Apparatus*

The participants and apparatus in Experiment 2 were the same as in the pilot study.

#### *4.2. Task & Procedure*

The design and tasks were almost the same as in Experiment 1. The difference in Experiment 2 was that there was no visual feedback for the users, only voice guidance. The beginning guide audio was "The target block is X", and it would then announce the number of the block of the users' hand in real time. The participants already knew the number of the target block. This cycle would continue until the task was completed, and then the audio would announce, "This round of the experiment ends". Before the formal experiment, participants were allowed to warm up with a practice session until they could understand and perform the task correctly. In total, the experiment consisted of the following: 12 subjects × 6 target size levels × 4 target regions × 2 blocks × 3 repetitions = 1728 target selection trials.

#### *4.3. Results*

#### 4.3.1. Selection Time

We found a main effect on the average time of different regions (F3, 33 = 13.496, *p* < 0.001), see Figure 9a. The post hoc tests showed a significant difference between regions A and C (*p* = 0.007) and regions A and D (*p* = 0.002). There was a significant difference between regions B and C (*p* = 0.042) and regions B and D (*p* = 0.002). Other regions had no significant differences (*p* > 0.975). Region B had the fastest completion time, and region D had the slowest.

**Figure 9.** Average times of Experiment 2. Error bars represent a 95% confidence interval: (**a**) average selection time with different regions; (**b**) average selection time with different target size levels; and (**c**) average selection time for different target size levels under different regions (A, B, C, and D).

As shown in Figure 9b, there was a primary effect on the average time of the different target sizes (F2.222, 24.445 = 24.893, *p* < 0.001). A post hoc test showed no significant difference between the 3 × 3 and 4 × 4 levels (*p* = 0.231). There was no significant difference between the 5 × 5 and 6 × 6 levels (*p* = 0.270). There was no significant difference between the 7 × 7 and 8 × 8 levels (*p* = 0.142). The 3 × 3 level had the fastest completion time, and the 8 × 8 level had the slowest completion time. The higher the target size level, the longer the time needed to select the target. The largest increase in selection time for adjacent levels was from the 6 × 6 to the 7 × 7 level. Thus, the target size of 6 × 6 (50.67 mm length and 40 mm width) provided a threshold of the most selections without a noticeable change in selection time.

Further analysis of target size level × target region on selection time showed there was no significant interaction (F4.912, 54.027 = 1.575, *p* = 0.184), see Figure 9c. The shortest selection time was needed when users selected a target in the 3 × 3 level. The second shortest level was the 4 × 4 level, while the 8 × 8 level took the longest time.

#### 4.3.2. Selection Error Rate

There was no significant effect concerning the average error rate of the different regions (F3, 33 = 0.909, *p* = 0.447), see Figure 10a. The post hoc tests showed no significant differences among all the regions (*p* = 0.670). Region B had the lowest completion error rate, and region C had the highest.

**Figure 10.** The error rate of Experiment 2. The error bars represent a 95% confidence interval: (**a**) average error rate with different regions; (**b**) average error rate with different target size levels; (**c**) average error rate for different target size levels under different regions (A, B, C, and D).

As shown in Figure 10b, there was no significant effect concerning the average error rate of the different target sizes (F5, 55 = 4.388, *p* = 0.002). The post hoc tests showed no significant differences among all the levels of target size (*p* > 0.156), except for the 3 × 3 level and 6 × 6 level (*p* = 0.030). The 3 × 3 level had the lowest completion error rate, and the 8 × 8 level had the highest completion error rate. The higher the target size

level, the higher the error rate needed to select a target. The largest increase in the selection error rate for adjacent levels was from the 4 × 4 to the 5 × 5. Thus, a target size of 4 × 4 (76 mm length and 60 mm width) provided a threshold of the most selections without a noticeable change in selecting error rate.

Further analysis of the target size level × target region on selection error rate showed there were no significant interaction (F5.122, 56.337 = 1.524, *p* = 0.196), see Figure 10c. On average, the 3 × 3 target size level had the lowest selection error rate. The second-lowest selection error rate was for the 4 × 4 level. The 8 × 8 level produced the highest error rate. The participants reached the lowest selection error rate (3.54%) when the target region was B (upper-right corner), and the highest error rate (6.31%) when the target region was C (bottom-left corner).

#### *4.4. Comparative Experiment 2*

The participants in Experiment 2 were the same as in the pilot study, so they were trained and familiar with the experiment. To eliminate this influence, we invited 12 external participants who did not know the experiment in advance. The experiment process was the same as experiment 2.

#### 4.4.1. Selection Time

We found a main effect on the average time of different regions (F3, 33 = 13.474, *p* < 0.001), see Figure 11a. The post hoc tests showed a significant difference between regions A and C (*p* = 0.007) and regions A and D (*p* = 0.003). There was a significant difference between regions B and C (*p* = 0.042) and regions B and D (*p* = 0.002). Other regions had no significant differences among them (*p* > 0.994). Region B had the fastest completion time, and region D had the slowest completion time.

**Figure 11.** The average time of comparative Experiment 2. The error bars represent a 95% confidence interval: (**a**) average selection time with different regions; (**b**) average selection time with different target size levels; and (**c**) average selection time for different target size levels and different regions (A, B, C, and D).

As shown in Figure 11b, there was a main effect on the average time of the different target sizes (F2.222, 24.445 = 25.009, *p* < 0.001). A post hoc test showed no significant difference between the 3 × 3 and 4 × 4 levels (*p* = 0.227). There was no significant difference between the 5 × 5 and 6 × 6 levels (*p* > 0.05). There was no significant difference between the 7 × 7 and 8 × 8 levels (*p* > 0.05). The 3 × 3 level had the fastest completion time, and the 8 × 8 level had the slowest completion time.

Further analysis of target size level × target region on selection time showed there was no significant interaction (F4.912, 54.027 = 1.574, *p* = 0.184), see Figure 11c.

#### 4.4.2. Selection Error Rate

There was no significant effect for the average error rate of the different regions (F3, 33 = 0.883 *p* = 0.46), see Figure 12a. The post hoc tests showed no significant differences among all the regions (*p* > 0.05). Region B had the lowest completion error rate, and region C had the highest completion error rate.

**Figure 12.** The error rate of comparative Experiment 1. The error bars represent a 95% confidence interval: (**a**) average error rate with different regions; (**b**) average error rate with different target size levels; and (**c**) average error rate for different target size levels under different regions (A, B, C, and D).

As shown in Figure 12b, there was no significant effect for the average error rate of the different target sizes (F5, 55 = 3.193, *p* = 0.013). The post hoc tests showed no significant differences among all the levels of target size (*p* > 0.109). The 3 × 3 level had the lowest completion error rate, and the 8 × 8 level had the highest completion error rate.

Further analysis of the target size level × target region on selection error rate showed there were no significant interaction (F6.461,71.069 = 1.085, *p* = 0.381), see Figure 12c. Compared to Experiment 2, the error rate of this experiment was slightly higher, and the average time was slightly longer, caused by the fact that new participants were not familiar with the experiment. The results showed that the regions (and levels) with the highest or lowest error rates were the same as in Experiment 2. The regions (and levels) with the fastest or slowest average time were the same as Experiment 2, as shown in Figures 11 and 12.

#### **5. Discussion & Conclusions**

In this work, we analyzed the users' common operational area regarding partitioning and the difference in spatial controllability between a sighted and a visually impaired individual. We introduced three experiments and a pilot study concerning the common spatial range and the thresholds of the target size level in the spatial region for a sighted and visually impaired individual. We compared the speed and accuracy of the target dimensions of six different levels and the difference in speed and accuracy among the four azimuth regions of A, B, C, and D in both visual and non-visual scenarios. Many of our performance study results were statistically significant, which allows us to draw many meaningful conclusions about human-computer interaction in spatial regions that can be used for designing techniques for sighted and visually impaired individuals. This paper focused on systematically analyzing the common operational range of one dimension and the threshold of two dimensions. The results are as follows:


Based on the above results and findings, we have developed a set of preliminary guidelines regarding target selection in spatial partitioning scenarios:


In the case of vision, researchers can refer to the design suggestions in Table 3 when studying the space operation capabilities between users and computer screens or designing interactive technologies based on spatial regions. In the case of non-vision, researchers can refer to the design suggestions in Table 4 when studying the space operation capabilities between users and computer screens or designing interactive technologies based on spatial regions.

**Table 3.** Design suggestions for selecting spatial targets under visual conditions.



**Table 4.** Design suggestions for selecting spatial targets under non-visual conditions.

Based on these results, we propose two techniques for two different application scenarios, described in the following paragraphs.

A spatial gesture recognition technique for surgery can help users select targets by using spatial region cognition and hand gestures during surgery. This technique is designed based on the partitioning strategies of a common operational spatial region array. This technique can meet the strict requirements of sanitary conditions during surgery (as opposed to a touchscreen and most other existing interfaces).

Non-visual selection is a system integrated with screen reading software allowing a visually impaired person to select targets easily. This technique is designed based on the partitioning strategies of a common operational spatial region array. Users can use this system to interact with the internet and web more easily. In addition, the user no longer needs a keyboard because this system uses Leap Motion to detect a users' hand motions and provides voice guidance when choosing targets and to do further work.

In the future, we will further expand the results of this study and contribute to technology accessibility for visually impaired individuals, including the exploration of a threshold for three-dimensional interaction.

**Author Contributions:** Methodology, validation, data curation, writing—review and editing, visualization, H.W.; conceptualization, formal analysis, resources, supervision, project administration, funding acquisition, J.Y.; software, data curation, methodology, writing—original draft preparation, Y.Z.; formal analysis, resources, supervision, project administration, investigation, Y.H.; investigation, supervision, methodology, resources, X.Z.; methodology, resources, formal analysis, supervision, S.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Natural Science Fund, grant (61741206).

**Acknowledgments:** The author thanks the editor and others for their comments and suggestions for this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

