# Movement Time and Subjective Rating of Difficulty in Real and Virtual Pipe Transferring Tasks
## 4 Discussion
### MT Modeling  
The literature [31; 32] has revealed that target size may be neglected in determining the ID when the ID is less than three. The ID in establishing Equation (4) was in the range of 3.3 to 5.1 bit, which was higher than three and the target size, i.e., the diameter of the pipe, should be considered. Equation (4) is an additive model considering gender, handedness, transferring direction, and real/virtual conditions. The \(\text{R}_{\text{adj}}^{2}\) of this equation was 0.92 indicating that 92% of the variation of the MT may be explained by this model. This model may be applied in predicting the MT in the corresponding pipe transferring conditions. The regression coefficients indicate the change of MT when an independent variable has changed one unit. Among all the regression coefficients in Equation (4), the regression coefficient of \(x_{2}\) (61.0) is the lowest, indicating that using either the dominant or non-dominant hand, on average, only leads to an MT difference of 61 ms. This is consistent with the results in Table 2 where five regression coefficients of handedness were not significant at \(\alpha\) = 0.05. Four of these five coefficients occurred in virtual pipe conditions, indicating that the insignificance of handedness occurred primarily when the participants were interacting with the virtual pipe. The regression coefficient of \(x_{4}\) (819.1) in Equation (4), on the other hand, was the highest among all regression coefficients. Transferring a real pipe, on average, needed 819.1 ms longer than transferring a virtual pipe. This implies that transferring a real pipe was less efficient than transferring a virtual pipe. This was consistent with the results in the ANOVA of the MT. The regression coefficient of \(x_{1}\) in Equation (4) indicates that the MT of female participants, on average, was 195.2 ms longer than that of their male counterparts. The \(\beta_{1}\) values in Table 2 show that the MT difference between the two genders occurred primarily in transferring the real pipe, especially in the lateral transfers. The hand sizes of female adults, in general, are smaller than those of male adults. Our female participants probably needed more time to grasp, move, position, and release the real pipe than their male counterparts due to their relatively smaller hand size even though we did not measure this size. While transferring a virtual pipe, hand size, on the other hand, played a minor role in the MT because both males and females pinched the pipe. The inverse of the regression coefficient of the ID indicates the information processing rate, or the performance, of the object transfer [2; 3; 15]. This inverse in Equation (4) is 3.5 bit/s (1/0.2823), which was the average of overall conditions. The \(1/\beta_{3}\) in Table 2 shows the information processing rate under each transferring condition. The values of transferring real pipe (1.7 to 2.3 bit/s) are lower than those of transferring virtual pipe (3.1 to 3.4 bit/s). This provides another piece of evidence, in addition to the ANOVA results, that transferring a real pipe was inefficient compared to transferring a virtual pipe. The information processing rate of Fitts' disc and pin transfer tasks were 7.5 to 10.4 bit/s and 8.9 to 12.6 bit/s [2], respectively. This rate involves finger, wrist, and arm motions, which were reported by [PERSON] et al. [1] to be 38, 23, and 10 bits/s, respectively. [PERSON] et al. [48] revealed that movements using fingers and wrist only produced the performance of 20 bits/s. The movements involved preferred foot and head movements that were in the range of 18 bits/s [10] and 5 to 7 bit/s [15; 18], respectively. All these information processing rates were higher than the values in our study. This could be attributed to the fact that the movements in the above-mentioned literature were rapid movements that the participants were requested to complete as fast as possible. Our participants were instructed to put the pipe exactly within the end circle at their self-selected pace.