## 4 Discussion  
### Task Completion Time, Touch Error Frequency, and Subjective Satisfaction  
As expected, the task completion times varied significantly by zones on the QWERTY soft keyboard. The results showed a couple of unique patterns that were somewhat different from the previous studies, which showed two findings for key entry using the thumbs [8; 9; 11; 22]: (1) the shortest task completion times were found near the center area of the keyboard (i.e., approximately around zone 7 for the left thumb and zone 9 for the right thumb in this study), where the thumbs were designated to stay before every movement for touch interaction (i.e., called the initial positions of the thumbs) for testing, and (2) the farther away from the initial positions of the thumbs the target keys were, the longer the task completion times became. First of all, the shortest task completion times were observed in zones 2, 10, and 13 in the present study. When considering the finding of the previous studies that the shortest touch times were observed around the thumbs' initial positions according to Fitts' law, this can be interpreted as the fact that the initial positions of the thumbs in the present study were likely to be located near those zones. That is, in this study, the initial positions of the thumbs were placed asymmetrically around zones 2 and 13 for the left thumb and zones 10 and 13 for the right thumb. It was unclear why the initial positions of the thumbs were found in these zones in the present study. However, we estimated that the habits of grasping a smartphone with the hands would influence this phenomenon, because participants were allowed to grasp the given smartphone in their preferred ways as usual in the present study. To give a plausible example, for two-thumb text entry using a QWERTY soft keyboard, users tend to grasp a smartphone (in particular,  
Figure 4: Subjective satisfactions in fifteen zones (the darker colors represent lower subjective satisfaction ratings). its lower part) with their dominant hand first and then wrap it using the other hand. Naturally, this could help the tip of the dominant thumb (i.e., the thumb-tip of the right hand in this study) to be located near the right border of the QWERTY keyboard section (approximately near zones 5 and 10 in the present study) because the back of the phone is likely to rest on the palm of the dominant hand--in particular, the deeper the smartphone is held in the palm of the dominant hand, the clearer this tendency could become. In addition, the tip of the non-dominant thumb (i.e., the thumb-tip of the left hand) may be located toward the center area of the keyboard (approximately near zones 2, 7, 8, 12, and 13 in the present study), since the non-dominant hand needs to grasp the smartphone over the dominant hand. However, this mechanism is one assumption based on the participants' debriefing session of the present study, and thus further study is warranted to verify this habitual way to grasp a smartphone and its relationship with the thumbs' initial positions for text entry. In addition, the zones with significantly longer task completion times were more prevalently observed in the bottom row and the very left column of the zones--this was also a little different from the aforementioned studies that showed the regular pattern that task completion times gradually increased as a target key moved from the center (i.e., the thumbs' initial positions) to the periphery areas on the QWERTY keyboard. We estimated that this propensity was strongly associated with the thumbs' initial positions that were asymmetrically found in the present study. A couple of pieces of evidence support this assumption. First, the zones with relatively longer task completion times were roughly matched with the keys on the keyboard that could be visually occluded due to the thumbs' initial positions.