## 2 Methods
### Data Analysis  
Binomial tests were performed at \(\alpha=0.05\) to determine which thumb, the left or right, was predominantly used for touch interaction on each alphabet letter key. The tests were conducted separately for left-handed and right-handed participants. Note that the measurements were not normally distributed, and thus, a non-parametric test (i.e., binomial test) was needed. The number of touches made by the left and right thumbs were counted, respectively, and the thumb usage rate (TU; unit: %) was computed for each letter key--the TU was defined as the ratio of the number of the left or right thumb touches to the total number of touches (i.e., left + right) made on a target letter key, and thus the abbreviations, TUL and TUR, were employed to represent the ratios of the left and right thumb touches, respectively. For each letter key, two binomial tests with different hypotheses were performed. The first binomial test was employed to determine if the TUL or TUR accounted for a significant majority of 50.0% or more on each letter key. This was done to see which thumb, the left or right, was particularly preferred for touch interaction per letter key. The second binomial test was conducted to determine whether the TUL or TUR had a significant superiority of 85.0% or more on each letter key. This was intended to see if one of both the left and right thumbs overwhelmingly dominated touch interaction on each letter key. Note that the criterion of 85.0% was a more conservative value as compared with the previous studies that an individual handedness was determined when 75.0% or more of a certain task was performed by either the left or right hand [24,25]. Further analyses were conducted to examine the factors that influenced the decision of the left or right thumb use (i.e., thumb choice) in the touch interaction with the letter keys. First, the effect of the distances between the preset thumb positions and the centers of the letter keys was investigated. The 26 alphabet letter keys were grouped according to the distances and were divided into three areas (Figure 3): (1) the left area that was relatively close to the preset positions of the left thumb; (2) the middle area that had the same distances from the preset positions of both the thumbs; and (3) the right area that was relatively close to the preset positions of the right thumb. Then, the TU values of the letter keys were examined as a function of these areas. Second, the Mann-Whitney U test was conducted to explore the effect of the difference in length between the left and right thumbs on the choice of which thumb to use to tap letter keys--that is, the thumb lengths of both hands were compared, and the difference in TU values between the longer and shorter thumbs was statistically examined. Note that since the measured data were not normally distributed, the Mann-Whitney U test was conducted instead of the \(t\)-test. However, this was investigated for only (1) the keys that were not unilaterally tapped by the relatively closer one of both the thumbs (i.e., TU \(<\) 85.0%) and (2) the keys that were located in the middle area (i.e., the keys G and V). For this analysis, both the left-handed and right-handed participants were categorized according to whether their left thumb was longer than their right thumb and vice versa, and thereby the following four groups were made: (1) the group of the left-handed participants with the relatively longer left thumb; (2) the group of the left-handed participants with the relatively longer right thumb; (3) the group of the right-handed participants with the relatively longer left thumb; and (4) the group of the right-handed participants with the relatively longer right thumb. In addition, the participants' TUL and TUR values were assigned to the corresponding groups. Note that the participants with the same thumb length on the left and right hands were excluded from the analysis.