# Effects of Smartphone Size and Hand Size on Grip Posture in One-Handed Hard Key Operations
## 3 Results  
A total of nine grip postures were identified from the experiment for power and volume key operations on the mockups, and of them, three grip postures (L3-R1-K1, L4-R1, and L3-R1-T1) were found to be dominant, having a total of 95% of use frequency, as shown in Figure 4. The grip posture L3-R1-K1 (holding the left side of a smartphone with three fingers, the right side with the thumb, and the back with the index finger) was most dominant with a frequency of 70.0% over 2430 (= 45 participants \(\times\) 9 device sizes \(\times\) 2 hard keys \(\times\) 3 repetitions) grip posture measurements. Lastly, L4-R1 (holding the left side with the four fingers and the right side with the thumb) and L3-R1-T1 (holding the left side with three fingers, the right side with the thumb, and the top with the index finger) were the second and third most dominant grip postures with 13.3% and 12.0% of frequency for hard key operations, respectively.  
The frequency distribution of grip posture varied significantly by smartphone size, as shown in Figure 5 (\(\chi^{2}(12)\) = 674.8, \(p\) \(<\) 0.001). The frequency of L3-R1-K1 linearly increased from 32.2% to 82.6% over the smartphone size range of 3.0 to 5.0 inches and then levelled off in the smartphone size range of 5.0 to 7.0 inches, while that of L4-R1 gradually decreased from 21.1% to 6.7% over the smartphone size range of 3.0 to 7.0 inches and that of L3-R1-T1 linearly decreased from 39.3% to 2.2% over the smartphone size range of 3.0 to 5.0 inches and became negligible (\(<\)1%) in the smartphone size range of 5.5 to 7.0 inches. Lastly, the skewness of a frequency distribution of the three dominant grip postures increased toward L3-R1-K1 as smartphone size increased: a slightly skewed frequency distribution (32.2% for L3-R1-K1, 39.3% for L3-R1-T1, and 21.1% for L4-R1) for the 3.0-inch smartphone to a highly skewed frequency distribution (84.4% for L3-R1-K1, \(<\)0.1% for L3-R1-T1, and 6.7% for L4-R1) for the 7.0-inch smartphone.  
Figure 4: The use frequency distribution of grip posture for operation of the hard keys of a smartphone.  
Lastly, the frequency distribution of grip posture varied significantly by hand width and hand length with a similar pattern as shown in Figure 6 (\(\chi^{2}(4)=75.3\), \(p<0.001\) for hand width and \(\chi^{2}(4)=103.4\), \(p<0.001\) for hand length). As hand width and hand length increased from small to large, the frequency of L3-R1-K1 decreased from 77.4% to 64.3% and from 77.2% to 64.0%, respectively. On the other hand, as hand width and hand length increased from small to large, the frequency of L4-R1 increased from 7.3% to 20.2% and from 5.6% to 21.9%, respectively. Lastly, as hand width increased from small to large, the frequency of L3-R1-T1 increased from 9.6% to 15.1% and then decreased to 11.4%; likewise, as hand length increased from small to large, the frequency of L3-R1-T1 increased from 10.7% to 14.1% and then decreased to 11.0%.  
Figure 5: The frequency distribution of grip posture by smartphone size for hard key operations on a smartphone.  
Figure 6: The frequency distribution of grip posture by hand size for hard key operations on a smartphone. (**a**) use frequency distribution of grip posture by hand width; (**b**) use frequency distribution of grip posture by hand length.