Soukoreff, R. W., & MacKenzie, I. S. (2002). Using Fitts' law to model key repeat time in text entry models. Poster presented at Graphics Interface 2002.

# Using Fitts' Law to Model Key Repeat Time in Text Entry Models

### R. William Soukoreff & I. Scott MacKenzie

Dept. of Computer Science
York University
will@acm.org, smackenzie@acm.org
Abstract
While Fitts' law provides a robust and accepted means to model rapid aimed movements, it should not be used for modelling key repeat times (zero-amplitude movements) which arise in text entry models.

Keywords: Text entry, Fitts' law, digraph typing model

## 1 Introduction

Recently, three models of text entry that use Fitts' law to model finger motion have been published: stylus or single-finger typing on a soft keyboard [1], single-thumb typing on a cell phone [2], and, two-thumb typing on a miniature Qwerty keyboard [3]. These publications have demonstrated the utility of Fitts' law for modelling finger movements during text entry. However, the findings described here suggest that Fitts' law should not be used to model repeat key press times.

### 1.1 Fitts' law

Fitts' law predicts the time for a person to make a rapid aimed movement [4, 5]. When modelling text entry, Fitts' law is used to calculate the time required to move a finger from one key to another. We write

 (1)

where MTij represents the time (in seconds) to move from key i to j, the Aij represents the physical distance from key i to j, Wj is the width of the target key, and a and b are constants, obtained through experimentation and linear regression.

In Equation 1, the intercept, a, has units of seconds and represents the time to perform a movement with zero distance, viz. where Aij is zero. The physical interpretation of this is the time to perform a repeat key press (e.g., typing the second "o" in the word "look").

### 1.2 Key Repeat

Two approaches have been taken to modelling repeat key presses. Of the three recently published models just cited, two [2, 3] use Fitts' law, so the repeat time degenerates to the intercept in the Fitts' law regression model (a, in Equation 1). The authors of the third paper [1] took a different approach. Fitts' law was used to model finger motions, but for repeat key presses they chose to define a constant, MTRepeat, representing the time to repeat a keystroke. Both approaches have merits, but our research shows that key repeat time is best modelled separately from Fitts' law. Our position is justified by reviewing the results from an experiment performed to build Fitts' law models of thumb movement times on a miniature keyboard.

## 2 Method and Materials

Nine volunteers participated in the study (four females, five males), ranging in age from 25 to 32 years (with a mean of 29.7 years). Eight were right-handed, one was left-handed, as reported by the subjects.

A Sharp EL-6053 pocket organiser, measuring 124 mm × 84 mm × 10 mm was used for this experiment. It includes a miniature Qwerty-style keyboard with 8 mm × 5 mm keys, a 3.6 mm gap between keys horizontally, and a 3.33 mm gap vertically.

A PIC micro-controller was interfaced to the keyboard hardware of the EL-6053 and programmed to emit ASCII characters in real time as keys were typed on the keyboard. The ASCII characters were transmitted through a serial cable at 1200 baud to a 400 MHz Pentium II computer running a Java program that time-stamped and recorded the ASCII characters. Particular attention was paid to lag, to ensure the accuracy of the final time-stamps.

### 2.1 Procedure

The subjects used their thumbs to perform a series of ten second long artificial typing tasks. We say "artificial" because subjects did not enter English text; rather, they entered repeated pairs of characters (see Table 1). For example, for the 1.60 bits, left-hand condition, subjects entered "DEDEDE…" as quickly as they could for ten seconds. Also, two tasks were used to measure MTRepeat. For the left thumb, subjects repeatedly typed the D key as fast as they could for ten seconds. Similarly, the J key was repeatedly typed by the right thumb.

### 2.2 Results

The movement times for all subjects were averaged, and linear regression was used to find the a and b Fitts' law constants. Note that the regression was calculated twice – both including and omitting the ID = 0 data points. The Fitts' law models appear in Table 2, and the observed times and Fitts' law models (calculated omitting the ID = 0 data points) appear in Figure 1.

The correlations were high for both thumbs, indicating that Fitts' law predicts the movement time with high accuracy for both thumbs. Note that the regression correlation values (r values in Table 2) are higher for the models that omit the ID = 0 data.

Table 1
Key Patterns Used for Generating
Left and Right Hand Fitts' Law Models
ID (bits)1 Left Hand
Pattern
Right Hand
Pattern
0 D J
1.60 D-E J-I
1.73 D-F J-H
2.12 E-X I-M
2.50 D-G H-K
2.99 S-G H-L
3.12 T-Z M-T
3.71 Q-B P-V

Table 2
Fitts' Law Models
Model Intercept
(ms)
Slope
(ms/bit)
n             r
Dominant:
including ID = 0:
98.53
153.14
92.02
72.11
7
8
0.976
0.962
Non-Dominant:
including ID = 0:
98.62
170.73
98.79
72.50
7
8
0.993
0.956

Figure 1. Fitts' law data and regression lines

The value for MTRepeat was calculated by dividing the elapsed time by the number of keystrokes made by the subject. The results from all subjects were averaged. See Table 3.

Table 3
Results of Measuring MTRepeat
Thumb MTRepeat (ms) Standard
Deviation
Dominant 181.57 23.74
Non-Dominant 208.28 31.88

## 3 Discussion

It is apparent from Figure 1 that while a wide range of index of difficulty values were used (0 to 3.71 bits) there is a large gap in values in the range 0 to 1.60 bits. This is an artefact of the physical geometry of the keyboard. Because keys are separated by a 3.33 to 3.6 mm gap, the shortest possible distance between neighbouring keys is 10.15 mm. Therefore, other than the (0 bit) repeat key task, the smallest index of difficulty value possible is 1.60 bits. So when constructing Fitts' law models of the keyboard there is a lack of data for low index of difficulty values, and hence we have a lack of confidence concerning predictions in the low index of difficulty region. Also, although circumstantial to our reasoning, others have suggested that Fitts' law does not apply when index of difficulty values are small. [6]

The Fitts' law intercepts obtained when the ID = 0 data points are not included in the linear regression (Table 2: 98.53 and 98.62 ms) are only slightly more than half of the measured MTRepeat values (Table 3: 181.57 and 208.28 ms). This indicates that Fitts' law intercept values are far too small to model key repeat.

The regression models match the data well for index of difficulty values greater than or equal to 1.60 bits, and a separately measured MTRepeat provides the best prediction for the ID = 0 value. Therefore, we conclude that when constructing or using text entry models, Fitts' law should be employed for inter-key movement times (with ID > 0 bits). However, a separate MTRepeat value should be used for key repeat times (ID = 0 bits).

Finally, we observe that using Fitts' law intercept values for key repeat times can lead to ridiculous results. For example, [7], reports a Fitts' intercept (a) value of 0.083 seconds, and proceeds to use this value for key repeat times. However, 0.083 seconds corresponds to 12 repeat key presses per second – a figure that is simply not possible.

## References

1. Soukoreff, R. W. and MacKenzie, I. S. (1995) Theoretical upper and lower bounds on typing speeds using a stylus and soft keyboard. Behaviour & Information Technology, 14, 370-379.

2. Silfverberg, M., MacKenzie, I. S., and Korhonen, P. (2000) Predicting text entry speed on mobile phones. Proc. of CHI 2000, 9-16.

3. MacKenzie, I. S. and Soukoreff, R. W. (2002) A model of two-thumb text entry. Proc. of GI 2002, in press.

4. Fitts, P. M. (1954) The information capacity of the human motor system in controlling the amplitude of movement. J. Exp. Psych. 47, 381-391.

5. MacKenzie, I. S. (1992) Fitts' law as a research and design tool in human- computer interaction. HCI, 7, 91-139.

6. Gan, K.-C. and Hoffmann, E. R. (1988) Geometrical conditions for ballistic and visually controlled movements. Ergonomics, 31, 829-839.

7. Zhai, S., Sue, A., and Accot, J. (2002) Movement model, hits distribution and learning in virtual keyboarding. Proc. of CHI 2002, 17-24.

Footnotes

1 Note that the target widths were taken to be 5 mm; the amplitudes were measured directly from the keyboard.