Trackball vs. Optical Mice: Unraveling the Mystery of Work Efficiency

Methods

When it comes to computer input devices, one cannot ignore the importance of Fitts' Law. Like many psychologists in the 1950s, Fitts was motivated to investigate whether human performance could be quantified using a metaphor from the new and exciting field of information theory. This field emerged from the work of Shannon, Wiener, and other mathematicians in the 1940s. The terms probability, redundancy, bits, noise, and channels entered the vocabulary of experimental psychologists as they explored the latest technique of measuring and modeling human behavior. Two well‐known models in this vein are the Hick-Hyman law for choice reaction time and Fitts’ law for the information capacity of the human motor system. Fitts’ particular interest was rapid‐aimed movements, where a human operator acquires or selects targets of a certain size over a certain distance. Fitts proposed a model—now “law”—that is widely used in fields such as ergonomics, engineering, psychology, and human‐computer interaction. The starting point for Fitts’ law is an equation known as Shannon’s Theorem, which gives the information capacity C (in bits/s) of a communications channel of bandwidth B (in s−1 or Hz) as (1.1) where S is the signal power and N is the noise power. Fitts reasoned that a human operator that performs a movement over a certain amplitude to acquire a target of a certain width is demonstrating a “rate of information transfer”. In Fitts’ analogy, movement amplitudes are like signals and target tolerances or widths are like noise. Fitts proposed an index of difficulty (ID) for a target acquisition task using a log term slightly rearranged from Eq. 1.1. Signal power (S) and noise power (N) are replaced by movement amplitude (A) and target width (W), respectively: (1.2) Fitts referred to the target width as the “permissible variability” or the “movement tolerance”. This is the region within which a movement is terminated.As with the log term in Eq. 1.1, the units for ID are bits because the ratiowithin the parentheses is unitless and the log is taken to base 2.Fitts’ idea was novel for two reasons: First, it suggested that the difficulty of a target selection task could be quantified using the information metric bits. Second, it introduced the idea that the act of performing a target selection task is akin to transmitting information through a channel—a human channel. Fitts called the rate of transmission the index of performance, although today the term throughput (TP) is more common. Throughput is calculated over a sequence of trials as a simple quotient. The index of difficulty (ID) of the task is the numerator and the mean movement time (MT) is the denominator: (1.3) With ID in bits and MT in seconds, TP has units bits per second or bits/s. A central thesis in Fitts’ work is that throughput is independent of movement amplitude and target width, as embedded in ID. In other words, as ID changes (due to changes in A or W), MT changes in an opposing manner and TP remains more‐or‐less constant. Fitts' Law was initially investigated in four experiment conditions, including two reciprocal or serial tapping tasks, a disc transfer task, and a pin transfer task. In the tapping condition, a participant moved a stylus back and forth between two plates as quickly as possible, while in the discrete variation, the participant selected one of two targets in response to a stimulus light. These tasks are commonly known as the "Fitts' paradigm" and can be easily updated using modern computing technology. Fitts published summary data for his experiments in 1954, which can still be reexamined today. The experiments involved four target amplitudes crossed with four target widths in the stylus-tapping conditions, and participants performed the tasks accordingly. Table 1.1 Data from Fitts’ erial tapping task experiment with a 1 oz stylus. An extra column shows the effective target width (We) after adjusting W for the percentage errors The combination of conditions in Table 1.1 yields task difficulties ranging from 1 bit to 7 bits. The mean MTs observed ranged from 180 ms (ID = 1 bit) to 731 ms (ID = 7 bits), with each mean derived from more than 600 observations over 16 participants. The standard deviation in the MT values was 157.3 ms, which is 40.2% of the mean. This is fully expected since “hard tasks” (e.g., ID = 7 bits) will obviously take longer than “easy tasks” (e.g., ID = 1 bit). Fitts calculated throughput by dividing ID by MT (Eq. 1.3) for each task condition. The mean throughput was 10.10 bits/s. A quick glance at the TP column in Table 1.1 shows strong evidence for the thesis that the rate of information processing is relatively independent of task difficulty. Despite the wide range of task difficulties, the standard deviation of the TP values was 1.33 bits/s, which is just 13.2% of the mean. One way to visualize the data in Table 1.1 and the independence of ID on TP is through a scatter plot showing the MT‐ID point for each task condition. Figure 1.2 shows such a plot for the data in Table 1.1. The figure also includes the best fitting line (via least‐squares regression), the linear equation, and the squared correlation. The independence of ID on TP is reflected in the closeness of the points to the Regression line (indicating a constant ID/MT ratio). Indeed, the fit is very good with 96.6% of the variance explained by the model. Figure 1.2 Scatter plot and least‐squares regression analysis for the data in Table 1.1The linear equation in Figure 1.2 takes the following general form: (1.4) The regression coefficients include an intercept a with units seconds and a slope b with units seconds per bit. Equation 1.4 exemplifies the use of Fitts’ law for predicting. This is in contrast with Eq. 1.3 which is the use of Fitts’ law for measuring.

Following the first publication of Fitts' law, numerous studies emerged in various forms. While their internal validity isn't disputed, inconsistencies exist, making cross-study comparisons challenging. These inconsistencies are due to inadequate details, different throughput calculation methods, and variations in data collection or usage. Standardizing Fitts' law research methodology is essential, especially in HCI. ISO 9241-9, now ISO 9241-411, provides this standardization by outlining performance testing procedures using Fitts' paradigm in one-dimensional (1D) and two-dimensional (2D) tasks.

This standard has been applied to various studies in the past 15 years, evaluating novel interactions or devices such as trackball game controllers, smartphone touch input, tabletop touch input, and Wiimote gun attachments.

Although ISO 9241‐9 provides the correct formula for Fitts’ throughput, little guidance is offered on the data collection, data aggregation, or in performing the adjustment for accuracy. The latter presents a particular challenge when using the 2D task. In this section we examine the best practice method for calculating Fitts’ throughput. We begin with Figure 17.7 which shows the formula for throughput, expanded to reveal the Shannon formulation for ID and the use of effective values for target amplitude and target width. The figure also highlights the presence of speed (1/MT) and accuracy (SDx ) in the calculation.
Figure 1.5 Formula for throughput showing the Shannon formulation for ID and the adjustment for accuracy. Speed (1/MT) and accuracy (SDx) are featured. Figure 1.6 Geometry for a trial. Whether using the 1D or the 2D task, the calculation of throughput requires Cartesian coordinate data for each trial. Data are required for three points: the starting position (“from”), the target position (“to”), and the trial‐end position (“select”). See Figure 1.4. Although the figure shows a trial with horizontal movement to the right, the calculations described next are valid for movements in any direction or angle. Circular targets are shown to provide a conceptual visualization of the task. Other target shapes are possible, depending on the setup in the experiment. The calculation begins by computing the length of the sides connecting the from, to, and select points in the figure. Using Java syntax:

double a = Math.hypot(x1—x2, y1—y2);
double b = Math.hypot(x—x2, y—y2);
double c = Math.hypot(x1—x, y1—y);

The x‐y coordinates correspond to the from (x1, y1), to (x2, y2), and select (x, y) points in the figure. Given a, b, and c, as above, dx and ae are then calculated:

double dx = (c * c — b * b — a * a)/(2.0 * a);
double ae = a + dx;

Given arrays for the from, to, and select points in a sequence of trials and the computed ae and dx for each trial, Ae is the mean of the ae values and SDx is the standard deviation in the dx values. With these, IDe is computed using Figure.1.5 and throughput （TP） is computed using Eq. 1.3. One final point concerns the unit of analysis for calculating throughput. The correct unit of analysis for throughput is an uninterrupted sequence of trials for a single participant. The premise for this is twofold:

•throughput cannot be calculated on a single trial;
•a sequence of trials is the smallest unit of action for which throughput can be attributed as a measure of performance.