About MouseTracker data

During every trial, the Runner program records the real-time x, y coordinates of the computer mouse. Because MouseTracker can record the mouse position about 70 times per second (70 Hz), depending on computer resources, approximately every 15 ms during the live portion of a trial, three pieces of information are recorded: raw time (how many milliseconds have elapsed), the x coordinate of the mouse (in pixels), and the y coordinate of the mouse (in pixels). Because these mouse trajectory data are rich—containing approximately 70 x, y coordinate pairs every second—there are many ways to carve up the data, various measures that could be computed, and several temporal and spatial scales of possible analysis.

Space rescaling

First, all trajectories are rescaled into a standard MouseTracker coordinate space (see image below). The top-left corner of the screen corresponds to “-1, 1.5” and the bottom-right corner corresponds to “1, 0”. In standard 2-choice designs, this leaves the start location of the mouse (the bottom-center) with coordinates “0, 0”. This standard space thus represents a 2 × 1.5 rectangle, which retains the aspect ratio of most computer screens.

 

Remapping

Next, for MouseTracker to average and compare trajectories, trajectories may optionally be re-mapped and overlaid. This can be done by horizontally or vertically flipping trajectories or by rotating them (see Analyzing data section for more information). A data set can involve multiple remappings. For this to be able to occur, the response buttons must be symmetrical about the axis of the "Start" button. This is easily done in the Designer software.

Time normalization

You can analyze MouseTracker data with time normalization and also without (retaining in raw time). By default, it's best to use time normalization. Time normalization is conducted because each recorded trajectory tends to have a different length. For instance, a trial lasting 800 ms will contain approximately 56 x, y coordinate pairs, but a trial lasting 1600 ms will contain approximately 112 x, y coordinate pairs (at 70 Hz). To permit averaging and comparison across multiple trials with different numbers of coordinate pairs, the x, y coordinates of each trajectory may be time-normalized into a given number of time-steps using linear interpolation. By default, MouseTracker assumes you'll time-normalize to 101 time steps, but you can change this to any value of your choice. Thus, the 56 coordinate pairs from the 800 ms trial would be fit to 101 pairs, just as the 112 pairs from the 1200 ms trial would be fit to 101 pairs. Thus, each trajectory is normalized to have 101 time-steps and each time-step has a corresponding x and y coordinate.

Raw time analysis

You can opt to retain trajectories in raw time (without time-normalization). If a raw time analysis is conducted, you decide how many raw time bins to create between 0 ms and some cutoff (e.g., 1500 ms). Rather than MouseTracker generating a user-defined number of normalized time steps, it generates a user-defined number of raw time steps. Thus, each step (i.e., coordinate pair) of a trajectory reflects the location of the mouse during some raw time bin (e.g., 500-600 ms). Trajectories are visualized as in a normalized time analysis, but measures of spatial attraction/curvature and complexity (MD, AUC, x-flips) are not available. Instead, velocity, acceleration, and angle profiles are generated for each trajectory and these profiles are averaged across all trials within a participant, separately for Condition 1 and Condition 2, and also averaged across all participants, separately for Condition 1 and Condition 2. This information can be plotted in the Analyzer program or viewed in the output .CSV file. For the angle profiles, the current angle of movement in degrees is calculated for every time bin, relative to the Start button.

Averaging

Each participant’s mean trajectory for one condition is computed by averaging together all the x coordinates of trajectories in that condition at each time-step, and all the y coordinates of trajectories in that condition at each-time-step. If doing a normalized time analysis, then averaging is very intuitive. Each participant’s mean trajectory for one condition has a user-defined number of x, y coordinate pairs. The first pair (e.g., 1) reflects the start of mouse movement and the last pair (e.g., 101) reflects the end of mouse movement when a response was clicked on. This would be true across all trials regardless of how long participants actually took. This is why time normalization is valuable. If doing a raw time analysis, then each participant's mean trajectory for one condition has a user-defined number of x, y coordinate pairs that each correspond with a raw time bin (e.g., 500-600 ms) up until the cutoff. What this means is mouse trajectory data that persists after the cutoff are discarded (with the trajectory data for that trial ending in mid-flight). Thus, if the raw time cutoff is 1500 ms (and we have, for instance, 20 equal raw time bins until 1500 ms), then the section of mouse trajectories that take place after 1500 ms will be discarded. Although this makes the analysis more difficult, a raw time analysis can be extremely useful for studies involving time-sensitive stimuli (e.g., spoken words or compound sequences of images, etc.) or simply if it is important to know in raw time (ms) where and what the mouse is doing.

Measuring spatial attraction

These preprocessed and averaged mouse trajectory data could be used in many ways and which ways are used depends on the research questions at hand. In many cases, one question is whether the trajectories for one condition travel reliably more closely to an unselected response relative to another condition. Or, it might be useful to know simply how much deviation or curvature exists in the trajectory in general. Prior studies have used two measures, which are fully implemented in the MouseTracker: maximum deviation (MD) and area-under-the-curve (AUC). For both of these measures, MouseTracker first computes an idealized response trajectory (a straight line between each trajectory’s start and endpoints). The MD of a trajectory is then calculated as the largest perpendicular deviation between the actual trajectory and its idealized trajectory out of all time-steps. Thus, the higher the MD, the more the trajectory deviated toward the unselected alternative. The AUC of a trajectory is calculated as the geometric area between the actual trajectory and the idealized trajectory (straight line). Area on the opposite side (i.e., in the direction away from the unselected response) of the straight line is calculated as negative area. See image above for a visualization of these.

For example, below is the trajectory from a trial that eventually clicked on response #2. To calculate this trial's MD and AUC values in reference to the unselected alternative, response #1, a straight line is produced. MD and AUC calculations appear below:

Measuring complexity

In some cases, it may be helpful to know how complex trajectories are. For example, if an unselected alternative simultaneously acts another attractor that exerts a force on participants’ mouse trajectories, this additional stress might manifest as less smooth, more complex and fluctuating trajectories. MouseTracker calculates x-flips and y-flips, which are the number of reversals of direction along the x-axis and y-axis, respectively. This captures the fluctuations in the hand’s vacillation between response alternatives along the x-axis and y-axis.

Distributional analyses

You may wish to examine the distribution of trajectories’ trial-by-trial spatial attractions toward an unselected alternative (indexed by MD or AUC). This can be especially useful for formally determining the temporal nature of one condition’s stronger attraction toward an unselected alternative relative to another condition. For instance, suppose a researcher finds that trajectories in Condition 1 are continuously more attracted toward the unselected alternative than trajectories in Condition 2. This is visually apparent by plotting the two mean trajectories and statistically apparent by a significant difference in MD or AUC between Condition 1 and Condition 2. Underlying this reliable continuous attraction effect, however, could be a subpopulation of discrete-like errors biasing the results. For instance, if half the trajectories in Condition 1 headed straight to the selected alternative, and the other half initially headed straight to the unselected alternative, followed by a sharp midflight correction redirecting the trajectory toward the selected alternative, the mean trajectories would exhibit a reliable attraction effect that appeared continuous although it was actually caused by several discrete-like errors. If such a subpopulation of discrete-like errors were biasing the results, the distribution of Condition 1 would be bimodal (some trajectories show zero attraction and the other trajectories show extreme attraction).

Bimodality may be tested by calculating the bimodality coefficient (b) and determining whether b > 0.555. If b > 0.555, the distribution is considered to be bimodal, and if b ≤ 0.555, it is considered to be unimodal. It is computed by the following equation:

In this equation, n is the number of observations, g₁ is skewness and g₂ is kurtosis. For testing bimodality, MouseTracker z-normalizes the MD and AUC values of trials within each participant, together across Condition 1 and Condition 2, for convenience. MouseTracker only generates these for MD and AUC values in reference to the response alternative that is the default comparison (default-compare column in the experiment .CSV file). You may also want to further alleviate concerns about latent bimodality by ensuring that the shapes of the two distributions are statistically indistinguishable. To accomplish this, the Kolmogorov-Smirnov test is used (available on the web: http://www.physics.csbsju.edu/stats/KS-test.html). For use with this test, MouseTracker conveniently z-normalizes the MD and AUC values of trials within each participant, separately across Condition 1 and Condition 2. This test, unlike the bimodality test, is inferential; if p < .05, the shapes of the two distributions reliably depart from one another.