[From Bruce Abbott (9705.1220 EST)]
In the prototypical tracking experiment, a participant seated at a computer
is asked to keep a cursor aligned with a target by moving the computer's
mouse. Meanwhile, the cursor's position is being affected by a disturbance,
which in the absence of counteracting mouse movements causes the cursor to
drift from the target's position. The disturbance, mouse position, and
cursor position are recorded during the run and then the the correlations
between each possible pair of these three variables is computed. The
classic result is a near-zero correlation between variation in cursor and
mouse positions and a nearly perfect negative correlation (generally in
excess of -.995) between variations in disturbance and mouse position. A
typical example from an actual run appears below:
Cursor Mouse
Mouse 0.093
Dist. -0.011 -0.997
This matrix demonstrates excellent control of cursor position; a plot of
mouse position and disturbance as functions of time would produce two lines
that were nearly mirror images of each other, whereas cursor position would
appear to vary little and with no apparent relationship to either mouse
position or disturbance. This is because mouse movements are essentially
cancelling the effect of the disturbance on the position of the cursor.
This analysis assumes that the participant was simply controlling cursor
position. However, there is another strategy participants could use in this
task to help keep the cursor on-target. Because the disturbance was made to
vary relatively smoothly, a participant could adjust the rate of
mouse-travel as required to reduce the rate of cursor-travel to zero. If
the cursor were already on-target, this strategy would tend to keep it
there. Of course, if the cursor were elsewhere, the rate of mouse-travel
would have to be adjusted so as to permit a residual drift of the cursor
back to target and then changed so as to zero out further drift. This
strategy would amount to a combination of position _and_ rate control of the
cursor.
Is there evidence that the participant who generated the correlation matrix
above used rate control in addition to position control? One way to get at
this question is to take the difference between successive disturbance,
cursor, and mouse positions; these differences provide the rates of change
in each of the three variables. Here are the results:
dCursor dMouse
dMouse 0.786
dDist. 0.382 -0.270
These correlations suggest that control over cursor _rate_ was poor: cursor
rate correlates moderately high with the rate of mouse movement and
moderately low with the rate of disturbance change, indicating that
mouse-rate was not very effective in zeroing out the rate of cursor
movement, and the correlation between the rates of disturbance change and
mouse movement, although negative, was very low. Nevertheless, I would
suggest that this matrix provides some small measure of evidence for some
very poor degree of rate control.
The analysis is complicated by the fact that positional control-actions
would tend to occur at the expense of rate-control. In addition, it seems
likely that positional control would entail a negative correlation between
disturbance and mouse rates. To the extent that positional mouse-action
fell behind (or got ahead of) the disturbance, the participant would have to
play "catch-up" (or "fall-back") and this would reduce the correlation
between disturbance rate and mouse rate. What these data show is that very
high correlations between disturbance and mouse-position can be achieved in
the absence of good control over cursor rate.
Comments?
Regards,
Bruce