[From Bruce Abbott (950120.2030 EST)]
Tom Bourbon [950119.1445]
Do sheep really moo? (;->
Bruce Abbott (950116.1730 EST)
What do you think your traditional colleagues would make of this one, and
its accompanying regression analysis shown below?
[Tom was referring to the regression of handle position on disturbance, in
which r = -0.995.] I really don't know. As they are being given only the
cursor and mouse positions, it will be interesting to see whether they even
compute the disturbance, let alone correlate it with mouse position. In
their situation, I think that I would naively conclude that handle position
changes to counteract the "drift" of the cursor from the target -- nothing
unusual going on there, just S-R. S: cursor drifts to left of target, R:
mouse moves to right to bring it back. Whether they will come up with
something different, who knows?
Another thing I would like to have done is to generate some
three-dimensional plots of these data (response surface), as well as
scatterplot matrices. Minitab has a new Windows-based version out that
apparently can do these, but I haven't seen it yet.I'm curious. Do you think those fancy plots would reveal something that
isn't seen in the original plots of mouse, target and cursor positions? Or
in the simple dsecriptive statistics? I'm just asking, not judging.
The best way to look at the data is to examine the time series for the
cursor positions, disturbances, and mouse position appropriately
superimposed (e.g., the three disturbances plus mouse position as four lines
of different color). I'm just curious as to whether those other plots might
show something interesting. For example, one could create a response
surface plot using cursor position, mouse position, and disturbance on the
three axes. Such plots might turn out interesting, or perhaps not. I just
like to view data in a variety of ways to "see what I can see." Things make
better sense to me when I can visualize them.
Have you calculated the variances of the three disturbances and compared
them with the variances of the three cursors? It's neat to see that when
the person controls the position of one cursor, reducing the variance of its
position, the variances of the uncontrolled cursors are usually greater
than they would have been had the person not controlled the other cursor.
Somewhere I wrote about how the variance that would have appeared in the
controlled cursor vanishes, only to show up as increased variances of the
handle and of uncontrolled variables that are affected only incidentally.
Yes. If the three disturbances are uncorrelated, the variances of the two
uncontrolled cursors sum with the variance of the handle. If control is
good, handle variance will nearly equal the variance of the disturbance
acting on the controlled cursor.
Do the PCT-analysis programs you have written estimate the reference value
from the data? When the data set contains only cursor and handle positions,
(i.e., lacks the disturbance tables), the disturbance values can be
calculated exactly only if the reference values are known (In THREECV1 all
three = 319).That sounds a little strange. Momentary cursor position is determined
entirely by handle position plus disturbance: c = h + d. The reference
signal does not enter into that calculation - the equation describes how
the *world* works, not how the control system works. I wonder what's
going on in the program.
I've already explained this in my reply to Rick's similar comment. The
cursor position data include an [unknown] added constant which is the screen
x-position of the targets. Speaking of which:
Rick Marken (950120.0900)
Perhaps I should have said "target" instead of reference
Nope. Still doesn't matter. The disturbance values CAN be calculated exactly
if we know only c and h (unless, of course, c=d+h+t, in which case we would
have to know t as well, as you note).
In other words, it still doesn't matter, unless c=d+h+t, which it does, so
it does matter. Rick, when I'm right, I'm right. (;->
Bill P.'s PCT analysis routine just blew up while trying to converge on K on
a run completed by one of my colleagues. It has worked fine up to now.
Guess it's debug time. Speaking of which, I have modified THREECV1 to
eliminate a serious glitch in the original: when you started a run, the
cursors had a tendency to fly off the screen, which required a quick mouse
response to recover from before the run-in time was over. The problem was
that the initial cursor positions did not include the initial disturbance
values.
Regards,
Bruce