# Stick patterns

[From Bill Powers (920721.1200)]

Pat Alfano (920721.1130) --

Hi, Pat.

The examiner arranges 2, 3, or 4 sticks in a pattern and the subject >who

is sitting across the table must arrange her sticks to look to her >as the
examiners sticks look to the examiner.

Did you verify somehow that the subjects actually understood the
instructions? The phrase "arrange your sticks to look to you as the
examiner's sticks look to the examiner" can't be understood unless the
person grasps the idea of transforming from one perceptual point of view to
another. It seems to me that the very ability you are testing for is
required in order to give meaning to the words of the instruction.

Assuming that all subjects succeeded, the next question is what time has to
do with this ability. If it takes some subjects longer than others to
accomplish the task, what is the difference between them?

places a stick at some random angle, and the subject places another stick
according to the instructions. This tests for the ability to rotate the
frame of reference by 180 degrees in the simplest possible way.

A rotation of 180 degrees is an ambiguous task, because it can go in either
direction. It's possible that time differences are due to the indecision as
to which way to commence the mental turning (in control-system terms, the
left and right errors are balanced, like a stick balanced on end, so only
some small chance deviation can start the correction process in one
direction or the other). If so, even the single-stick task would prove
variable in time to completion.

To test that hypothesis, I would seat the subject at right angles to the
examiner, to left and right, instead of directly opposite. Now the rotation
required is only 90 degrees, and there is no ambiguity in the direction of
mental movement required. Rotation times should now be shorter, and less
variable. I would repeat this experiment for many angles between 0 and 180
degrees plus and minus.

As baseline measurements, you should determine for each subject how long it
takes to reorient one or more sticks by 180 (or 90) degrees from the
original position. This time should be subtracted from the total time
during the real task, or the total time should be measured in units of this
baseline time. The time should be reduced to manipulation time per stick
before the data are combined.

Another dimension to test for would be the ability to remember the target
pattern (shown briefly) long enough to reproduce it as it is, or in the
opposite orientation. This would test for the accuracy of the reference
signal and the decay of accuracy with time delays.

Did you check to see whether the different strategies inherently required
different amounts of time to carry out? How about some examples of those
strategies?

Notice that what you are interpreting as two dimensions of reversal
(discrete variables), I am interpreting as an angular rotation (a
continuous variable).

Given that subjects persist in taking different lengths of time for this
task, I would begin to look more closely at how they accomplish the task,
recording each discriminable movement -- how it begins, runs its course,
and ends, and how much delay there is before the beginning of the next
movement. I would note how often the subjects look at the experimenter's
array (you could have them press a button to illuminate the experimenter's
array, using the same hand they use to move the sticks). If the subjects
take different times to do the task, it is for a reason. The reason may be
different for every subject, or there may be common kinds of reasons. It is
highly unlikely that variations in a task on this macroscopic scale are due
to random noise in the system; you are not using threshold stimuli, nor is
there any uncertainty to speak of in perceiving orientation or executing
the gross movements required. Randomness in the data is most likely to mean
that there's nothing to measure, as you've defined the problem.

I'd videotape the proceedings and then write up a detailed description of
each person's behavior during each repetition of the task. This would
probably show you why there are variations in the time to completion.

Is this a phenomenon you really want to understand? Or is it just that
you'd like to get some significant statistics without doing more
experiments? If the former, I'll be glad to come up with whatever other
suggestions I can think of. If the latter, forget it. Why waste your time
on phenomena that you have to use statistics even to see? Once you get the
right slant on the problem, the phenomena will be big and obvious.

By the way, I have a start on the motion-illusion thing, but won't do more
with it until after the meeting.

Best,

Bill P.