Statistics; frustration

[From Bill Powers (930412.1000 MDT)]

Gary Cziko (930411.2210 GMT) --

Fascinating about the chi-squared phenomenon. I suppose it could
be argued that in counting votes there is never an instance of a
fractional vote, but what if the measure consisted of points on a
continuous scale, like temperature? Then your chi-squared measure
would depend on whether you used kelvin, centigrade, or
fahrenheit units.

···

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Greg Williams (930412 - 2) --

"After a short while in the insoluble problem situation and
with pressure applied to force behavior, the animal develops a
response to the situation that has no adaptive value in the
sense that it is adequate to the situation or in the sense
that it is superior to any number of other possible responses.
Nevertheless, the appearance of the behavior is associated with
a decline in resistance to jumping.

I guessed at either catatonia or incessant disorganized behavior,
which is evidently wrong. However, if the above quote is a
paraphrase of Maier, the experimenter evidently put the
application of "pressure" into some non-experimental category
(pay no attention to that man behind the curtain), and failed to
note that the animals settled down to a behavior that
consistently resulted in escape from the "pressure" situation. By
focussing on where the animals' escape behavior ended up, he
failed to mention where it did NOT end up -- on the pedestal or
box where the noxious stimulus could affect it. The animals could
then be seen not as being "less resistant to jumping" but "more
skilled at avoiding the noxious stimulus."

It's pretty hard to claim that the behavior of jumping off the
pedestal (whatever the futile destination) had "no adaptive value
in the sense that it is adequate to the situation." We can only
presume that it was as adequate as possible, from the rat's point
of view. Evidently, the total intrinsic error was less when the
rat jumped than when it stayed on the pedestal. I assume that
during the pilot phase of the experiment, the experimenter
increased the noxious stimulus until it was sufficient to "make"
all the rats jump. Was that discussed? This would guarantee that
the "pressure" itself caused more intrinsic error than any
outcome of jumping did.

Did the experimenter suggest anything that the rat might have
done that would have had more adaptive value in the experimental
situation?

I can think of several hypotheses to explain the stereotypy of
the responses.

1. When reorganization fails to decrease intrinsic error, the
focus of reorganization switches to other control systems. This
leaves the abandoned control system functioning according to the
last reorganization that took place.

2. A decrease in the success of choice of target (position or
symbol) from 100% to 50% was not sufficient to cause
reorganization to start at the level of position vs. symbol
control.

3. Reorganization focusses exclusively on the control system
associated with the largest intrinsic error. That would be the
"pressure" stimulus, which was always large enough to result in a
jump away from the noxious stimulus even at the expense of
hitting the wall and falling. The only organization that would
terminate this stimulus was jumping, so the organization always
returned to jumping rather than not jumping. The directional
control, not being reorganized, remained as before and thus
appeared stereotyped.

By suitable variations in the experimental conditions, these
hypotheses could be tested. For example, if the strength of the
noxious stimulus were gradually reduced, a point would be found
where the rat would be as likely to stay on the pedestal as jump.
This would be the point where the penalty of falling was
considered by the rat to be about the same as the penalty for not
jumping. I would then predict that reorganization of the
directional criterion would again commence, and the stereotypy
would disappear. This would test the third hypothesis.

To test the second hypothesis, the experimenter could increase
the penalty for failing to hit the open door; the net could be
electrified to varying degrees, so the penalty could be increased
until reorganization commenced again.

The first hypothesis, which does not exclude the other two, is
already tested by the "symbol" response. Moving the location of
the symbol results in the rat's jumping toward the symbol,
counteracting the disturbance caused by moving the location of
the symbol. Control for position could be tested if the two doors
were made movable on the wall, so the rat would have to vary its
direction of jumping in order to maintain a constant arrival at
the position of one door. If the rat continued to jump at the
place on the wall where the door was, the directional control
itself would have ceased to be variable, whereas if the rat
jumped at the same door regardless of the symbol, we might
conclude that we're just looking at two kinds of symbol response
(the door itself being a symbol).

Unfortunately, the experimenters don't seem to have been testing
the predictions of any model, especially not this one, so these
manipulations weren't done. They didn't mention WHY the rats were
jumping for the open door -- is that how they got fed? Or didn't
it really matter?

Retraining the rats for a different criterion of directional
control results in the newly learned behavior becoming
stereotyped. This fits hypothesis 3, and perhaps the other two as
well.

Thus the typical behavior in the no-solution problem situation
is a loss in variability and a tendency to execute some
response repeatedly. When the animal enters the situation with
a response, this response is the one that is likely to be
maintained. In other words, the reward response becomes
transformed into a stereotype and the reward ceases to have its
effect in determining the choice made.

The interpreter does not consider the other possible Gestalt,
which is that behavior _changes_ until its effects are as
adaptive as possible. The principle of reorganization says that
organized behavior will continue in the same form until it (or
something) causes an increase in intrinsic error. All control
behavior is stereotyped until there is some reason to alter its
organization. So there is no "tendency to execute some response
repeatedly." There is only a tendency to continue opposing
disturbances in a particular way as long as intrinsic error does
not increase and no other way of opposing them works better. This
is true of all control behaviors, like the way we walk or eat.

I just scanned over your post, and found that there was no
mention of whether the "pressure" stimulus continued to be
applied throughout the experiment. It seems to have receded into
the background, as just part of the experimental conditions.

That thought reminds me that there is one more dimension of
behavior that could be reorganized, which is the timing of the
jumps. If a rat stays on the pedestal until the noxious stimulus
takes it by surprise, it will certainly experience the noxious
stimulus. According to the Robertson and Glines results with
human beings, the next stage of the solution would be for the rat
to be poised, ready to jump, when the noxious stimulus occurs,
its reaction time becoming very short. Did the experimenters
record reaction time?

And then, if the rats can do sequence control, they could come
across the ultimately effective organization (within the given
limits) by anticipating the noxious stimulus and jumping before
it occurs.

This, I would guess, would trap the rats hopelessly in
superstitious behavior. Because the intrinsic error due to the
noxious stimulus is never allowed to occur, removal of the
noxious stimulus altogether would be undetectable. The rat would
_imagine_ the noxious stimulus and jump, so it would never
actually experience the stimulus. It would then exhibit the
greatest stereotypy of all. The experimenter puts it on the
pedestal. It immediately jumps, controlling for either position
or symbol according to whichever form of control existed when
reorganization ceased. The only intrinsic error it experiences is
whatever is caused by falling 50 percent of the time (which, by
hypothesis 2, may not be enough to start reorganization). In
fact, I suppose that one could simply lock both doors, and the
rat would continue to jump and fall with no successes and no
noxious stimulus. It may not mind falling as much as the
experimenter thinks it does. It would continue to jump as if a
noxious stimulus had occurred, which I would attribute to the
imagination connection. It might possibly continue to
congratulate itself on yet another total escape from that awful
Bad Thing that happens on the platform.

Another variant would be to use a stimulus light to announce the
imminence of the noxious stimulus. After a while, the stimulus
light alone would suffice. Eventually, I suppose, even that
wouldn't be necessary.

The only way out would be for the penalty of falling to be made
progressively more severe until either reorganization started up
again or the rat died or went nuts.

In general, the type of response made, the manner of execution,
and the type of abortive behavior that may appear under
conditions of frustration show lack of variation and a degree
of stereotypy that perhaps exceeds in specificity the execution
of responses developed or maintained under ordinary learning
conditions where reward is given in connection with response.
This occurs despite the fact that there is nothing in the
punishing situation that demands or encourages highly specific
behavior."

The Gestalt here is much the same as the one that leads to the
conclusion that reinforcement maintains behavior. The
experimenter evidently sees variability in behavior as the norm,
and consistency as the exception (perhaps because of much
experience with doing behaviorial experiments with the wrong
model in mind). Clearly, the experimenter expects behavior to
occur only when it is demanded or encouraged by punishment or
reward. If this is the underlying theoretical stance, the
experimenter should take the results as described so far as
disproving that theory, and should be looking for a completely
different explanation that fits the observations. At this point
in the presentation, it seems that the experimenter is simply
pointing out a paradox. Perhaps the experimenter is trying to
show what is wrong with the attribution of behavior to punishing
or rewarding causes. If so, he is well on the way.

Oh -- one last thought. Intrinsic error could be reduced a little
further if the rat avoided crashing into the closed doors. It
could just jump directly into the net. Then the only remaining
controlled variable would be the (imaginary) noxious stimulus.
----------------------------------

I welcome comments, especially in light of previous predictions
by some netters regarding what the rats might do in the
situation outlined above. I urge caution in additional
predictions aloing the lines of "the rats become
crazy/catatonic ...

The turtle makes progress by sticking out its neck. I have
learned that my initial prediction was wrong, which is
interesting. Knowing that, I have been able to use the added
information in this post to stick my neck out again, being a
little more detailed about the connection with the theory of
reorganization. There is a lot we don't know about
reorganization; this is the sort of interaction between fact and
theory that can refine the model and make it more realistic. I
don't mind guessing wrong. I do that all the time.
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Best to all,

Bill P.

[From Jan Talmon (930416 22:05)]
Two messages on one day. This can only mean that I'm going on holidays
and the backlog of CSG-L posts will increase next week.

Just an observation on Bill Powers remark in (930412.1000 MDT) - Note the
backlog...- on how to lie with the Chi-square statistic.

Although I have only marginal training in statistics, I think that the
Chi-square is mostly - if not only - used to compare observed frequencies
with expected/predicted frequencies of events. To be more precise it are
not the relative frequencies that are compared by the actual counts. So
counting 1, 2 and 5 for the occurences of three different events might
not be a statistical prove that the third event occurs more often than the
other 2, but when the counts are 100, 200 and 500 than it will certainly be
statitically significant (yak. I even now use a term I normally won't use).
I don't see how units like Kelvin, Centigrade or Fahrenheit play a role in
counting.

Jan Talmon