Figure 1. Mean RTs of correct responses from Experiment 1.
In two experiments, mechanisms of associative learning were studied
with speeded choice response procedures. Sequential effects in reaction
time and error rate suggested that associations between targets and distractors
were strengthened across trials of perfect target-distractor correlation and
wiped out after a single inconsistent trial. The results support the notion that
rule-like representations of association are formed and tested based on
co-occurrences and incompatible with various contiguity-based models, e.g.,
models in which associations are assumed to be memorized instances of
co-occurrences or direct connections between elements. It is suggested
that the sequential effects may reflect the working of a hypothesis-testing
mechanism under conditions of limited memories.
Associative learning has been a central topic in psychology. Recently, some theorists suggest that two distinct mechanisms may be responsible for associative learning, one based on memorization of instances of co-occurrences and the other based on rule learning (e.g., Shanks, 1994; Perruchet, 1994; Nosofsky, Clark, & Shin, 1989). Others have attempted to explain various kinds of associative learning with a single rule-based mechanism (e.g., Holland, Holyoak, Nisbett and Thagard, 1986; Anderson, 1983; Newell, 1989).
There is little doubt that much of our knowledge is based on learning of rules. The problem of main concern here is the extent of rule learning: Is rule learning implicated when learning is unintended ?
Previous studies (Miller, 1987; Logan & Etherton, 1994) indicated that response latency and response accuracy can reflect subjects' sensitivity to the co-occurrence or correlation between target stimuli and to-be-ignored distractors. Such results are interesting because they seem to suggest unintended associative learning. However, the associative representation and learning mechanism underlying such behavioral effects have never been investigated.
In two experiments, two classes of models of the target-distractor association were tested. The first (reintegration models) posits that an association is re-computed on each trial based on target-distractor correlation across the current trial and many previous trials. The second class of models (rule-testing models) posits that target-distractor associations are rule-like representations that are compared with the target-distractor co-occurrence on each trial. The representation is enhanced, maintained, or discarded depending on whether it is consistent, irrelevant or inconsistent with the co-occurrence.
According to the reintegration models, associative strength is more-or-less a
function of the
correlation across a certain number of previous trials. Therefore, the
change of
associative strength
across trials should be relatively smooth. According to the rule-testing
models,
an association
established on several correlated trials could be invalidated and wiped out by
one or two trials. The
experiments were designed to allow these properties to be inferred from
sequential effects of reaction
time (RT) and error rate (ER).
RTs and ERs following a sequence of perfectly correlated trials were measured.
If the
correlated sequence remains effective after a long sequence of uncorrelated
trials, performance should
depend on whether the target-distractor co-occurrence is consistent with the
correlation (valid trials)
or not (invalid trials): Performance on valid trials should be better than
on invalid
trials.
Subjects. 24 UCSD undergraduates served as subjects in partial fulfillment of a course requirement.
Stimuli and Apparatus. The stimuli on each trial consisted of a visual display and a tone. The visual display was a single upper-case letter (X or Y) at the center of a VGA color monitor. The letter was in yellow with a black background. Each letter subtended 0.60 * 1.76 degrees of visual angle from a typical viewing distance of about 50 cm. The tones were 300 Hz or 1200 Hz in frequency and were delivered through the PC internal speaker.
Task. Subjects were encouraged to focus on responding to the letters and ignore the tones.
Design and Procedure. Each block began with instructions indicating the target- response mapping. Each trial began with a fixation signal (+) at the center of the screen. After 500 ms, the fixation cross was replaced by the target letter. A tone was presented in synchrony with the letter. The letter and the tone lasted for 200 ms. Subjects press a key with left hand to indicate one letter and press another key with right hand to indicate the other letter. Subjects were told to respond as quickly as they could while keeping their error rate below 6% of all trials per block. They were also told that the tones were irrelevant and should be ignored. They were given the feedback message "Error" if they pressed the wrong key and "Too Slow" if the response was not made within the 1700 ms time limit. There was an 1100 ms interval between a correct response or the offset of the feedback message and the fixation signal of the next trial.
The basic unit of manipulation for the experiment was a sequence of 21 trials. Each sequence involves three consecutive segments: a segment which contained trials in which the target and the distractor were perfectly correlated (e.g., all Xs occurred with the high tone and Ys with the low tone), a segment in which the target and the distractor were uncorrelated, and lastly, a probe trial, which was either valid or invalid with respect to the correlated segment. Half of the sequences (sequence one) started with 4 uncorrelated "filler" trials, followed by 12 correlated trials, followed by 4 uncorrelated trials and the probe trial. The other half of the sequences (Sequence two) started with a 12-trial correlated segment followed by 8 uncorrelated trials and a probe trial. As a result, both the number of the correlated trials (12) preceding the uncorrelated segment and the correlation before a probe trial (80%) were the same for sequence one and sequence two. However, with sequence one, the probe trial was separated from the correlated segment by 4 uncorrelated trials. With sequence two, the probe trial was separated from the correlated segment by 8 uncorrelated trials.
The sequential order within both the correlated segments and uncorrelated segments was quasi-random: (1) The two targets occurred in the first and second half of a segment equally often; (2) The intertrial transitions from the last trial of the uncorrelated segment to the probe trial, in terms of letter repetition/nonrepetition and tone repetition/nonrepetition, were equally frequent.
An experimental session consisted of 14 blocks, each consisting of four
21-trial
sequences
linked together without break.
Figure 1. Mean RTs of correct responses from Experiment 1.
Mean correct RTs across the 21-trial sequence one and sequence two were presented in Figure 1.
There was a huge difference between performance (RTs and ERs) on valid trials
and those on invalid trials
immediately following the 12-trial correlated segment. This difference
dissipated
quickly. There was
no difference between RTs and ERs on valid and invalid probe trials after 4
uncorrelated trials
(sequence 1) [RT: t(23) < 1; ER: t(23) < 1], which contained 2 invalid
trials,
and 8 uncorrelated
trials (sequence 2) [RT: t(23) < 1; ER: t(23) < 1], which contained 4
uncorrelated trials.
If the correlation over the 12 trial-correlated segment had any effect, it must
have been
short-lived, since no validity effect existed on trials separated from the
correlated
segment by 4
uncorrelated trials. Since on the average the 4 uncorrelated trials included
two
invalid ones, each
invalid with respect to one of the two target-distractor pairs comprising the
correlated segment, the
association from the correlated segment might have been wiped out by a single
invalid trial. This
kind of result was predicted by the rule-testing models. This interpretation,
however, crucially
depends on the assumption that a representation of the target-distractor
association has been
maintained and possibly strengthened across the 12 correlated trials, for
otherwise there would be
nothing to be wiped out by the invalid trial in the first place. A
reintegration
model in which the
recent instances are heavily weighted might equally or better account for the
results.
The degree of performance decline on invalid trials may reflect how well the target- distractor association has been established from the correlated sequence. By examining the degree of performance decline on invalid trials as a function of the number of perfectly correlated trials preceding each of the invalid trials, one obtains evidence about how remote a trial that remains effective on the association can be.
Such evidence is critical to both models. The rule-testing models is to be
favored
only if
there is evidence suggesting that a target-distractor association is maintained
across a long sequence
of trials before being wiped out by an invalid trial. The reintegration
model must
be constrained by
the same evidence in terms of the relative weights assigned to previous co-
occurrences in re-
computing an association.
Except for the following differences, the methods used for this experiment were the same as in Experiment 1.
Subjects. 20 new subjects were tested.
Design. Sequences of three different lengths were constructed: those of 6-trials, 10- trials, and 14-trials. Within each sequence the target and the distractor on all trials except the last two were perfectly correlated. The last two trials were invalid with regard to the correlated segment. Each of the three sequences varied in the distribution of the two target- distractor pairs. With blocked distributions, one target-distractor pair was repeated for the first half of the correlated segment and another target-distractor pair repeated for the second half of the segment. With random distributions, the two target-distractor pairs occurred in random order with equal frequency in each half of the correlated segment. Each of three sequences was balanced in terms of the frequency of two different intertrial transitions (target and distractor repetition/nonrepetition) leading to the first invalid trial. There were 36 sequences for each of the three sequential lengths, half with the blocked distribution and half with the random distribution. There were 12 experimental blocks, each consisting of 90 trials which contained 9 sequences, 3 for each the sequences of different length.
Figure 2. Mean reaction times of correct responses from Experiment 2.
Two important results were obtained from this experiment:
1. Performance (RT and ER) on the first invalid trial declined more as the preceding correlated sequence became longer (Figure 2 shows only RT). This was true for both the blocked and the random trial distributions. Performance were poorer on the first invalid trial following 12 correlated trials than following 8 or 4 correlated trials. Both RT and ER following 8 correlated trials differed significantly from those following 12 correlated trials [RT: t(19) = 3.33, p < .005; ER: t(19) = 3.60, p < .005]. The interaction between the length of the correlated sequence and the correlation distribution (not including the 4-trial correlated sequences) was insignificant for both RT and ER [RT: F(1, 19) < 1; ER: F(1, 19) < 1].
2. Performance on the first trial of each sequence was analyzed as a
function of
its validity
with respect to the correlation of the previous sequence and the length of the
correlated sequence. It
turns out that only trial validity had an effect*valid trials were slower
and less
accurate than invalid
trials [RT: F(1, 19) =39.12, p < .001; ER: F(1, 19) = 2.73, p > .05].
This is
not as strange as it
may first seem because, with respect to the last two trials, the "valid"
trials were
invalid and the
"invalid" trials were valid. In addition, this "inverse validity effect" was
not smaller
when the
correlated trials on the previous sequence were more numerous. The interaction
between the validity
of the first trials and the length of the previous correlated sequence was not
significant [RT: F(1,
19) < 1; ER: F(1,19) < 1].
With random distributions of target-distractor pairs, the two targets and two distractors occurred with equal probability in each position of the previous sequence. Consequently, a trial could be invalid with respect to those recent trials only because the association between the target and the distractor was invalid.
Results from this experiment support rule-testing models in two ways. First, rule- testing models assume that successive positive evidence from each trial is used to maintain or strengthen the association. This was supported by the finding that target-distractor co- occurrences as far back in the sequence as 8 and 12 trials contributed to the performance decrement on invalid trials. Second, according to the rule-testing models, a target-distractor association, after being invalidated, would have no effect on subsequent trials. This prediction was supported by the finding that RTs and ERs on trials right after two invalid trials were affected only by the validity with respect to the invalid trials, and was in no way affected by the number of correlated trials preceding the two invalid trials.
The performance decline on the first invalid trial might be explained by a
reintegration
model which assumes as many as 12 trials back in sequence being more or less
incorporated in an
association on each trial. However, this particular model would be
inconsistent
with the result from
Experiments 1: a segment of 12 trials that were correlated but for the last 4
trials, which included 2
invalid trials, had no effect on the ensuing probe trial. Nor would it be
consistent
with the even
stronger evidence from this experiment that one invalid trials completely
eliminated the effects of
the preceding correlated sequence.
The reintegration models represent a class of contiguity-based models of associative learning. Other contiguity-based models might make the same predictions in the studied experimental setting. For example, associations are often conceived as analogous connections between elements that are weight-adjusted on each trial based on new co-occurrences. It can be shown that this notion is just as inconsistent with the results here as the reintegration models was.
Overall, these two experiments suggest a mechanism of associative learning analogous to conscious reasoning in which consistent evidence is used to maintain or strengthen an existing hypothesis, and inconsistent evidence is used to reject the hypothesis. The experimental logic was similar to those for suggesting hypothesis-testing-type learning based on many "anomalous" findings in earlier studies of animal and human learning (see Levine, 1975). Earlier studies, however, were not concerned with whether hypothesis testing can characterize learning that are apparently incidental and involves to-be-ignored elements as did the present study.
In addition, there is an important difference between conscious hypothesis
testing and the
rule-testing that has been shown to characterize the findings from this study.
While in conscious
hypothesis testing one is not likely to pick up a rejected hypothesis again
simply
because there is a
new piece of evidence for it, it seemed to be the case in this study (result
2 of
Experiment 2). This could
be a consequence of limited memories when speeded responses are required.
In other words, the
sequential effects found in this study may reflect the working of a hypothesis-
testing mechanism when
past instances are not available.
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