Bob
and John's conclusions from this researchBob
and John's conclusions from this research
The results of this experiment merit several conclusions. First, the weight of evidence more strongly favors a signal detection account of the pigeons= choice behavior in this task than does the HTT/default response account. Interpreted within this signal detection framework, we also established that the variance of the distribution of strength of evidence associated with the Different displays was substantially greater than that of the Same displays (s5Same < s5Different). Further, the variance estimates associated with color, shape, and redundant signal distributions were, within the limits of measurement error, probably equivalent (s5color = s5redundant _ s5shape). Finally, the results suggest that performance with redundant displays was equal to the additive combination of discriminative performance on color and shape trials (d'redundant = d' color + d' shape). Together, these observations best fit the predictions of a unidimensional decision model -- one suggesting that these birds were making their discriminations based on the extraction of a single type of information from the different types of textured stimuli. Figure 7 visually depicts these conclusions and their structural implications for the decision space used by the birds while performing this textured Same-Different task.
High Threshold versus Signal Detection Models of Discriminations. Historically with human subjects in a wide variety of tasks, the high threshold model has failed to account for the shape of ROC plots. Almost invariably, the deviations with human subjects are like those observed here with the pigeons, showing systematic differences in the directions predicted by a signal detection account. The present results add to a reasonably large literature suggesting that signal detection theory nicely accounts for the discriminative performance of pigeons, and to the much smaller literature suggesting that it does a better job than its most frequently proposed alternative. In conjunction with Wixted's (1993) results based on a sample/no-sample matching task, the present results involving target/no-target stimuli in a same/different task offer little support for the conceptually appealing high threshold/default response model as an adequate account of pigeon choice behavior. Instead for these two different types of discriminations, where a default response strategy was a distinct possibility because of the asymmetrical nature of the to-be-discriminated stimuli, a signal detection account offered a better description of the underlying decision processes.
While little support for HTT was found in the present experiment, there remain several other situations in which asymmetrical stimuli have been used or asymmetrical responding has been observed where such an account remains plausible, including the memory of event duration by pigeons (Spetch & Wilkie, 1983), and the memory for sample modality by rats (Wallace, Steinert, Scobie, & Spear, 1980). It would be quite interesting to examine these types of discrimination using the biasing protocol employed here to see how well HTT and SDT would fare in these settings.
In fairness, it should be noted that the high threshold model has only one free parameter (p) whereas the signal detection model tested here has two free parameters (d' and s). Although the signal detection model was penalized by the loss of one additional degree of freedom in the chi-square goodness-of-fit tests, for example, the comparison of two models involving different numbers of parameters is not always a straightforward exercise. A more elaborate modification of the high threshold account, such as Luce's low threshold model (which similarly has two free parameters) might have described these data accurately. We did not pursue this latter model in greater detail for several reasons. First, we chose to concentrate on the 1-parameter HTT because of its direct relation to currently proposed mechanism of pigeon choice behavior. Second, it has been historically quite difficult to distinguish Luce's model from signal detection theory on the basis of quantitative fits. Lastly, it should be noted that SDT assumes that pigeons always make their choice based only on subjective information from the evidence dimension. While this assumption is unlikely to be true in the extreme (Blough, 1996), as long as their rates of guessing were constant across the different biasing conditions, this consider would not change the conclusions reached in this article.
The Difference in Signal & Noise Variance. While a SDT account was found to better describe the results, it did require estimating signal distributions for color, shape, and redundant Different trials with standard deviations nearly a factor of three greater than that of the Same/noise distribution. This result was not anticipated, although given the asymmetric nature of the stimuli in terms of structure and number, it is perhaps not surprising. Wixted (1993) also found unequal variances in his sample/no-sample matching task, although in that particular case it was the noise distribution that was wider than the signal distribution. Unlike a simple red vs. green discrimination task, which involves stimuli that lie on a single physical continuum, both the present experiment and Wixted=s may have involved discriminations among qualitatively distinct stimuli that may have been responsible for this difference in the variance of the signal and noise distributions. Both discriminations involved in some sense the discrimination of the presence and absence of a particular type of stimulation. The wider variance of the noise distribution in Wixted=s sample/no-sample discrimination would seem to make good sense, as the absence of an event seems inherently more difficult to encode then its physical presence. The current experiment required the pigeons to discriminate a uniform display from a Different display that contained the additional presence of a highly variable target. As such, the greater width of the signal distribution in the latter case also seems to make intuitive sense.
But what factors associated with the Different displays was specifically responsible for this effect? We investigated several possibilities, all of which we eventually rejected as the source of this variability. The first possibility we considered is that the assortment of targets used in this experiment varied in their discriminability. Some targets (e.g., red dots in brown dots) were much less discriminable than others (e.g., yellow triangles in blue triangles). Perhaps the mixture of salient and non-salient target stimuli produced more variability than the various types of uniform stimuli (such as all red dots or all yellow triangles). Although this intuitively appealing explanation can actually be rejected analytically, we nevertheless identified and classified the target/distractor combinations that yielded the best performance and separated them from those that yielded the worst performance (see Cook, Katz, & Cavoto, 1997). As indicated earlier, separate ROC analyses of these more homogeneous discriminability groupings of the Different trials yielded the same higher estimates of s for all levels. That is, the ratio of the signal to noise s was approximately 3 in all of these cases (although d' for the discriminable stimuli was, of course, much greater than d' for the less discriminable stimuli).
Next we tried classifying the Different trials according to whether the pigeon pecked the target area (which generally produced a higher d') from those in which they did not peck at the target (which yielded lower d' estimates). Separate analyses based on these differences in pecking behavior also produced no change in the estimates for signal distribution variance from those analyses described above.
Another possibility is that the relatively wide signal distribution variance may have resulted from the variable nature of the target=s spatial position from trial to trial. Sometimes the target was on the left side of the screen and sometimes it was on the right. When the target appeared on the left, subjects may have been biased to choose the left hopper, and when it appeared on the right they may have been biased to choose the right hopper. To evaluate this possibility, we again reclassified the Different trials based on target location in two ways (left versus right and center versus periphery). Again we fit the models to these more homogeneous location data sets, and in both cases the estimates of the signal distribution=s variance remained stubbornly higher.
These analyses based on target discriminability, target pecking behavior, and target location, all failed to reveal the reason for the wider estimate of the signal variance. Thus, perhaps our first intuition that the origin of the variance differences lie with the Different displays is incorrect. It is important to remember that these estimates are computed by fixing the value of the noise distribution at 1. As such, the problem can be conceptualized a little differently. Instead of the Different stimuli producing unexpectedly high variability, the Same stimuli may have been producing unexpectedly low variability. Such a perspective would suggest that Auniformity@ may be distinctive psychologically less variable attribute, a possibility that has been considered in the human Same-Different literature to explain such phenomena as Afast same responses@ (Krueger, 1978).
Although the psychological source of the unequal variance in the signal and noise distribution remains an intriguing mystery, the fact that they differ at all leads to an important consideration in judging choice accuracy among different conditions. Specifically, any model of how pigeons integrate color and shape information on redundant trials cannot rely solely on accuracy information as derived from a single test condition. Had only a single biasing condition been conducted, the information about the relative widths of the signal and noise distributions could not have been computed. Under such single test conditions, researchers adopt by necessity the simplifying assumption that the two distributions have the same standard deviations (e.g., Mulligan & Shaw, 1980). Had that strategy been used here, incorrect conclusions would have been reached. For example, we could have relied on hit and false alarm rates from the unbiased (i.e., equal presentation probability) condition only. By adopting the assumption that the variances of the signal and noise distribution were equal, d' scores could be easily obtained from published tables. Using that approach, the mean d' scores from color, shape, and redundant trials in the unbiased condition turn out to be 1.90, 1.91, and 2.91 respectively. The implication of these values is that performance in the redundant condition is significantly less than the additive combination of performance in the color and shape conditions, a result that would have led us to reject incorrectly the unidimensional model.
In conclusion, the present research demonstrated that a signal detection analysis of ROC data provides an efficient way to differentially evaluate models of multidimensional perception and choice in pigeons. Using this approach, two multiple-channel models were rejected in favor of a simpler unidimensional account. Because the pigeon's job was primarily to detect the presence of a generalized target composed from a variety of values from different dimensions and their combination, perhaps this type of common encoding of the Different displays is not surprising. Such a general coding scheme for the display would permit the animals to both work with large numbers of stimuli and transfer to novel exemplars as found by Cook et al.(1995; see also Wasserman et al., 1995). What is the possible psychological identity of this proposed dimension of discrimination? One possibility is that the birds have learned a conceptual Same-Different rule which is then used to judge all of the displays. For reasons outlined in those papers, both Cook et al. (1995) and Wasserman et al. (1995) put forth this idea as the best explanation of their novel stimulus transfer results. Nevertheless, the present results are also consistent with another unidimensional possibility considered, but rejected, by these same authors. The idea here is that the birds are simply discriminating the training and transfer displays based on a lower level perceptually-driven Acontrast@ detection strategy, rather than employing a higher level conceptual strategy. Recently, Young and Wasserman (1997; see also Young, Wasserman, & Garner, 1997) offered a third unidimensional possibility, reporting evidence for the idea that the critical dimension may involve the encoding of a display=s entropy. Entropy is an information-theoretic measure of the relative variability created by the number and nature of different elements in multi-element mixed displays. While the present experiment cannot distinguish among these three alternative conceptions of the critical dimension (but see Cook, Katz, & Cavoto, 1997), its results do clearly support their pivotal idea that only a single kind of general information/rule is involved in the discrimination of these types of multi-element Same-Different displays by pigeons.
Dynamic
Texture Stimuli 
Same-Different
& SDT 
Same-Different
w/ Multiple Stimuli
Dr.
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