Great apes have been shown to be intuitive statisticians: they can use proportional information within a population to make intuitive probability judgments about randomly drawn samples [, J.E., J.C., J.H., E.H., and H.R., unpublished data]. Humans, from early infancy onward, functionally integrate intuitive statistics with other cognitive domains to judge the randomness of an event []. To date, nothing is known about such cross-domain integration in any nonhuman animal, leaving uncertainty about the origins of human statistical abilities. We investigated whether chimpanzees take into account information about psychological states of experimenters (their biases and visual access) when drawing statistical inferences. We tested 21 sanctuary-living chimpanzees in a previously established paradigm that required subjects to infer which of two mixed populations of preferred and non-preferred food items was more likely to lead to a desired outcome for the subject. In a series of three experiments, we found that chimpanzees chose based on proportional information alone when they had no information about experimenters’ preferences and (to a lesser extent) when experimenters had biases for certain food types but drew blindly. By contrast, when biased experimenters had visual access, subjects ignored statistical information and instead chose based on experimenters’ biases. Lastly, chimpanzees intuitively used a violation of statistical likelihoods as indication for biased sampling. Our results suggest that chimpanzees have a random sampling assumption that can be overridden under the appropriate circumstances and that they are able to use mental state information to judge whether this is necessary. This provides further evidence for a shared statistical inference mechanism in apes and humans.

To control for potential associative learning explanations, we lastly tested chimpanzees in experiment 3, again using populations of new food types (100:10 versus 10:100). Before the test, subjects experienced that both experimenters would always draw preferred food items out of their population. However, while E1 sampled blindly from the more favorable population, E2 sampled from the less favorable one while looking into the bucket. In the subsequent test, both experimenters drew in the same manner as before but this time from identical populations containing equal proportions of preferred to non-preferred food items (55:55 versus 55:55). We found that chimpanzees preferred the sample drawn by the experimenter who had before sampled the statistically unlikely (preferred) food type significantly above chance level (Mean= 64.8% of trials; t = 4.438, df = 17, p < 0.001; CI [0.577, 0.718]; see Figure 3 ). Again, we did not find an effect of trial number (X= 0.007, df = 1, p = 0.933), indicating that subjects did not learn within the test session which experimenter was favorable (see also trial 1 performance: 66.7%). Moreover, we did not find an effect of experimenter’s ID, neither when considering only experiment 3 (X= 0.803, df = 1, p = 0.370) nor when considering whether it was the same or the opposite one compared to experiment 1 (X= 1.142, df = 1, p = 0.286), indicating that subjects did not perform better when the positive experimenter was the same as in the first experiment (also see Table S4 ).

We did not find any effect of trial number within the conditions for the two experiments, indicating that chimpanzees did not learn within a session which of the two populations or experimenters was the rewarded one (X= 2.693, df = 2, p = 0.260). First trial performance confirmed the choice pattern: 45% of subjects chose the sample coming from the more attractive population in the first trial of the visual access condition compared to 60% in the no visual access condition and 78% in the random condition. The identity of the experimenter did not influence the chimpanzees’ choice (X= 1.130, df = 1, p = 0.264; see also Tables S2 and S3 for detailed results of experiments 1 and 2).

In experiment 2, when subjects did not have any prior information about potential choice biases and drawing was random, chimpanzees chose the sample from the more favorable population at the highest levels (Mean= 88.9% of trials), significantly above chance level (t = 11.78, df = 17, p < 0.001) and significantly more often than in the visual access condition (estimate ± SE = 3.261 ± 0.355, df = 2, p < 0.001, CI [2.416, 4.548]) and in the no visual access condition of experiment 1 (estimate ± SE = 2.177 ± 0.352, df = 2, p < 0.001, CI [1.234, 3.317]; see Figure 2 ).

We found that subjects’ choice in experiment 1 was significantly influenced by conditions (GLMM; X= 44.26, df = 1, p < 0.001). More specifically, in the visual access condition, when experimenters looked into the buckets, chimpanzees preferentially picked the sample drawn from the less favorable population (Mean= 33.8%), significantly different from what would be expected by chance (t = −3.58, df = 19, p = 0.002). Thus, subjects based their choice on the experimenters’ choice biases rather than on the proportional composition of the population. In contrast, when the same experimenters sampled blindly in the no visual access condition, subjects’ choice was different; here, they tended to choose the sample from the more favorable population more often, albeit not above what would be expected by chance (Mean= 57.1% of trials; t = 1.37, df = 19, p = 0.187), but a comparison of the two conditions revealed that subjects chose the proportionally favorable population significantly less often in the visual access condition than in the no visual access condition (estimate ± SE = −1.083 ± 0.204, df = 2, p < 0.001, confidence interval [CI] [−1.714, −0.496], see Figure 2 ). This pattern was not due to any order effects, since it held equally for both orders of presentation of the test conditions (X= 0.007, df = 1, p = 0.931). Moreover, the effect was not driven by single individuals. Apart from one young female showing the opposite pattern and two subjects showing no difference between conditions, all remaining 17 individuals chose the sample from the more attractive population numerically more often in the no visual access condition.

To examine chimpanzees’ baseline performance in this task without any prior information about experimenters’ choice biases, we tested them in experiment 2 with new food types in the same proportions as before (200:20 versus 20:200). Similar to the no visual access test, both experimenters drew blindly from the populations.

We used an established paradigm [] in which chimpanzees faced two mixed populations of preferred and non-preferred food items and could choose from which of the two populations they wanted to receive a sample. In contrast to previous studies where drawing was always random, we here varied whether sampling was random or not (method adapted from []). To examine whether chimpanzees could integrate knowledge about others’ choice biases and visual access into their statistical inferences, we first demonstrated to them that two experimenters, E1 and E2, had specific and opposing biases regarding two types of food in experiment 1: E1 preferred the type of food liked less by the apes themselves (carrot), whereas E2 showed the same preferences as the apes (peanut). These choice biases were established as follows: E1 repeatedly drew only carrots from a population with mostly peanuts (200 peanuts and 20 carrot pieces), and E2 showed the reverse patterns, repeatedly drawing only peanuts from a population with mostly carrots (20 peanuts and 200 carrot pieces). During the subsequent two test conditions, subjects witnessed the two experimenters sampling from their respective populations and were allowed to pick one of the samples. As the samples were hidden inside E1’s and E2’s fists, they had to infer from which population or experimenter they would most likely receive a favorable food item as a sample. The crucial manipulation between conditions was whether the experimenters looked into the bucket during sampling (visual access condition, see Figures 1 A and 1B ) or drew blindly (no visual access condition, see Figures 1 C and 1D). The order of these two test conditions was counterbalanced across subjects.

(A–D) In the visual access condition, experimenters looked into the buckets while sampling (A) before offering the subject a choice between the two samples hidden in their fists (B). In the no visual access condition (C and D), a screen was placed between experimenters and buckets, blocking the experimenters’ view into the populations. Moreover, in this condition, the experimenters’ faces and bodies were oriented away from the table, further emphasizing a lack of visual access to the buckets during sampling.

Discussion

The current study shows that chimpanzees were able to flexibly adapt their choice as a function of statistical and psychological information in a paradigm that required them to reason probabilistically from population to sample. In the visual access condition of experiment 1, when biased experimenters drew samples while looking into the bucket, chimpanzees preferred the sample drawn by the experimenter with the preference for the favorable food type, mostly disregarding the proportional composition of the populations. This suggests that subjects expected the drawing to be based on the experimenters’ choice biases and, therefore, non-random in this condition. When the same biased experimenters drew samples from the same populations in the no visual access condition blindly, subjects switched and now showed a slight preference for the proportion-wise more favorable population despite the experimenters’ biases. Hence, depending on whether or not the experimenters had visual access to the buckets while drawing, subjects based their choice either on the experimenters’ choice biases or rather on the mere proportional composition of the population. In experiment 2, when chimpanzees did not have any information about potential biases of the experimenters and they drew blindly, subjects chose the sample drawn from the favorable population at higher levels than in both conditions of experiment 1. Results of these two experiments suggest that chimpanzees, without any prior information, assumed random sampling and expected the sample to reflect the population's distribution. If they, however, had reason to assume that the experimenters were biased, subjects’ choice reflected these biases; the severity of this influence was dependent on whether the experimenters had visual access or not.

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Call J. How the great apes (Pan troglodytes, Pongo pygmaeus, Pan paniscus, and Gorilla gorilla) perform on the reversed contingency task: the effects of food quantity and food visibility. 10 Buttelmann D.

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Tomasello M. Do great apes use emotional expressions to infer desires?. However, despite the fact that we did not find any indication for learning within test sessions, we cannot exclude that subjects might have learned during the demonstration of experiment 1 to simply associate one of the populations or experimenters positively or negatively and pick or avoid this one in the visual access condition where the setup was identical to the demonstration. The difference between conditions could congruently be explained by a change in setup in case of the no visual access condition (presence of a barrier) or the elapsed time in case of experiment 2. We believe this scenario is unlikely considering that chimpanzees and other nonhuman primates are known to have severe difficulties learning rules that clash with their natural predisposition to choose the larger of two (preferred) food amounts []. Furthermore, the shortness of the demonstration exposure makes any rule-learning explanation additionally implausible. Nevertheless, we sought to address this alternative explanation in experiment 3, in which chimpanzees were required to infer an experimenter’s choice bias from statistical information (and according behavioral cues) without being differentially rewarded in the demonstration. In the test, subjects intuitively preferred the sample drawn by the experimenter who had previously drawn the statistically unlikely (and preferred) food type in the demonstration over the experimenter who drew blindly (and therefore randomly). This suggests that chimpanzees were able to use statistical information, in particular a violation of statistical likelihoods, to infer an experimenter’s choice biases and draw conclusions about the sampling process. At the same time, it corroborates our hypothesis that subjects do not rely on associatively learned rules in this kind of task. It should be noted that, even though there is evidence that great apes have some understanding about human preferences or desires [], we do not intend to make any strong claims about how chimpanzees interpreted the experimenter’s choice bias in our study. It is possible for example that the subjects inferred that experimenter 1 seems to like (drawing or giving) peanuts. It is similarly possible that they simply noticed that experimenter 1, for whatever reason, draws peanuts when she has the possibility to do so. We cannot disentangle these two possibilities, and for the interpretation of our data, it is sufficient to assume the latter option.

While chimpanzees showed a remarkable flexibility and sophistication in this study, one may wonder why they did not perform better in the no visual access condition of experiment 1. Subjects in this condition chose the sample of the proportionally attractive population on average in 57% of trials as compared to 89% in experiment 2, although we used the exact same proportions in both experiments. The most likely explanation for this difference is that chimpanzees in experiment 2 did not have any information about potential biases of the experimenters, which left the randomness of the draw the only aspect to consider (results of this experiment also demonstrated that subjects had not remembered any “good” or “bad” labels for the experimenter from the previous experiment). By contrast, in the no visual access condition of experiment 1, chimpanzees had to overcome what they had just experienced—namely, that E1 always extracted carrots from the peanut population, and E2 always extracted peanuts from the carrot population. This information was even repeated (in reminder trials) right before the no visual access condition. Thus, this condition required two extra steps compared to experiment 2: (i) chimpanzees had to recognize and understand the indicators of blind drawing, and (ii) they had to weigh the indicators of “biased sampling” and “blind sampling” against each other and choose accordingly. Therefore, our task design required a fair amount of cognitive flexibility, which might have been too demanding for some of the subjects.