Open questions concerning the cognitive structure and development of intuitive statistical

Eckert, Call, et al. (2018) demonstrated that the analogue magnitude system most likely underlies intuitive statistical reasoning abilities both in chimpanzees and human adults. This finding raises a couple of questions concerning the exact nature of this mechanism:

First, does this mechanism compute probabilities over individual objects, i.e. discrete quantities, or rather over continuous magnitudes such as surface area or volume? In the studies conducted in the course of this dissertation, subjects could have reasoned about proportions of discrete quantities (e.g. a population of 40 peanuts vs. 10 carrot pieces depicts an 80% chance of drawing a peanut as a random sample) or about proportions of continuous quantities (e.g. the total volume of a bucket is filled 80% with peanuts and 20% with carrots, so chances of drawing a peanut are likewise 80%). Similarly, infants in the previously described studies (e.g. Denison & Xu, 2010a, 2014) might have reasoned about, e.g. the relative frequencies of red and white Ping-Pong balls, or about the proportion of the colors red and white.

Theoretically, both options are conceivable: As mentioned above, many studies investigating quantitative abilities in nonhuman primates (and likewise in infants) controlled for various continuous dimensions such as surface area or duration and found that great apes and monkeys indeed do possess the ability to represent discrete numerical information (e.g., Beran, 2007; Cantlon & Brannon, 2007a; Thomas et al., 1980). Similarly, they are also able to reason about continuous quantities, such as amounts of liquids (see, e.g. Beran, 2010; Call & Rochat, 1996; Muncer, 1983; Suda & Call, 2004, 2005). Both types of representations are most likely mediated by an analogue magnitude system (see, e.g. Cantlon et al., 2009 and Lourenco, 2015 for reviews), signatures of which were also found in tasks requiring intuitive statistical

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inferences (Eckert, Call, et al., 2018; for details on the debate on whether there is a separate approximate number system which is supporting only discrete numerical judgments, see section 3.3.1.2.). For human children, research found some evidence that proportional reasoning seems to be easier when dealing with continuous compared to discrete quantities (Boyer, Levine, & Huttenlocher, 2008; Jeong, Levine, &

Huttenlocher, 2007; Spinillo & Bryant, 1999), giving a first hint that intuitive statistics might primarily be computed over continuous magnitudes. Future studies should test both human infants and great apes in a statistical inference task disentangling continuous and discrete quantities to further inform this debate.

A second set of questions regarding the cognitive structure of intuitive statistics concerns its developmental trajectory as well as its relation to formal (i.e. symbolic) statistical reasoning. For humans, research already shed some light on the developmental pathway of numerical abilities regarding absolute set sizes and found some interesting patterns. First, there seem to be large individual differences in the accuracy of the analogue magnitude system (Halberda, Mazzocco, & Feigenson, 2008), which appear to be consistent over development (Starr, Libertus, & Brannon, 2013). In fact, early inter-individual differences in accuracy even seem to be predictive of later explicit mathematical achievement (Feigenson et al., 2013; Libertus, Feigenson, & Halberda, 2013b; Mazzocco, Feigenson, & Halberda, 2011; but see Gilmore et al., 2011; Libertus et al., 2013a). Moreover, the system´s accuracy seems to increase during childhood, with lowest precision levels in infancy which improve over the course of development until adulthood (Halberda & Feigenson, 2008; Pica et al., 2004; Xu & Spelke, 2000). These findings raise the question whether the development of statistical abilities follows similar patterns. More specifically, do we find better accuracy in statistical reasoning tasks in older compared to younger individuals? And are early inter-individual differences in accuracy predictive of later formal statistical reasoning? As described earlier, there already is some evidence contrasting these predictions. One study (Girotto et al., 2016), for example, found that 3- to 4-year-old children failed in intuitive statistical tasks, in which pre-verbal infants repeatedly succeeded (Denison & Xu, 2010a, 2014), even when verbal demands were reduced. This may be a first hint that, in contrast to abilities dealing with absolute quantities, intuitive statistics develop in a non-linear way. Future research will have to examine whether the older children’s failure in this study was truly due to cognitive limitations, or rather due to performance limitations caused by extraneous task demands. Another hint pointing towards a nonlinear development of intuitive statistics comes from a study demonstrating that 4-year-old children formed more rational inferences (considering base-rate information), compared to older children and adults (Gualtieri & Denison, 2018). To my knowledge, there are no studies investigating the developmental trajectory of any quantitative ability in nonhuman great

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apes. Moreover, all apes tested in intuitive statistical tasks, so far, were adults or adolescents. In order to shed more light on the developmental trajectory of intuitive statistics, ideally, one would need to conduct longitudinal studies with both humans and great apes, using the same active-choice paradigm at certain time points throughout life stages starting in infancy with continuous tests until adulthood.

In conclusion, the present dissertation depicts an important first step in investigating the evolutionary roots of intuitive statistics. It demonstrates that exploring such capacities in nonhuman great apes has enormous potential for gaining insights both into the origins of human statistical reasoning, as well as into the cognitive architecture of our closest living relatives. I am sanguine that this work will serve as a stepping stone to stimulate more research in this promising new field of comparative cognition.

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