I know that the behaviour of children less than one year old does not have what it takes to be able to draw the conclusion that that child demonstrates - to us - that he/she/they understand probability. I'm taking a very strong stance here. I would take the exact same stance regarding monkey behaviour. — creativesoul
Well then what's the point in me discussing the contents of any experiments with you? They're clearly unnecessary. Whatever magical power you've used to
just know things without needing to employ any scientific methodology or empirical investigation of any sort, simply apply that to the issue of indigenous tribes and you'll have your answer, carved in stone for you (or however such divine knowledge arrives).
Alternatively, you could consider the possibility that where thousands of hours have been dedicated to carefully constructing experiments, carrying them out and analysing data on a subject you
claim to be interested in, you might, at least, show the slightest respect for that work by not dismissing their results out of hand without even looking on the basis that you've 'had a bit of a think about it'.
From the paper;
There is no consensus about the proper interpretation of the probability calculus (2, 3). Regardless of interpretations, however, the basic laws of probability rest on the same extensional considerations, notably, the principle that the probability of an event equals the sum of the probabilities of the various ways in which it can occur.
They were presented with a set of four chips of two different colors, and had to bet on the color of a randomly drawn chip (Fig. 2A). The odds were 3:1 in favor of the prevalent color. In each task, we considered as correct the bet on the more likely color. The Mayan groups did not differ reliably from each other (bilingual correct: 19 of 20; monolingual correct: 14 of 20), χ2(1 n = 40) = 2.8, P = 0.10. Accordingly, in the following analyses, we collapsed their answers into one group. All groups of participants performed better than chance: Mayan adults (correct: 33 of 40), χ2(1 n = 40) = 16.9, P = 0.0004; Mayan school children (correct: 16 of 20), χ2(1 n = 20) = 7.2, P = 0.007; Italian controls (correct: 18 of 20), χ2(1 n = 20) = 12.8, P = 0.0003. These responses seem to reflect a trend due to experience or maturation: Mayan children performed worse than Mayan adults who, in turn, performed worse than Italian controls. A Jonckheere’s test, however, did not reveal a reliable trend in the data, P = 0.39.
In principle, participants might solve the previous tasks by applying some superficial heuristic, rather than a proper chance evaluation. For example, they might bet on the more favorable outcome by considering the absolute number rather than the proportion of possibilities in its favor. To test whether preliterate participants succeed because they apply this “numerosity” heuristic (13), and extend our results, we used a second task [similar to 11] that would show more directly the use of probabilistic reasoning. In each trial, participants had to bet on which of two sets was more likely to yield a winning chip. The simplest trials did not ask for any estimation of proportions, given that one or both sets contained just winning chips (Fig. 3 A and B). Two other trials did ask for this estimation because both sets contained some winning chips (Fig. 3C). In one case, the favorable set contained a larger proportion as well as a greater number of winning chips. In the other case, it contained a larger proportion but not a greater number of winning chips. If preliterate Maya are able to compare the ratio of winning to nonwinning chips across sets, they should succeed in this crucial trial. Indeed, in each trial, all groups performed above chance level (as shown by binomial tests). Task A: all participants performed correctly, P = 0.0009. Task B-left panel: Mayan adults (correct: 33 of 40), P = 0.0002, Mayan school children (correct: 18 of 20), P = 0.0002, Italian adults (correct: 20 of 20), P = 0.0009. Task B-right panel: Mayan adults (correct: 32 of 40), and Mayan school children (correct: 16 of 20), P = 0.006, Italian adults (correct: 18 of 20), P = 0.0002. Task C-left panel: Mayan adults (correct: 37 of 40), P = 0.0009, Mayan school children (correct: 18 of 20), P = 0.0002, Italian adults (correct: 19 of 20), P = 0.0002. Task C-right panel: Mayan adults (correct: 35 of 40), P = 0.0004, Mayan school children (correct: 17 of 20), P = 0.002, Italian adults (correct: 18 of 20), P = 0.0002).
In three tasks, there were k chips of the same color and one chip of a different color. Thus, when k > 3, participants could notice that each chip having the predominant color neighbored k − 1 same-colored chips and only 1 differently-colored chip. Accordingly, they could bet on the “same color” outcome. In three other tasks, there were k pairs of same-colored chips. Thus, participants could notice that each chip had just another chip of the same color and several [actually, 2(k − 1)] chips of different colors. Accordingly, they could bet on the “different color” outcome. As shown in Fig. 4, the rate of Maya’s bets on the same color relation follows the same tendency as the probability of such an outcome.‡ For each participant, we computed an index Q of the quality of their prediction pattern, by normalizing the expected value of the number of correct bets (ref. 15; see also SI Study 3. Probability and Combinatorics). Q ranges from −1 (worse quality) to +1 (best quality). All groups performed above chance level: Monolingual Maya, mean Q = 0.37, SD = 0.53, t(19) = 3.07, P = 0.003, d = 0.69; Bilingual Maya, mean Q = 0.85, SD = 0.25, t(19) = 14.89, P < 0.0001, d = 3.33; Mayan school children, mean Q = 0.58, SD = 0.42, t(19) = 6.20, P < 0.0001, d = 1.39; Italian controls, mean Q = 0.81, SD = 0.38, t(19) = 9.56, P < 0.0001, d = 2.14. A reliable trend (Maya children < Maya adults < Italians, P = 0.03) indicated that performance increased with age and experience, suggesting that some probabilistic intuitions develop into adulthood (24). Unlike in Studies 1 and 2, adult bilingual Maya outperformed monolingual ones, t(38) = 3.67, P = 0.0007, d = 1.16. It is difficult to attribute this result to cultural factors, given that our bilingual and monolingual participants were equally preliterate, and lived in similar socio-economic conditions. Because Study 3 tasks involve mental manipulation of multiple possibilities, this result seems to support evidence for bilingual advantages in reasoning tasks of this sort (16). Despite differences in absolute performance levels, however, the above-chance performance of all groups points to a shared ability to treat possibilities in a combinatorial way.
I haven't cited these sections because I think you might be interested in the results (you've demonstrated you've little interest in anything but supporting your own prior beliefs). I've quoted them to stand as an example of how to investigate some matter you're interested in
- An understanding of the remaining open issues in the field.
- Careful study design, including controls for multiple confounding factors (culture, age, language acquisition).
- Sequential attempts to remove ambiguity in interpretation.
- Appropriate use of statistical techniques to minimise bias.
- Willingness to accept results which cloud the overall picture and offer potential interpretations.
The study took four researchers three years of work to set up, negotiate with contributing authorities and run, plus two statisticians to assist with the results interpretation.
But by all means, if you want to 'have a bit of a think about it' and tell me how they're all wrong be my guest.