Model fitting data from syllogistic reasoning experiments

The data presented in this article are related to the research article entitled “Probabilistic representation in syllogistic reasoning: A theory to integrate mental models and heuristics” (M. Hattori, 2016) [1]. This article presents predicted data by three signature probabilistic models of syllogistic reasoning and model fitting results for each of a total of 12 experiments (N=404) in the literature. Models are implemented in R, and their source code is also provided.


Value of the data
Data provided in a unified form are useful for prospective meta-analyses, given that definitions of syllogistic form are confused in the psychology literature.
Model fitting results indicate whether and how one model is better and could be suggestive for developing new models.
Model R code could contribute to a deeper understanding of the theory and its new developments.

Data
The dataset of this article provides participants' response proportions as logical conclusions for each syllogism, model predictions for each experiment, and goodness-of-fit statistics of models. Tables 1 and 2 show the comparison of the probabilistic representation theory (PRT) [1] with other models (the transitive-chain theory (TCT) [2] and the probability heuristic model (PHM) [3], respectively).  show the comparison of three models (i.e., PRT, PHM, and a probabilistic extension of the mental model theory [pMM] [1,4]) using data of Experiment 1 in [5], Experiment 2 in                [5], Experiment 2, first Test in [4], Experiment 2, second Test in [4], Experiment 1 in [2], Experiment 3 in [6], Experiment with adult participants in [7], Experiment in [8], Experiment 1 in [1], and Experiment 2 in [1], respectively. Tables 13 and 14 show the comparison of PRT and PHM using data from syllogisms with generalized quantifiers, Experiment 1 in [3] and Experiment 2 in [3], respectively.

Experimental design, materials and methods
In this article, syllogistic terminology is according to the orthodox Aristotelian manner. Standard syllogisms are constructed with two premises and one conclusion, each belonging to one of the following four moods: A: All X are Y I: Some X are Y E: No X are Y O: Some X are not Y The subject (S) and predicate (P) in the conclusion are called end terms, and a term that does not appear in the conclusion is called a middle term (M). The two terms X and Y in the first premise correspond to P and M, or M and P; similarly, X and Y in the second premise correspond to S and M, or M and S. As each premise has two possibilities for correspondence, the relative positions of these terms can be one of the subsequent four possibilities, called figures:   The type of syllogism is indicated by symbols such as AI2, which indicates the first premise as A, the second premise as I, and the corresponding figure 2. Participants are given all or a considerable part of the entire 64 variations of premise pairs, and they select (or generate) a sentence as a logically valid conclusion. For example, in a typical experiment, participants are sequentially given a pair of premises such as (IO2): Some practitioners are mediators. Some sophists are not mediators.
Participants are supposed to choose one from the following conclusion candidates: The data set provides the proportion for each response (i.e., A, I, E, O, or N). In some experiments [1,2,4,5], choice options were given to participants as instantiated above, while in other experiments [3,[6][7][8], participants were asked to generate their own conclusions.
PRT and PHM can predict individual performance on syllogisms with generalized quantifiers, including "most …" and "few …." For the evaluation of these models, some tasks (shown in Tables 13 and 14) included the following types of assertions in addition to the standard ones: M: Most sophists are practitioners. F: Few sophists are practitioners.