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Gepubliceerd in: Psychological Research 3/2003

01-08-2003 | Original Article

A latent class model for individual differences in the interpretation of conditionals

Auteurs: Frank Rijmen, Paul De Boeck

Gepubliceerd in: Psychological Research | Uitgave 3/2003

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Abstract.

We investigated the hypothesis that there are three levels of performance associated with conditional reasoning: (1) Unsophisticated reasoners solve a modus tollens by accepting the invited inferences, treating the conditional as if it were a biconditional. (2) Reasoners of an intermediate level can resist the invited inferences, but cannot find the line of reasoning needed to endorse modus tollens. (3) Sophisticated reasoners do not draw the invited inferences either, but they do master the strategy to solve a modus tollens.
On a first set of six problems, solved by 214 adolescents, an unrestricted latent class analysis revealed the existence of a large subgroup of reasoners with a biconditional interpretation of the conditional, and a smaller subgroup with a conditional interpretation.
On a second set of 24 problems, solved by the same participants, a restricted latent class model corroborated the existence of a large subgroup of unsophisticated reasoners and a smaller subgroup of reasoners of an intermediate level. No evidence was found for the existence of a subgroup of sophisticated reasoners.
As expected, the class of biconditional reasoners was associated with the class of unsophisticated reasoners, and the class of conditional reasoners was associated with the class of reasoners of an intermediate level. Furthermore, the former showed a biconditonal response pattern on truth table tasks, whereas the latter showed a conditional response pattern.
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1
The authors opted for two different types of latent class analyses on the two problems sets instead of one joint analysis on all 30 problems together (the six problems of the first set and the 24 problems of the second set) for the following two reasons. First, for the set of six DA+ and AC+ problems, different interpretations of the conditional should lead to qualitatively different answers: conditional reasoners should answer 'undecidable', whereas biconditional reasoners should answer ''necessarily true'. For the set of 24 MP+ and MT+ problems, the correct answer is independent of the interpretation of the conditional. Interpretation is only supposed to affect the difficulty of those problems. The consequence is that the answers on the MP+ and MT+ problems can be dichotomized (correct/incorrect) without much loss of information, unlike the answers on the DA+ and AC+ problems, calling for a different modeling approach for the two sets of problems. Second, The two different types of analyses reflect two stages in modeling. We will first check whether there are latent classes corresponding with the interpretation of a conditional by conducting an unrestricted latent class analysis on the DA+ and AC+ problems. If the existence of different interpretations is revealed, we can be confident that it is appropriate to construct a confirmatory model for the set of MP+ and MT+ problems, based on the three-level hypothesis for conditional reasoning.
 
2
We would like to thank an anonymous reviewer for suggesting effect coding for the independent variables of the logistic regression, so that the intercept corresponds to the mean on a logistic scale of the solution probabilities.
 
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Metagegevens
Titel
A latent class model for individual differences in the interpretation of conditionals
Auteurs
Frank Rijmen
Paul De Boeck
Publicatiedatum
01-08-2003
Uitgeverij
Springer Berlin Heidelberg
Gepubliceerd in
Psychological Research / Uitgave 3/2003
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI
https://doi.org/10.1007/s00426-002-0092-7

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