ABSTRACT
Se describen las bases conceptuales y operacionales de los tests de resolución de problemas por analogía estableciendo énfasis en las analogías de figuras. Se expone brevemente la importancia del estudio de dicho constructo hipotético para el abordaje de la capacidad intelectual. Se citan lineamientos teóricos sobre el mismo y se describen las características y mecanismos cognitivos fundamentales implicados en la resolución de matrices de figuras. En cuanto a este último punto, se aborda la comprensión de las relaciones y correlatos entre relaciones figurales tomando el modelo de proporción A:B::C:D propio de la tradición psicométrica desde principios del Siglo XX. Se establecen además vínculos conceptuales con aportes de autores pertenecientes a la vertiente cognitiva de estudio del razonamiento analógico y con escuelas de la Psicología General. Se pretende brindar un marco ideal para la creación de matrices figurales de 2 x 2 que midan el constructo. Con el objetivo de evitar sesgos en la medición, se plantean seis sugerencias básicas puestas al servicio tanto de la confección de estos reactivos, como de su administración. Dichas sugerencias son las siguientes: (1) considerar el doble camino de resolución de la matriz, (2) desarrollar una estrategia unívoca de resolución, (3) tomar en cuenta n estrategias para generar nk ítemes, (4) crear ítemes a ser resueltos únicamente por la vía del razonamiento analógico, (5) consideraciones en cuanto a las opciones de respuesta y (6) consideraciones referidas a la administración.
This paper describes the conceptual and operational bases of analogical problem - solving tests, placing emphasis on figural analogies. The importance of the study of such a hypothetical construct to the understanding of intellectual capacity is briefly outlined. The significance of the construct in relation to mental development and individual maturation from childhood to adulthood is also explained in a concise way. Theoretical considerations about analogical reasoning are quoted and the fundamental characteristics and cognitive mechanisms involved in the resolution of figural matrix items are described. In this respect, the nature of relations and correlations between relations of figures is elucidated taking into account the A:B::C:D proportional model which has been researched by psychometrists since the beginning of the 20th Century. This model suggests the existence of two pairs of relations between elements, where element A is to element B as element C is to a missing element D (Figure 2). Items created on the basis of this structure usually contain given answers, only one of which is correct. On the other hand, linkages are established with contributions from experts defending the cognitive perspective of the study of analogical reasoning, and also with General Psychology schools like Gestalt and Gardner's theory of multiple intelligence. Finally, an ideal framework for the creation of 2 x 2 figural matrices that can measure analogical reasoning is intended to be provided. With the purpose of reducing item bias, six essential suggestions for the preparation and administration of items are offered. These suggestions are: (1) the constructor should consider the double resolution pathway of a proportional analogy (horizontal as well as vertical, i.e. A:B::C:D and A:C::B:D). In doing so, the probability of generating non-controlled rules of analogical relation to one of these pathways will be reduced. These accidental rules correspond to resolution logics different from those chosen by the designer, therefore affecting item manipulation and control. (2) Strongly related to the latter, given that each rule or combination of rules creates one different resolution strategy, each proportional analogy item should incorporate only one of these strategies to be applied horizontally as well as vertically. (3) Given that one or more rules may be used for the same item, a few rules are more than enough to prepare a large group of strategies and, therefore, a large item bank. Also, it is possible to take into account n strategies to produce nk items, being k the number of items apparently different from each other that nevertheless share the same resolution strategy. (4) Items that can be solved by applying ways of reasoning different from those of the proportional analogies should not be constructed. For instance, the designer should not allow superficial comparisons among some matching attributes of the item as a problem solving method, since this procedure does not require the consideration of the whole matrix structure (Gestalt's) which should serve as a basis for the analogical reasoning task. Therefore, pairing analogies should be rejected as they allow for this kind of resolution pathways (e.g. matching circle C with circle D2 in the 4th item of Figure 2, without taking into account the other matrix figures). (5) Alternative responses should contain one clearly correct answer to be discovered by using only analogical reasoning; wrong answers should not replace the correct one just because they are more appropriate considering alternative non-pretended ways of reasoning; all alternatives should share similarities and be distributed on a random basis. (6) The bias arising from administration conditions should be taken into account, including the possible verbal contamination during completion of this non-verbal test.
ABSTRACT
En el estudio del funcionamiento diferencial del ítem (DIF - differential item functioning) la medición de su tamaño proporciona información relevante. Entre las medidas del DIF más utilizadas se encuentra el logaritmo de la razón común de las posibilidades de Mantel-Haenszel (Mantel-Haenszel Log Odds Ratio, MH-LOR). En el trabajo que se informa se analiza la similitud de los resultados al aplicar MH-LOR y una medida obtenida en el marco de la teoría de respuesta al ítem (TRI), a la que se denomina LOR-TRI, sobre datos reales y sobre datos simulados sin DIF. Los datos reales corresponden a una prueba de 20 ítem de razonamiento verbal, respondida por egresados del ciclo medio de enseñanza y por alumnos universitarios. Cada ítem presenta un par de palabras - base entre las cuales existe algún tipo de relación y cuatro opciones de pares de palabras entre las que se debe elegir aquel cuya relación sea la más cercana a la del par base. Para los datos simulados se consideraron las respuestas a un test de 20 ítem generadas según el modelo logístico de tres parámetros. Los grupos fueron elegidos de una población normal estándar con tamaño muestral 1,000 y se efectuaron 100 repeticiones. Tanto para los datos reales como para los simulados el modelo logístico adecuado es el de tres parámetros, sin embargo se observó que el ajuste del modelo de Rasch condujo a resultados de LOR-TRI, similares a MH-LOR. Para los respectivos errores estándar se observó la misma particularidad en cuanto a la similitud, siendo ésta aún más destacada
In the study of differential item functioning (DIF), measuring its size is of great relevance. An easily interpreted measure is the Mantel-Haenszel Log Odds Ratio (MH-LOR): its sign shows the group which the item favors and its value is zero when the item does not show DIF. This research also considers a measure of DIF named LOR-IRT because it is linked to the log odds ratio and is formulated on the basis of the item parameters within the item response theory (IRT) framework. In order to study the similarity between the LOR-IRT measure according to the number of parameters of the adjusted model and MH-LOR, the DIF was analyzed through real data as well as non-DIF simulated data. The real data consists of a 20-item verbal reasoning test taken by [ ... ] senior high school and university students [ ... ] The simulated data includes answers to a 20-item test based on the three-parameter logistic model [ ... ] After analyzing the DIF of the verbal reasoning items on the basis of real data, we concluded that the LOR-IRT obtained upon the adjustment of the one-parameter logistic model (the Rasch model) led to results similar to those of MH-LOR [ ... ] The similarity between the corresponding standard errors is outstanding [ ... ]
Subject(s)
Humans , Adolescent , Adult , Psychological Tests/statistics & numerical data , Psychometrics/methods , ArgentinaABSTRACT
En este trabajo se propone una presentación del Modelo Lineal de Puntuaciones utilizando la notación moderna de la teoría de probabilidades. De este modo se logra resolver cierta ambigüedad notacional presente en la bibliografía que resta claridad a la deducción de las propiedades del modelo. En el enunciado de los supuestos se utiliza la esperanza condicional y operando con ella se deducen con rigor las propiedades principales que fundamentan la Teoría Clásica de Tests.