Human Cognitive Abilities — Ch. 1 (Carroll)

Carroll, J. (1993). Human Cognitive Abilities [Chapter 1]. New York: Cambridge. “The Study of Cognitive Abilities”

In the opening chapter of his volume on cognitive abilities, Carroll defines key concepts, such as ability, state, trait, cognitive task, aptitude, achievement and factor, used in the study of cognitive ability. He also summarizes the process of conducting psychological tests to identify and measure differences in ability.

Using the example of physical ability (i.e., strength) as demonstrated by the ability to lift a barbell of increasing heaviness, the most reliable quantified measure of strength is the weight value at which the subject has a 50% chance of being able to successfully complete the task (i.e., lift the barbell). One can then plot these measures against various characteristics (age, gender, health, etc.). One can also create person characteristic functions, which are curve plots of an individual’s probability of successful weight lifting performance. The 50% probability mark represents the liminal or threshold level. If correlation btw performance on this task with other similar strength tasks is high, one could conclude that strength ability generalizes over a series of physical strength tasks. If the correlation is close to zero, one would conclude that the other tasks measure other abilities. If the correlations were positive but not that high, one would conclude that the tasks measured strength ability along with some other ability (or abilities).

An ability is a trait if it exhibits some degree of stability over a relatively long period of time. Abilities that are highly variable should be considered states.

Definition of ability: “The possible variations over individuals in the liminal levels of task difficulty (or in derived measurements based on such liminal levels) at which, on any given occasion in which all conditions appear favorable, individuals perform successfully on a defined class of tasks” (p.8). “…Refers only to variations in individuals’ potentials for present performance on a defined class of tasks” (p.16).

Cognitive task is defined as “any task in which correct or appropriate processing of mental information is critical to successful performance” (p.10). Cognitive ability is “any ability that concerns some class of cognitive tasks” (p.10). A cognitive process is characterized by a situation in which “mental contents are operated on to produce some response” (p.10). The mental contents could include representations or encodings from short or long-term memory; and the response may or may not be observable. “Cognitive abilities can sometimes be more sharply defined by associating them with classes of particular task components” (p.11). Carroll more specifically defines an elementary cognitive task (ECT) as “one of a possibly very large number of tasks in which a person undertakes, or is assigned, a performance for which there is a specifiable class of “successful” or “correct” outcomes or end states which are to be attained through a relatively small number of mental processes or operations, and whose successful outcomes depend on the instructions given to, or the sets or plans adopted by the person” (p.11). Carroll also introduces the usefulness of schematically describing an ECT via a Dual Time Representation.

Aptitude is “a cognitive ability that is possibly predictive of certain kinds of future learning success” (p.16). Also, “an ability is an aptitude if it helps in predicting degree of learning beyond a prediction from degree of prior learning” (p.17). Achievement is “the degree of learning in some procedure intended to produce learning, such as a formal or informal course of instruction, or a period of self-study or a topic, or practice of a skill” (p.17).

General process to discover and identify abilities:
1. Construct psychological tests
2. Administer to a substantial representative sample of individuals who are homogeneous in any attribute that might be associated with levels of performance in a similar way across tests (e.g., gender, SES, age).
3. Conduct an item analysis (eliminate those that failed to show adequate discrimination among individuals)
4. Calculate correlations among scores on different tests (a “correlation analysis“)

The Pearsonian correlation coefficient “indicates the degree to which there is similarity or overlap in the abilities called upon for different members of the sample on which the correlation is computed” (p.19). “What ability or abilities the tasks measure depends upon what combination of abilities a given individual possesses….The correlation provides only an indication of the extent to which the task provides equal opportunities for the individual to use whatever abilities he/she possesses” (p.21).

Individual differences on a test can be said to be the “immediate manifestations of individual differences in an underlying ability” (p.22) or latent trait. “A factor, if it is well established in a number of empirical investigations, is a latent trait reflecting differences over individuals in ability characteristics or potentials” (p.22).

“…A cognitive ability can be viewed as an intervening variable, i.e., a calculational convenience, as it were, in linking together a particular series of observations” (p.23).

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