Human Mental Abilities Lecture 2 Leonardo Gabales 1 Lecture 2 Psychometric models of intelligence I: Spearman’s g-Theory Thurstone’s Primary Mental Abilities Horn & Cattell’s Gf-Gc Theory 2 The Psychometric Approach … is based on utilization of psychological tests that generate scores on quantitative scales that are analyzed by correlative & factor-analytic methods to identify ability dimensions that are considered to form the structure of individual differences in cognitive abilities. (Gustafsson & Undheim, 1996) 3 Spearman’s ‘g’ Theory Charles SPEARMAN (1904): proposed a theory of intelligence that has many supporters 100+ years later! Charles Spearman 1863-1945 An attempt to understand relationships displayed across a number of correlation coefficients Correlations indicate the degree of linear association (i.e., relationship) between two variables Can be either positive or negative Range from -1.00 to 1.00 (zero correlation = no relation) 4 Positive: as scores on one variable increase, scores on the other variable also tend to increase X Y Negative: as scores on one variable increase, scores on the other variable tend to decrease X Y Zero: no systematic relationship between scores on the two variables X Y 5 Correlations between tests Reasoning Tests Tests 1 Reasoning Tests … x x+1 … y + + + + + + + + + + + + + + + + + + x+1 + + + … + + + y + + + + + + + + + + + + … x Knowledge Tests 1 Knowledge Tests 6 Spearman’s ‘g’ Theory Positive manifold: virtually all correlations among cognitive measures are positive According to Spearman this is due to a common cause affecting performance on all cognitive tasks – i.e., ‘g’ or general intelligence As correlations are never perfect, Spearman suggested two further causes of individual differences unique to every task - 'error' variance & a specific factor S2 S1 g Sy Sx Total variance = ‘g-variance’ + ‘s-variance’ + error 7 Spearman & Factor Analysis Realising difficulties in interpreting large correlational matrices, Spearman developed a new statistical procedure: Factor Analysis Based on a correlation matrix, factor analytic techniques extract a small number of basic components or ‘factors’, which account for the interrelationships in the data Spearman claimed that factor analysis reflected the basic properties of psychological functioning However … FA is (only) a statistical procedure Different FA procedures will result in different solutions FA provides ‘suggestions’ for a taxonomy of tests / tasks 8 ‘g’ Theory: A Two-factor Theory ‘g’ reflects overall cognitive functioning: Psychological processes generating 'g' reflect physiological processes from a large part of the CNS ‘Specifics’ ('s') reflect localised functioning: Specific factors are machines (i.e., more localised functions of the CNS) 9 Spearman’s ‘g’ Theory ‘g’: the essence of intelligence Highly intelligent people do all cognitive tasks better than persons of low intelligence As ‘g’ is present in all cognitive tasks it appears to reflect a form of general ‘mental energy’ 10 Testing ‘g’ Tests differ in the amount of ‘g’ that they measure - some are better measures of ‘g’ than others Much work has been conducted to discover principles that allow for the construction of good measures of ‘g’ According to Spearman, intelligent behaviour involves working with the relationships between fundaments Spearman formulated 2 ‘noegenetic laws’ which he claimed were involved in the best measures of ‘g’ 11 The Noegenetic Laws Eduction of Relations Given 2 fundaments (f1 & f2) find a relationship between them: f1 <-------- r (?) --------> f2 Eduction of Correlates Given f1 & a relation (r) find a fundament (f2) in a given relation to f1: f1 <-------- r --------> f2 (?) 12 The Noegenetic Laws These principles underpin performance on many psychometric tests: Analogical reasoning tasks: MOTHER is to CHILD as MARE is to _____? f1 <-- r (?) --> f2 f1 <-- r (?) --> f2 Series completion tasks: A C E G _ _ f1 <-- r --> f2 (?) f1 <-- r (?) --> f2 f1 <-- r --> f2 (?) 13 Raven’s Progressive Matrices The RPM – one of the most widely used psychometric tests available – was explicitly developed to test both noegenetic laws Three different instruments: Coloured Progressive Matrices (5-11 years) Standard Progressive Matrices (6 years – adult) Advanced Progressive Matrices (superior intellect) 14 General Intelligence- ‘g’ Thus, good measures of ‘g’ seem to require: Good reasoning skills The ability to cope with novelty Knowledge of properties of fundaments Transformation & manipulation of information Speed in working through a task 15 Louis Thurstone Louis THURSTONE (1887-1955) challenged Spearman’s ‘g’-factor model on both conceptual & methodological grounds Thurstone argued that ‘g’ was based on wholly false premises & could not provide a valid representation of the structure of human mental abilities The ‘g’ factor extracted from one battery of tests was distinct from the ‘g’ factor extracted from another battery of (different) tests 16 Thurstone & Primary Mental Abilities Thurstone accepted positive manifold – BUT noted the existence of clusters of high correlations for subsets of variables i.e., Despite the overall positive manifold within the correlations from a battery of tests, there are clusters of relatively high (& low) correlations amongst subsets of the tests included Clusters indicated the need to distinguish different types of abilities The mind consists of a number of relatively independent ‘faculties’ rather than some unitary trait – Primary Mental Abilities (PMAs) 17 Verbal Comprehension t1 1 t2 + 1 + + 1 t4 t5 + + + 1 + + + t6 + + + + 1 + + 1 t7 t8 + + + + + + 1 + + + + + + t9 + + + + + + + 1 + + 1 t1 t2 t3 t4 t5 t6 t7 t9 t3 Inductive Reasoning Spatial Ability Verbal Comprehension Inductive Reasoning t8 Spatial Ability 18 Thurstone & Factor Analysis Thurstone developed a method of multiple-factor analysis (based on different rotation techniques) which allowed for the discovery of groupings of variables Thurstone viewed FA not only as a means to identify PMAs, but also as a tool to guide more sophisticated tests of them Remember... Different factor structures can be produced in the same data by varying the FA procedures employed (e.g., extraction or rotation methods) There is an INDEFINITE number of possible factor solutions for any given correlation matrix, & FA alone CANNOT determine which solution should be accepted 19 Thurstone’s (1938) 7 PMAs Thurstone initially identified 7 Primary Mental Abilities: Verbal Comprehension Inductive Reasoning Numerical Fluency Word Fluency Spatial Ability Memory Perceptual Speed Each PMA was considered to behave ‘as a functional unity that is strongly present in some tests & almost completely absent in many others’ 20 Primary Mental Abilities Thurstone suggested that ‘g’ should be replaced by a number of correlated PMAs – a multiple factor theory Note: While Thurstone’s initial formulations did not include the general factor, his later writings provided for the possibility that the intercorrelations of PMAs could define a general ability factor similar to Spearman’s ‘g’ However… it was quickly realised that both general & group factors exist By 1960 over 20 PMAs had been identified leading to theories outlining the organisation of mental abilities 21 Masters of the (Cognitive) Universe Spearman's theory is sometimes described as a ‘monarchic’ conception of intelligence: i.e., it postulates one (& only one) underlying general factor that reigns supreme over all cognitive functions In contrast, Thurstone's theory is described as an ‘oligarchic’ conception of intelligence: i.e., there is not a single monarch or a completely free interaction of individuals, but several equally important rulers of the cognitive domain 22 Raymond B. Cattell Proposed the theory of fluid & crystallised intelligence in 1941 as a ‘modification’ of Spearman’s ‘g’-factor theory: “g is too g” Postulated the existence of two relatively distinct ‘second order’ factors of intelligence: Gc (crystallised intelligence) Accumulated knowledge (‘knowledge-bound pragmatics’) Gf (fluid intelligence) 23 Abstract reasoning (‘knowledge independent mechanics’) Fluid & Crystallised Intelligence Gf & Gc are not independent r ≈ .50 MOTHER is to CHILD as MARE is to _____? Oblique factor rotation allows for correlated factors 24 Gf vs Gc The main distinction between Gf & Gc is the amount of education &/or acculturation that is implicated in the item content, or cognitive processes engaged in measures of these constructs Gf depends only minimally on education or acculturation, whereas Gc is largely determined by these processes Investment theory of Intelligence Knowledge as a result of invested (fluid) intelligence 25 Gf/Gc Theory: Horn & Cattell Gf/Gc Theory has been further elaborated by Cattell, John Horn, & their colleagues The original conceptualisation of Gf/Gc theory inherently provided for the possibility that further factorially distinct cognitive abilities would be identified Structure of PMAs suggest several (fairly) distinct forms of ability – known as second order (or broad ability) factors Each broad ability is proposed to be structurally equivalent & contribute to intellect Gf/Gc theory is (arguably) the most widely accepted hierarchical model of human intelligence (Pallier et al., 2001) 26 Broad Abilities The most recent formulations of Gf/Gc theory postulate the existence of 9 broad abilities: Gf – Fluid reasoning Gc – Acculturated knowledge Gv – Broad visualisation Ga – Broad auditory ability SAR – Short-term acquisition & retention (STM) TSR – Tertiary storage & retrieval (LTM) Gs – Broad speediness CDS – Correct decision speed Gq – Quantitative reasoning (?) See e.g., Horn (1998) or Horn & Noll (1994, 1997) for reviews 27 “If you put water into a cup, it becomes the cup. If you put water into a bottle, it becomes the bottle. If you put water into a teapot, it becomes the teapot.” (Bruce Lee) 28 Two-stratum Gf/Gc model The elaborated Gf/Gc Theory is a two-stratum model of cognitive abilities Gf Gc First stratum: a large number of specific or ‘narrow abilities’ reflecting an extension of Thurstone’s PMAs Second stratum: a limited number of ‘broad abilities’ derived from the common variance among the first stratum abilities Gv Ga Gs SAR TSR CDS Gq II: Broad Abilities I: Narrow Abilities 29 Gf/Gc Theory Supported by: Developmental trends Brain damage studies Different predictive validities Construct validity / FA evidence Performance Gc Gf Time/Age See e.g., Horn (1998) 30 Summary Psychometric theories of intelligence Factor Analysis Benefits & limitations! Intelligence – general intelligence or multiple abilities?! There is still much debate in the literature (see e.g., Bowman et al., 2002) 31 “… We are taught to be “on guard” because incorrect beliefs can become so emotionally based that it is very difficult to accept the evidence that threatens them. Yet this teaching can have very little influence. We can look back at the examples from our history and say, “My, how absurd,” but not let that lesson do much to alter our beliefs in our own time. The example of such a belief that I wish to bring to your attention in this chapter is the belief in a concept of general intelligence.” (John Horn) 32