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Chapter 5

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University of Toronto Scarborough

Chapter 5Topic 5ATheories and Individual Tests of Intelligence and Achievement Definitions of Intelligence An operational definition defines a concept in terms of the way it is measuredthis is different than real definition Operational definitions of intelligence suffer from two dangerous short comings1 they are circular intelligence tests were invented to measure intelligence not measure it 2 operation definitions block further progress in understanding the nature of intelligence they foreclose discussion on the adequacy of theories and intelligence Operational definitions leave much to be desired In contrast a real definition is one that seeks to tell us the true nature of the thing being defined Expert Definitions of Intelligence Read page 153 for the different expert definitions In spite of the diversity in viewpoints of intelligence two themes recur again and again in expert definitionsexperts tend to agree that intelligence is 1 the capacity to learn from experience and 2 the capacity to adapt to ones environment One concern is that very few contemporary intelligence tests appear to require the examinee to learn something new or to adapt to a new situation as part and parcel of the examination processLayperson and Expert Conceptions of Intelligence Another approach to understanding a construct is to study its popular meaningand this is much more scientific than it appears In an experiment where both laypersons and experts rated the importance of behaviours to their concept of an ideally intelligent person answers turned out to be very similar In order of importance experts saw verbal intelligence problemsolving ability and practical intelligence as crucial to intelligence In their conception of intelligence experts and laypersons alike consider verbal ability and problem solving to be essential aspects of intelligence Some disagree also occurredexperts believed that practical intelligence was an essential component while laypersons felt social competence as a third component these two nominations share one property in common contemporary tests generally make no attempt to measure either of thesemain reason is inertia A Primer of Factor Analysis There are two forms of factor analysis confirmatory and exploratory In confirmatory factor analysis the goal is to conform that test scores and variables fit a certain pattern predicted by theory The central purpose of exploratory factor analysis is to summarize the interrelationships among a large number of variables in a concise and accurate manner as an aid in conceptualization the underlying variables are then called factorsThe Correlation Matrix The beginning point for every factor analysis is the correlation matrix a complete table of intercorrelations among all the variables There are just too many intercorrelations for the viewer to discern the underlying patterns for all the variables by just looking at it intuitivelyThe Factor Matrix and Factor Loadings The factor matrix consists of a table of correlations called factor loadings The factor loadings values from 100 to 100 indicate the weighting of each variable on each factor A factor is nothing more than a weighted linear sum of the variables that is each factor is a precise statistical combination of tests used in the analysis In a sense a factor is produced by adding in carefully determined portions of some tests and perhaps subtracting out fractions of other tests Factor loadings are nothing more than correlation coefficients between variables and factorsGeometric Representation of Factor Loadings It is customary to represent the first two or three factors as reference axes in two or three dimensional spacethe factor ladings can then be plotted for examinationThe Rotated Factor Matrix An important point is that the position of the reference axes is arbitrary and can be rotated around if it produces a more sensible fit with the factor loadings In a rotation to positive manifold the computer program seeks to eliminate as many of the negative factor loadings as possible In a rotation to simple structure the computer program seeks to simplify the factor loadings so that each test has significant loadings on as few factors as possible The goal of both criteria is to produce a rotated factor matrix that is straightforward and unambiguous as possibleThe Interpretation of Factors In order to interpret or name a factor the researcher must make a reasoned judgement about the common processes and abilities shared by the tests with strong loadings on that factor A major use of factor analysis is the identification of a small number of marker tests from a large test battery and instead of using a cumbersome battery of 24 tests a researcher could just select several tests with strong loadings on the five factors in reference to the example provided in the textbookIssues in Factor Analysis If there is no gold to be found then none will be foundFactor analysis will yield meaningful results only when the research was meaningful to begin with An important point is that a particular kind of factor can emerge from factor analysis only if the tests and measures contain that factor in the first place GIGO garbage in garbage outthe quality of the output depends upon the quality of the input Sample size is also crucial to a stable factor analysisin general you should have at least 5 subjects for each test or variable Finally it cannot be overemphasized the extent to which factor analysis is guided by subjective choices and theoretical prejudices Crucial choice between orthogonal axes and oblique axes With orthogonal axes the factors are at right angles to eachother which means they are uncorrelated With oblique axes the factors are correlated among themselves Some researchers prefer oblique axes to always be used whereas others take a more experimental approachGalton and Sensory Keenness The first theories of intelligence were derived in the Brass Instruments era of psychology at the turn of the twentieth century The sensory keenness theory of intelligence proved to be psychometric dead
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