IDENTIFYING GENERAL FACTORS OF INTELLIGENCE: A CONFIRMATORY FACTOR ANALYSIS OF THE BALL APTITUDE BATTERY

Transcription

1 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT NEUMAN ET AL. IDENTIFYING GENERAL FACTORS OF INTELLIGENCE: A CONFIRMATORY FACTOR ANALYSIS OF THE BALL APTITUDE BATTERY GEORGE A. NEUMAN, AARON U. BOLIN, AND THOMAS E. BRIGGS Northern Illinois University Research supports a hierarchical factor structure of intelligence that is consistent with the second-order factor model proposed by Gustafsson in which five first-order factors yield a single second-order factor of General Intelligence (g). Gustafsson s model was tested with structural equation modeling via the Ball Aptitude Battery (BAB), a measure of aptitudes and vocational interests. This study focuses on the tests from the BAB that are believed to measure various aspects of intelligence: Numerical Computation, Numerical Reasoning, Inductive Reasoning, Analytical Reasoning, Paper Folding, Idea Fluency, Idea Generation, Vocabulary, Associative Memory, Auditory Memory, Clerical, and Writing Speed. Results indicate that the factor structure of the BAB is consistent with Gustafsson s second-order factor model of intelligence. Implications of this finding are discussed. The debate over the structure of intelligence can be traced to the beginnings of psychology. Spearman (1904), Thurstone (1938), Cattell (1940), Guilford (1967), and many others have proposed competing theories of intelligence with empirical findings as supportive evidence. Statistical procedures such as structural equation modeling (SEM) provide methodologies to consider simultaneously the components of these models and their relationships (Jöreskog & Sörbom, 1981). SEM provides researchers with the ability to test competing models of intelligence and select the model with the best fit to empirical data. Many studies using the SEM approach now support a hierarchical factor structure of intelligence that is consistent with Gustafsson s second-order factor model (Carroll, 1993; Cattell & Horn, 1978; Gustafsson, 1984; Educational and Psychological Measurement, Vol. 60 No. 5, October Sage Publications, Inc. 697

2 698 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Undheim, 1976, 1978, 1981; Undheim & Gustafsson, 1987). In the second-order factor model, five first-order factors including Fluid Intelligence (Gf), Crystallized Intelligence (Gc), General Fluency (Gr), Perceptual Speed (Gs), and Broad Visualization (Gv) yield a single second-order factor of General Intelligence (g). The hierarchical nature of the second-order factor model is consistent with and reconciles the competing theories proposed by Spearman (1904), Thurstone (1938), and Cattell (1940). These theories differ primarily in their degree of abstraction and specificity of constructs. In the Spearman (1904) model, performance on intellectual tasks is affected by two factors only: a general factor common to all tasks (g) and a specific factor for each particular task (s). In the second-order factor model, Spearman s g factor corresponds to the general, second-order construct at the top of a hierarchical arrangement of increasing abstraction. In a similar manner, Spearman s s factor is represented as test-specific variance at the indicator level of the hierarchy. Thurstone s (1938) model includes seven primary mental abilities (PMA), such as verbal comprehension, word fluency, induction, space, and perceptual speed, which are very similar to the Spearman s factor and are likewise represented in the hierarchical second-order factor model as test-specific variance at the indicator level of the hierarchy. Cattell s (1940) model of intelligence includes five general factors of intelligence: General Fluid Intelligence (Gf), General Crystallized Intelligence (Gc), General Visualization (Gv), General Fluency (Gr), and Perceptual Speed (Gs). Because Cattell placed the most emphasis on his Gf and Gc factors, his model is often called the fluid-crystallized theory of intelligence. Cattell s five general factors are represented in the hierarchical second-order factor model by the five first-order factors. Although the second-order factor model provides a good fit to empirical data and existent theories, several alternative models are possible. For example, Rindskopf and Rose (1988) described a sequence of four nested models in order of increasing parsimony: (a) a bifactor, general-plus-correlatedgroup factors model; (b) a correlated first-order factors model; (c) a hierarchical second-order factor model; and (d) a single general factor model. In addition, Gustafsson and Balke (1993) described a fifth alternative, a nested factors model with uncorrelated first-order constructs that vary in their degree of generality. Mulaik and Quartetti (1997) evaluated the merits of these five alternative models. They concluded that the hierarchical, second-order factor model is preferable because of its relative parsimony and because of problems inherent in testing the nested factors model. The purpose of the current research was to test whether the factor structure of a general aptitude battery such as the Ball Aptitude Battery (BAB) is consistent with the hierarchical, second-order factor model of intelligence using a SEM approach. To determine the factor structure of an aptitude battery, it is necessary to define precisely what constructs are measured and what con-

3 NEUMAN ET AL. 699 structs are not measured. Previous exploratory factor analysis research has shown that the 20 tests of the BAB assess a variety of abilities including verbal fluency, spatial reasoning, musical ability, grip, and several other specific abilities (Sung & Dawis, 1981). Dawis, Goldman, and Sung (1992) found that the four factors of cognitive ability, hand and arm strength, finger dexterity, and idea fluency accounted for 65% of the variance in one subset of 14 tests from the BAB. In addition, the factor structure of the BAB has been shown to be invariant across groups based on gender, ethnicity, and SES (Dawis et al., 1992; Sung & Dawis, 1981). The present study focused on those tests from the BAB that are believed to measure various aspects of intelligence: Numerical Computation, Numerical Reasoning, Inductive Reasoning, Analytical Reasoning, Paper Folding, Idea Fluency, Idea Generation, Vocabulary, Associative Memory, Auditory Memory, Clerical, and Writing Speed. To identify the factor structure of an aptitude battery, it is also necessary to define what is not measured. The tests not included in the current analyses measure aptitudes other than intelligence, such as finger dexterity, grip, rhythm, and pitch discrimination (Sung & Dawis, 1981). If the BAB tests included in the analyses are measuring various aspects of intelligence, then the factor structure of the complete battery of 12 tests should conform to the established factor structure of intelligence as represented by the second-order factor model. Based on previous research and theory (Dawis et al., 1992; Sung & Dawis, 1981), we propose that the 12 tests mentioned above can be described with a first-order factor structure consisting of five constructs that correspond to four of the constructs of the second-order factor model as follows: (a) Reasoning Ability and (b) Memory are both closely related to the Gf construct, (c) Numerical Ability is similar to the Gc construct, (d) Verbal Ability corresponds to Gr, and (e) Perceptual Speed corresponds to Gs. These five first-order constructs can be used to assess a still higher order construct: the more general construct of cognitive ability (g). It should be noted that the Gv factor of the second-order factor model is not considered in this study due to the lack of an appropriate measure. Researchers have found it difficult to isolate the Gv factor unless it is overmeasured (Cattell & Horn, 1978), and performance on the one test of the BAB, which certainly contains a visual component, the Paper Folding test, is believed to be more attributable to reasoning ability. In addition, the Gf factor could be considered a second-order factor in the proposed model because it is actually composed of two first-order factors: Reasoning Ability and Memory. However, previous research (Gustafsson, 1984) has suggested that Gf and g are nearly identical, making the distinction between them at the second-order level of the analysis unnecessary.

4 700 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Proposed Models First-Order Model (Hypothesized) To compare the factor structure of an aptitude battery such as the BAB to Gustafsson s second-order factor model, it is necessary to demonstrate the similarity of the tests used for the comparison. The BAB tests used in the current study as well as the tests administered in previous research (Carroll, 1993; Cattell & Horn, 1978; Gustafsson, 1984; Horn, 1972; Undheim, 1976, 1978, 1981; Undheim & Gustafsson, 1987) on the factor structure of intelligence are shown in Table 1. The first-order target model is outlined in Figure 1 and proposes that the 12 aptitude tests can be used to measure five first-order oblique constructs. Based on previous research (Dawis et al., 1992; Sung & Dawis, 1981), the following relationships are hypothesized. First, the Inductive Reasoning, Analytical Reasoning, and Paper Folding tests measure the more general construct of Reasoning Ability (Gf1). All three of these tests are concerned with relational concepts: The Inductive Reasoning test assesses the ability to perceive relational similarities, the Analytical Reasoning test assesses the ability to perceive ordered relationships, and the Paper Folding test assesses the ability to perceive three-dimensional relationships. Second, the Associative Memory and Auditory Memory tests measure the more general construct of memory (Gf2). Third, the two numerical tests Numerical Computation and Numerical Reasoning measure the more general construct of numerical ability (Gc). Both of these tests measure the ability to perform relatively simple arithmetic functions and should therefore reflect knowledge that was learned in elementary school and subsequently crystallized. Fourth, the Idea Fluency, Vocabulary, and Idea Generation tests should measure the more general construct of verbal fluency (Gr). The Vocabulary test is thought to measure verbal knowledge, and both the Idea Fluency and Idea Generation tests are assumed to measure the verbal expression of ideas. Fifth, the Clerical and Writing Speed tests are predicted to measure the construct of Perceptual Speed (Gs). The Clerical test is assumed to measure the speed with which individuals perceive details, and the Writing Speed test is thought to be a measure of response speed. It is assumed that the ability to perceive details is closely related to the ability to reproduce details. Complete descriptions of the BAB tests are provided in the Method section. Alternative First-Order Models Given that one objective of this analysis is to verify the factor structure of the BAB, four alternative first-order models were constructed. The first alternative first-order model included the cross loadings from Idea Generation to

5 NEUMAN ET AL. 701 Table 1 Test Used to Define First-Order Factors of Intelligence Ball Aptitude Battery (BAB) Test Description Corresponding Test Description Factor Numerical Add, subtract, multiply, Arithmetic Reasoning Simple Gc Computation and divide (Undheim, 1976) computation Numerical Determine the pattern Number Series Test Provide the next two Gc Reasoning of a number series (Gustafsson, 1984) numbers in a series Inductive Identify a common Circle Reasoning Identify the rule used Gf Reasoning element in a set pictures (Undheim, 1976) to blacken rows of circles Analytical Arrange wood chips in a Raven Progressive Identify the missing Gf Reasoning diagram using multiple Matrices figure using multiple rules (Gustafsson,1984) rules Paper Folding Determine how the un/ Punched Holes Determine how the un/ Gf folding of a punched (Undheim & folding of a punched piece of paper will look Gustafsson, 1987) piece of paper will look Idea Fluency Develop alternative uses Word Fluency Develop alternative Gr for a given object (Undheim & uses for a given Gustafsson, 1987) object Idea Generate a rapid and Word Listing Generate a rapid and Gr Generation abundant flow of (Undheim & abundant flow of words/ideas Gustafsson, 1987) words/ideas Vocabulary Select the closest Synonyms, WISC Matching similar Gr synonym Vocabulary words, assigning (Undheim & words to classes Gustafsson, 1987) Associative Memorize and recall a WISC Digit Span Memorize and recall Gf Memory list of numbers and (Undheim & a list of numbers letters Gustafsson, 1987) Auditory Memorize and recall a Auditory Number Memorize and recall Gf Memory list of numbers and Span, Auditory a list of letters or letters Letter Span numbers (Gustafsson, 1984) Clerical Identify a similar series Symbol Identities Identify a similar Gs of numbers in two (Undheim & series of numbers in columns Gustafsson, 1987) two columns Writing Speed Write quickly and Marking Speed Write 11 as many Gs accurately (Undheim & times as possible Gustafsson, 1987) Note. WISC = Wechsler Intelligence Scale for Children. Perceptual Speed and from Idea Fluency to Reasoning Ability. The Idea Generation test has a perceptual speed component requiring the rapid generation of words and ideas. The Idea Fluency test has a reasoning component requiring the development of alternative uses of a given object. The second and third alternative first-order models varied the number of first-order con-

6 702 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Figure 1. The proposed measurement model. Note. NC = Numerical Computation; NR1 = Numerical Reasoning odd items; NR2 = Numerical Reasoning even items; AM = Associative Memory; AU1 = Auditory Memory odd items; AU2 = Auditory Memory even items; AR = Analytic Reasoning; IR = Inductive Reasoning; PF = Paper Folding; IF = Idea Fluency; VO1 = Vocabulary odd items; VO2 = Vocabulary even items; IG = Idea Generation; CL = Clerical; WS = Writing Speed. structs. If fewer constructs can adequately model the entire content domain, then the more general but still reliable constructs can be used to describe the factor structure of the BAB. A three-factor model will be assessed that combines the indicators of Numerical Ability (Gc), Reasoning Ability (Gf1), and Verbal Ability (Gr). The order in which the indicators are combined is based on previous research with the BAB (Sung & Dawis, 1981). In addition, a one-factor model combining all indicators to form a single construct will be assessed. Finally, a five-orthogonal-factor model will also be tested. Second-Order Models (Hypothesized and Alternative) The hypothesized second-order model is outlined in Figure 2 and proposes that the five first-order constructs can be combined into a single second-order construct of general cognitive ability. In addition, previous re- search suggests that the path between the first-order Gf factor and the second- order g factor is very close to unity (Gustafsson, 1984). Fixing this path at 1.0 would provide a more parsimonious solution than the hypothesized second-order model and also provide a more clearly defined g factor (because several indicators would load directly on g). The Gf = g model was assessed in this research as an alternative to the hypothesized second-order model. In the Gf = g model, all indicators that previously loaded on the Gf1 factor load directly on g.

7 NEUMAN ET AL. 703 Figure 2. The proposed model. Note. NC = Numerical Computation; NR1 = Numerical Reasoning odd items; NR2 = Numerical Reasoning even items; AM = Associative Memory; AU1 = Auditory Memory odd items; AU2 = Auditory Memory even items; AR = Analytic Reasoning; IR = Inductive Reasoning; PF = Paper Folding; IF = Idea Fluency; VO1 = Vocabulary odd items; VO2 = Vocabulary even items; IG = Idea Generation; CL = Clerical; WS = Writing Speed. Subgroups Analyses To determine if the factor structure of the BAB is consistent across groups, the best-fitting first-order model was also subjected to a subgroups analysis. Male-only, female-only, Caucasian-only, and minority-only model fits were tested. The subgroups analyses were conducted by fixing one factor loading on each latent variable and then allowing the latent variables to freely intercorrelate. Subgroup models were assessed both for fit and consistency of standardized path coefficients. Method Database The database for this study was composed of more than 9,000 examinees who have taken the test battery between 1975 and The sample of 1,390 in the present analyses was composed of all individuals who had completed all 12 of the tests of interest, tested between 1984 and Approximately 60% of the data were collected from various organizational settings used for earlier predictive validity assessments, 25% of the data were collected from high school seniors, and 15% were collected by community counselors in their private practices. In this sample, 636 (45.8%) were male and 754

8 704 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT (54.2%) were female; 1,218 (87.6%) were White and 153 (11.0%) were of minority status. The mean age of the sample was 28.3 (SD = 10.91). To increase the degrees of freedom and the number of indicator variables used to define each latent variable, 3 of the 12 tests used in this research were split into odd and even half tests. The tests that were split included Numerical Reasoning, Auditory Memory, and Vocabulary. The remaining tests were deemed inappropriate for division into half tests due to test format, item content, or an inadequate number of items. Correlations between and reliability estimates for the 9 full tests and 6 half tests are provided in Table 2. Aptitude Batteries Described below are the 12 BAB tests analyzed in the present study. With the exception of the Clerical and Writing Speed tests, which are designed as speeded tests, all BAB tests are designed so that 95% of examinees are able to complete the tests within the allotted time period. Scores on all of the BAB tests are calculated by summing the number of correct responses given in the allotted time. This scoring system provides composite test score distributions that are continuous and approximately normal (Dawis et al., 1992). See Table 1 for a comparison of the BAB tests used in this study and tests used in previous studies to define the latent variables of the second-order factor model. 1. Numerical Computation. This test measures the ability to perform mathematical operations such as adding, subtracting, multiplying, and dividing. The task is to compute as quickly and accurately as possible the solutions to math problems. Test takers are given 13 minutes to complete the test. 2. Numerical Reasoning. This test measures the capacity for symbolic reasoning and problem solving. The task of this test is to determine the pattern that repeats itself in a series of numbers and then to give the next number that would logically follow. The test is administered in 20 minutes. 3. Inductive Reasoning. This test measures the ability to identify a rule and to reason from specific information to a general principle. The task of this test is to identify the subset of three pictures in a set of six that have a common element among them. The test is administered in 8 minutes. 4. Analytical Reasoning: This test measures the ability to reason from a general principle to specific information, from specific examples to a general principle, and the ability to organize related concepts in a systematic way. This test measures the ability to organize objects in a systematic manner by requiring the arrangement of a number of wood chips within a diagram. Scores are determined by the accuracy of the wood chip configuration. Time limits vary from item to item. Overall administration time varies depending on the response time of the examinee but generally ranges from 15 to 30 minutes. 5. Paper Folding. This test measures the ability to visualize in two-dimensional space. This is a multiple-choice test with five alternatives in which respondents must determine how the folding and unfolding of a piece of paper with one hole in it will look. The test is administered in 10 minutes.

9 Table 2 Reliabilities, Standard Deviations, and Correlations Between Measures Zero-Order Correlations Measure Reliability SD Clerical.89 a Idea Fluency.73 a Inductive Reasoning.60 b Writing Speed.81 a Paper Folding.83 a Idea Generation.79 a Numerical Computation.89 b Associative Memory.76 b Analytical Reasoning.76 b Vocabulary (odd).93 a Vocabulary (even).94 a Auditory Memory (odd).76 a Auditory Memory (even).75 a Numeric Reasoning (odd).82 a Numeric Reasoning (even).83 a Note. N = 1,390. All correlations are significant at p <.001. a. Cronbach s alpha calculated on present sample. b. Test-retest with 6-week interval. 705

10 706 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 6. Idea Fluency. This test measures the ability to develop alternative uses of a given object. Four objects are given (one at a time) for this test, and it is administered in 8 minutes. 7. Idea Generation. This test measures the ability to generate a rapid and abundant flow of words and ideas and measures expressional fluency of words and ideas. The test is administered in 10 minutes. 8. Vocabulary. This test measures the ability to choose the right word that represents an idea and knowledge of the English vocabulary. Each item is a word embedded in a short phrase. The examinee must select the closest synonym to the test word from five choices. The test is administered in 22 minutes. 9. Associative Memory. This test measures the ability to memorize and recall combinations of numbers and letters. Examinees are given 2 minutes to study the list of 13 number-letter combinations and minutes to recall the letters that were paired with the numbers on the list. 10. Auditory Memory. This test measures auditory aptitude, or the ability to remember a series of numbers. The test has 28 number strings and requires 13 minutes to administer. 11. Clerical Test. This test measures perceptual speed and accuracy, requiring the identification of the similarity of a series of numbers in two columns. The test is administered in 5 minutes. 12. Writing Speed. This test measures the capacity to write quickly and accurately, requiring the copying of a sentence repeatedly. The test is administered in 1 minute. Estimation Method and Fit Criteria All parameters were estimated using maximum likelihood estimation. Assessment of overall model fit was based on both absolute and incremental fit indices. Absolute indices include the 2 likelihood ratio test, the standardized root mean residual (RMR), and the root mean square error of approximation (RMSEA) (Cudeck & Browne, 1983; Steiger, 1988). Given the large sample size, the 2 likelihood ratio test was used only when comparing nested models and even then was interpreted with caution (i.e., changes in 2 in a relative sense rather than a strict statistical sense). A good fit of the model was indicated by a standardized root mean residual (SRMR) of less than.05 and a RMSEA of less than.05 (Browne, 1982). The Tucker-Lewis index (TLI) (Tucker & Lewis, 1973) was used to compare alternative models, and the comparative fit index (CFI) (Bentler, 1990) was used to compare the noncentral 2 to the null model. Given the relatively low number of indicators in the models being tested, fairly conservative cutoffs of.95 were used for these indices. The relative normed fit index (RNFI), a relative fit index comparing higher order models to the best fitting and worst fitting measurement models, was used in assessing the second-order factor structure (Mulaik et al., 1989). A RNFI value greater than.90 was considered indicative of good second-order model fit. The parsimonious fit index (PFI), used to compare models with different degrees of freedom (James, Mulaik, & Brett, 1982), was used to compare the alternative second-order models.

11 NEUMAN ET AL. 707 Table 3 Summary of Fit Indices for the First-Order Model Alternatives Fit Index Model Description 2 df RMSEA SRMR TLI CFI Null Uncorrelated measures One factor All indicators load on a single construct Uncorrelated Five orthogonal factors five factor Three factor Combines first three proposed constructs Five factor Five correlated proposed constructs no cross loadings Five factors see Figure with cross loadings Note. RMSEA = root mean square error of approximation; SRMR = standardized root mean residual; TLI = Tucker-Lewis index; CFI = comparative fit index. All 2 statistically significant (p <.01). N = 1,390. Results First-Order Model Fits A summary of fit indices for the hypothesized and alternative first-order models is provided in Table 3. As indicated in the table, the fit of the models improves when moving from the one-factor model to the hypothesized five-factor model. More important than improvements in fit are the overall fit indices of the hypothesized model, which do not meet the a priori criteria for acceptance. However, the alternative first-order model with cross loadings for Idea Fluency and Idea Generation does meet most of the a priori criteria for acceptance. The low RMSEA (.052) and SRMR (.035) and the TLI (.97) and CFI (.98) all indicate a good fit of the alternative first-order model. Consequently, all second-order models will include these cross loadings unless otherwise indicated. Second-Order Model Fit The poor fitting uncorrelated five-factor model, 2 (57) = , p <.001 (see Table 3), and the relatively high factor intercorrelations (see Table 4) all

12 708 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Table 4 Factor Intercorrelations and Standardized Factor Loadings Parameter Estimates General Parameter/Variable Intelligence Factor correlations 1. Numerical Ability Reasoning Ability Verbal Ability Memory Perceptual Speed Factor loadings Numerical Computation.78 Numerical Reasoning (odd).93 Numerical Reasoning (even).95 Inductive Reasoning.64 Analytical Reasoning.84 Paper Folding.82 Idea Fluency Vocabulary (odd).76 Vocabulary (even).77 Idea generation.26 Associative Memory.48 Auditory Memory (odd).73 Auditory Memory (even).81 Clerical.77 Writing Speed.96 Note. N = 1,390. All parameters were statistically significant (p <.001). suggest the potential for a second-order solution. Using the five-factor uncorrelated model as an upper bound of fit and the five-factor correlated model as the lower bound of fit, the RNFI index of the second-order target model can be calculated. As indicated in Table 5, the hypothesized secondorder structure adequately models the intercorrelations among the first-order factors (RNFI =.98). Also, the hypothesized second-order model results in a marginally better fit than the Gf = g model. Parameter Estimates for Second-Order Model The parameter estimates for the target model are provided in Table 4. The lower order parameter estimates in the second-order model closely resemble those of the first-order model. Of greater interest are the high correlations between the first-order factors and the general intelligence construct (g). Table 4 indicates that the correlations between the first-order factors can be accounted for by a single second-order construct.

13 NEUMAN ET AL. 709 Table 5 Summary of Fit Indices for the Higher Second-Order Model Fit Index Model Description 2 df RMSEA SRMR TLI CFI RNFI PFI Target (1st order) Measurement model Uncorrelated Five-factor 2, five factor orthogonal G = Gf a Gf has a unit loading on G Target structural See Figure model Note. RMSEA = root mean square error of approximation; SRMR = standardized root mean residual; TLI = Tucker-Lewis index; CFI = comparative fit index; RNFI = relative normed fit index; PFI = parsimonious fit index. All 2 statistically significant (p <.001). N = 1,390. a. Idea Fluency was constrained to only load on the verbal ability factor for purposes of identification. Subgroups Analysis Subgroup analyses were conducted by fixing a path on each factor and freeing the variances and covariances among the latent factors. The Caucasian-only, male-only, and female-only models all fit the data well. The low RMSEA values (.046,.055, and.052, respectively) and the high CFI values (.98,.97, and.98, respectively) suggest a good fit for the respective models. A summary of fit indices for all of the subgroup models is listed in Table 6. The minority subgroup model did not converge after 2,500 iterations. In addition, all standardized path coefficients were consistent between the overall model, the Caucasian-only model, the male-only model, and the female-only model. Discussion The results of the present study provide support for previous research regarding the factor structure of intelligence (Carroll, 1993; Cattell & Horn, 1978; Gustafsson, 1984; Horn, 1972; Undheim, 1976, 1978, 1981; Undheim & Gustafsson, 1987). Administering tests similar to those used in past intelligence aptitude research, we confirmed results found by Gustafsson (1984) and Undheim and Gustafsson (1987). The results of the current study provide support for the previous research on the hierarchical second-order factor model (Carroll, 1993; Cattell & Horn, 1978; Gustafsson, 1984; Horn, 1972; Undheim, 1976, 1978, 1981; Undheim & Gustafsson, 1987). The results of the current study also supported the recommendations of Mulaik and Quartetti (1997) to test the hierarchical model compared to the other models outlined by Rindskopf and Rose (1988): a bifactor, general-plus-correlated

14 710 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Table 6 Summary of Fit Indices for Subgroups Fit Index Group Description 2 df RMSEA SRMR TLI CFI Target All subjects, N = 1, Majority Caucasians, N = 1, Minority All non-caucasians, Did not N = 153 converge Males N = Females N = Note. RMSEA = root mean square error of approximation; SRMR = standardized root mean residual; TLI = Tucker-Lewis index; CFI = comparative fit index. All 2 statistically significant (p <.001). group factors model, a correlated first-order factors model, and a single general factor model. Overall, the results of these analyses identified broadband aptitude constructs. Using the factor structure coefficients as weights (or unit weighting those greater than.40) and combining the appropriate standardized scores on the 12 tests, five first-order broadband aptitude measures (i.e., Numerical Ability, Reasoning Ability, Verbal Ability, Memory, and Perceptual Speed) can be computed. This is consistent with the Cattell-Horn (1978) conceptualization of intelligence. After standardizing these first-order factors, an even broader band aptitude construct can be computed by combining these five scores. Using such a procedure would allow researchers and practitioners to select aptitude constructs to match the level of analysis of the criteria being investigated. More important, by demonstrating that the factor structure of an aptitude battery such as the BAB conforms to the established factor structure of intelligence, these results serve to validate the use of these aptitude batteries as a test of general intelligence. Also, although previous research has confirmed the predictive validity of the BAB for traditional intelligence criteria such as GPA and ACT scores, the value of using the BAB as a measure of intelligence is its established validity as a predictor of job performance in various occupations (Dong, Sung, & Dohm, 1985; Sung, 1979a, 1979b, 1979c; Sung & Dawis, 1981; Sung, Dawis, & Dohm, 1981). Knowing the cognitive ability requirements of a particular position provides organizations with another tool in helping to plan their clients career paths. In addition, establishing the criterion-related validity of an aptitude battery makes the battery a good candidate for use in selecting applicants on the basis of cognitive abilities as well as more specific aptitudes. Several future research topics are suggested from the results in the current study. Further research is needed to determine the nature of the group-specific variance in the factor structure of the BAB. Although the failure of the

15 NEUMAN ET AL. 711 minority-only model to converge is not surprising given the small sample size and heterogeneity of the population, the fact remains that the second-order factor model is based largely on a Caucasian population. An in-depth investigation is needed to determine whether group differences exist. With the accumulation of larger samples for minorities, this issue could be considered. Additional research with other test batteries such as the General Aptitude Test Battery (U.S. Department of Labor, 1980) would also help to determine the generalizability of the hierarchical second-order factor model of intelligence. The factor structure of other aptitude batteries can be readily tested using the second-order factor model. The second-order factor model provides a framework for considering how other test batteries mirror the Gustafsson (1984) model of intelligence. The fit of other test batteries to the secondorder model can be considered even when they do not include all of the tests in Gustafsson s model. For example, it would be possible to compare an aptitude battery that contains only a subset of the tests administered in previous intelligence research. Aptitude batteries measuring a subset of the first-order factors should also conform to the second-order factor model. References Bentler, P. M. (1990). Comparative fit indices in structural models. Psychological Bulletin, 10, Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in multivariate analysis (pp ). Cambridge, UK: Cambridge University Press. Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. New York: Cambridge University Press. Cattell, R. (1940). A culture-free intelligence test, I. Journal of Educational Psychology, 31, Cattell, R., & Horn, J. (1978). A check on the theory of fluid and crystallized intelligence with description of new subtest designs. Journal of Educational Measurement, 15, Cudeck, R., & Browne, M. W. (1983). Cross-validation of covariance structures. Multivariate Behavioral Research, 18, Dawis, R. V., Goldman, S. H., & Sung, Y. H. (1992). Stability and change in abilities for a sample of young adults. Educational and Psychological Measurement, 52, Dong, H., Sung, Y., & Dohm, T. (1985). The validity of the Ball Aptitude Battery: Relationship to high school academic success (Technical Report No. 6). Glen Ellyn, IL: Ball Foundation. Guilford, J. (1967). The nature of human intelligence. New York: McGraw-Hill. Gustafsson, J. (1984). A unifying model of the structure of intellectual abilities. Intelligence, 8, Gustafsson, J., & Balke, G. (1993). General and specific abilities as predictors of school achievement. Multivariate Behavioral Research, 28, Horn, J. L. (1972). State, trait, and change dimensions of intelligence. British Journal of Educational Psychology, 42, James, L. R., Mulaik, S. A., & Brett, J. (1982). Causal analysis models, assumptions, and data. Beverly Hills, CA: Sage. Jöreskog, K. G., & Sörbom, D. (1981). LISREL: Analysis of linear structural relationships by the method of maximum likelihood (Version V). Chicago: National Educational Resources.

16 712 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S., & Stilwell, C. D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105, Mulaik, S. A., & Quartetti, D. A. (1997). First order or higher order general factor? Structural Equation Modeling, 4, Rindskopf, D., & Rose, T. (1988). Some theory and applications of confirmatory second-order factor analysis. Multivariate Behavioral Research, 23, Spearman, C. (1904). General intelligence objectively determined and measured. American Journal of Psychology, 15, Steiger, J. H. (1988). Aspects of person-machine communication in structural modeling of correlations and covariances. Multivariate Behavioral Research, 23, Sung, Y. (1979a). Prediction of certified public accountants job performance using the Ball Aptitude Battery (Technical Report No. 2). Glen Ellyn, IL: Ball Foundation. Sung, Y. (1979b). Validation study of Ball Aptitude Battery for apprentice carpenters (Technical Report No. 1). Glen Ellyn, IL: Ball Foundation. Sung, Y. (1979c). A validation study of mum sticker, puller, and harvester selection tests for Pan American Plant Company (Technical Report No. 4). Glen Ellyn, IL: Ball Foundation. Sung, Y., & Dawis, R. (1981). Technical manual: Ball Aptitude Battery. Glen Ellyn, IL: Ball Foundation. Sung, Y., Dawis, R., & Dohm, T. (1981). Administrator s manual: Ball Aptitude Battery. Glen Ellyn, IL: Ball Foundation. Thurstone, L. (1938). Primary mental abilities. Psychometric Monographs, 1. Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, Undheim, J. O. (1976). Ability structure in year-old children and the theory of fluid and crystallized intelligence. Journal of Educational Psychology, 68, Undheim, J. O. (1978). Broad ability factors in 12- to 13-year-old children, the theory of fluid and crystallized intelligence, and the differentiation hypothesis. Journal of Educational Psychology, 70, Undheim, J. O. (1981). On intelligence IV: Toward a restoration of general intelligence. Scandinavian Journal of Psychology, 22, Undheim, J., & Gustafsson, J. (1987). The hierarchical organization of cognitive abilities: Restoring general intelligence through the use of linear structural relations. Multivariate Behavioral Research, 22, U.S. Department of Labor, Employment and Training Administration. (1980). Manual for the USES General Aptitude Test Battery. Washington, DC: Government Printing Office.