General and non-general intelligence factors simultaneously influence SAT, SAT-V, and SAT-M performance

Abstract

This study compared two views that differ about the composition of the SAT: one view that proposes both general intelligence and non-general intelligence factors predict SAT, SAT-V, and SAT-M performance and a second view that proposes that just a general intelligence factor or “g” predicts SAT, SAT-V, and SAT-M performance. The results suggested that structural equation models (i.e., SEMs) that included multiple factors (i.e., general intelligence, metacognitive awareness, and performance avoidance-test anxiety) as predictors were significantly better at explaining the SAT and SAT-M data than were SEMs that included: (i) just a general intelligence factor as a predictor or (ii) just metacognitive + social-personality factors as predictors (i.e., metacognitive awareness, performance avoidance-test anxiety). Moreover, this multiple factor SEM was also suitable for explaining the SAT-V data. However for the SAT-V, the results also suggested that a SEM that included just a general intelligence factor as a predictor was better at explaining the SAT-V data than was a SEM that included multiple factors as predictors (i.e., general intelligence, metacognitive awareness, and performance avoidance-test anxiety) or a SEM that included just metacognitive and social-personality factors as predictors (i.e., metacognitive awareness, performance avoidance-test anxiety).

1. Introduction

A recent survey reports that 90% of higher education institutions consider the SAT to be of “moderate” or “considerable” importance in the admission process (Clinedinst & Hawkins, 2010; see also Zwick, 2012). Indeed, “for students in the United States the SAT (i.e., the Scholastic Assessment Test) is one of the most, if not the most, important measure of academic achievement (Hannon, 2012a, pp. 816).” Nevertheless, the SAT is shrouded in controversies including those about ethnic disparities, gender differences, and construct validity.

This latter controversy—construct validity—is of particular importance because any insight about what the SAT is actually measuring is of great interest to researchers, parents, and students. Indeed, as noted by Hannon and McNaughton-Cassill (2011, p. 528), Richard Atkinson, a well-known cognitive psychologist, proposed dropping the SAT as a requisite for admissions to the University of California because, as he exclaimed in his speech, ‘Who knows what it measures?’ (Cloud, 2001, p.62). Since Atkinson’s speech researchers have sought to gain insight into the composition of the SAT and, of course, differing views have emerged. For example, whereas Frey and Detterman (2004) propose that the SAT is mainly a test of general intelligence or “g”, Hannon and McNaughton-Cassill (2011) propose that the SAT is composed of both multiple cognitive/metacognitive factors (i.e., working memory, knowledge integration, epistemic belief of learning) and multiple social/personality factors (i.e., test anxiety, and performance avoidance goals). The purpose of this paper is to compare these differing views about the composition of the SAT. Below is a review of research examining the SAT-intelligence relationship, the SAT-cognitive/metacognitive-social/personality relationships, and a discussion about the overlapping contributions of these two views. The last section describes the present study.

1.1. SAT scores and measures of intelligence

Although the relationships between most measures of academic achievement and intelligence are well established only recently have researchers reported a relationship between the SAT and intelligence. The first seminal study was by Frey and Detterman (2004) who showed that SAT scores correlated well with a number of measures of intelligence including the California Test of Mental Maturity, the Otis-Lennon Mental Ability Test, the Armed Services Vocational Aptitude Battery (i.e., the ASVAB), and Ravens Advanced Progressive Matrices. Indeed Frey and Detterman observed large, across-the-board SAT-intelligence correlations ranging from 0.530 using the Coop School & College Ability Test to 0.820 using the ASVAB. Such large correlations have led some researchers to suggest that the SAT is primarily a measure of general intelligence or “g” (e.g., Frey & Detterman, 2004). Presumably intelligence measures are such good predictors of the SAT because the SAT requires students to continuously think or use their intellect as they solve analogies, solve novel math problems, and answer questions about novel passages.

Subsequent research examining the relationships between ACT scores and a variety of intelligence measures also reports correlations with magnitudes similar to those observed between SAT scores and intelligence measures (i.e., range of r = 0.560 to 0.825; e.g., Koenig, Frey, & Detterman, 2008). Other studies have replicated and/or extended Frey and Detterman’s (2004) SAT-intelligence findings using both Raven’s Advanced Progressive Matrices and Reynolds Intellectual Assessment Scales (e.g., Beaujean et al., 2006; Rohde & Thompson, 2007). However the magnitudes of the SAT-intelligence correlations observed in these latter studies (e.g., r = 0.429 for Beaujean et al., 2006 and r = 0.389 for Rohde & Thompson, 2007) are more analogous to Frey and Detterman’s smaller, unadjusted 0.483 SAT-Raven’s Advanced Progressive Matrices correlation, rather than their more impressive adjusted 0.720 SAT-Raven’s Advance Progressive Matrices correlation or their 0.820 SAT-intelligence correlation using the ASVAB.¹

As extraordinary as these successes have been there are, nevertheless, some criticisms about using measures of intelligence as predictors of the SAT. For instance, it is not surprising that Frey and Detterman (2004) observed a large 0.820 correlation between SAT scores and the ASVAB since Carl Campbell Brigham, the creator of the original SAT, modeled the SAT after Army intelligence tests, like the ASVAB (see Frey & Detterman, 2004 and Lemann, 1999 for a discussion of this point). In addition, although measures of intelligence are excellent predictors of important real-world outcomes including academic and job success (Gottfredson, 1997; Higgins, Peterson, Pihl, & Lee, 2007), researchers still debate about what intelligence actually is. Indeed, contemporary cognitive researchers have proposed explanatory constructs such as information-processing speed (Jenson, 1987), inspection time (Deary, 2000), working memory capacity and functions (Kyllonen & Christal, 1990; Oberauer, Sűß, Wilhelm, & Wittman, 2008), and knowledge integration (Hannon & Daneman, 2014) with varying success (for reviews, see Deary, 2002; Detterman, 2002).

Rather than use one of these four explanatory constructs for intelligence, the present study adopts Horn and Cattell’s (1967) explanation for fluid intelligence, where fluid intelligence is a relatively culture-free ability that is used to solve novel problems and adapt to new situations (Engle, Tuholski, Laughlin, & Conway, 1999, p. 313). Specifically, when the term ‘intelligence’ is used here it refers to a latent variable that is measured by tests of cognitive abilities, including two tests of cognitive abilities that were not only designed to assess fluid intelligence but are also considered to be very good measures of intelligence, namely Raven’s Advanced Matrices and Cattell’s Culture Fair Test (Engle et al., 1999). Indeed, Frey and Detterman used Raven’s Advanced Progressive Matrices as a measure of intelligence or ‘g’ and observed that it correlated well with the SAT, unadjusted r = 0.483 and adjusted r = 0.720. Presumably intelligence measures are such good predictors of the SAT because the SAT requires students to constantly use their fluid intelligence or problem solving abilities to answer questions about novel reading passages, to solve novel analogies, and to solve novel math problems.

1.2. SAT scores and measures of cognitive/metacognitive and social/personality factors

In contrast to suggesting that a single factor, such as general intelligence (i.e., g), predicts the SAT, a recent study by Hannon and McNaughton-Cassill (2011) suggests that multiple factors, assessed with measures not originally designed to assess general intelligence (i.e., g), account for a large amount of variance in SAT scores (See Hannon, 2012a, who observed similar results; also see Ashcraft and Krause (2007) who discuss the relationship between working memory, math anxiety, and math performance in general). In Hannon and Mc-Naughton-Cassill’s study not only did overall SAT, SAT\\V, and SAT-M scores correlate with the cognitive/metacognitive measures of working memory (e.g., Daneman & Carpenter, 1980; Daneman & Merikle, 1996), knowledge integration (e.g., Hannon, 2012b, 2013, 2014), and epistemic belief of learning (e.g., Schommer, 1990), but they also correlated with the social/personality measures of test anxiety (e.g., Sarason, 1978) and performance avoidance goals (e.g., Elliot & McGregor, 1999). Indeed, these authors showed that, when combined, their cognitive/metacognitive/social/personality measures explained 43.4% (i.e., r = 0.659), 44.6% (i.e., r = 0.668), and 28.0% (i.e., r = 0.529) of the variance in overall SAT, SAT\\V, and SAT-M scores respectively. In the broader context of predicting the SAT, Hannon and McNaughton-Cassill’s correlations (i.e., range of r = 0.529 to 668) are comparable to SAT-intelligence correlations (range of r = 0.380 to 0.820). For the purposes of the present study cognitive, metacognitive, and social/personality factors will be labelled as C + MC + S/P factors.

There are also theoretical explanations as to why Hannon and McNaughton-Cassill’s (2011) C + MC + S/P factors predict the SAT. Working memory capacity, an individual’s capacity to process/integrate and simultaneously store/retrieve text-based information (Engle et al., 1999; Hannon & Daneman, 2001a), predicts the SAT because the SAT requires students to process, assimilate and/or discard large amounts of information in a short period of time (Hannon & McNaughton-Cassill, 2011).² Knowledge integration, the cognitive ability to integrate prior knowledge from long-term memory with new text-based information, also predicts the SAT because the SAT requires students to access their knowledge about definitions of words and facts/rules about math and then apply or integrate this prior knowledge with questions assessing passage comprehension, analogies, arithmetic, and math word problems (Hannon, 2012a; Hannon & Daneman, 2006). The SAT is also predicted by metacognitive awareness or beliefs about the complexity of knowledge and the value of integration during learning (Hannon & McNaughton-Cassill, 2011, p. 531). For the purposes of this paper metacognitive awareness is measured by epistemic belief of learning (See Burton & Daneman, 2007; Daneman & Hannon, 2001; Rukavina & Daneman, 1996 for more on epistemic belief of learning). Presumably students with more mature beliefs about learning are more likely to use cognitive processes that lead to greater integration of knowledge (e.g., Burton & Daneman, 2007; Rukavina & Daneman, 1996), which, in turn, will likely lead to higher SAT scores.

Test anxiety, characterized as a personality state that includes bodily, behavioral, emotional, and/or cognitive reactions in a testing situation (McIllroy, Bunting, & Adamson, 2000; See Hembree, 1988 for more about the influences of test anxiety) also predicts the SAT (Hannon, 2012a, 2015; Hannon & McNaughton-Cassill, 2011). Indeed, test anxiety-SAT correlations range from −0.41 to −0.31 (e.g., Hannon, 2012a, 2015; Hannon & McNaughton-Cassill, 2011) and studies suggest that test anxiety explains much of the well-known gender and ethnic differences in the SAT (e.g., Hannon, 2012a, 2015). Students with greater levels of test anxiety are more likely to reactive negatively in SAT testing situations and therefore are more likely to perform more poorly on the SAT (e.g., Elliot & Church, 1997; Hannon, 2012a, 2014, 2015; Hannon & McNaughton-Cassill, 2011). Both test anxiety and the SAT are also influenced by performance-avoidance goals, a type of achievement motivation that is typically operationalized as one’s desire not to perform poorly. According to Elliot and Church (1997), in SAT testing situations students with higher performance avoidance have a greater propensity to avoid studying and consequently, are more likely to perform poorly.

1.3. Relationships between general intelligence and cognitive/metacognitive/social/personality factors

Given the complexity of general intelligence it is likely that the relationship between the SAT and general intelligence is at least partially a consequence of a subset of C + MC + S/P factors inherent to general intelligence rather than general intelligence per se (see Detterman, 2002 for an analogous argument about the relationship between working memory and general intelligence). For example, knowledge integration measures, which assess a reader’s ability to integrate prior knowledge with new text-based information, predict both general intelligence (Hannon & Daneman, 2014) and the SAT (e.g., Hannon & McNaughton-Cassill, 2011). Accordingly, knowledge integration and general intelligence likely overlap in their predictive powers of the SAT. Similarly, because working memory measures predict both general intelligence and the SAT (Engle et al., 1999) quite possibly working memory and general intelligence overlap in their predictive powers of the SAT. Moreover, because knowledge integration and working memory are correlated (Daneman & Hannon, 2007), quite possibly they also overlap in their predictive powers of the SAT. Finally, because test anxiety predicts both general intelligence (e.g., Cassady & Johnson, 2002) and the SAT (Hannon, 2012a, 2015), quite possibly test anxiety and general intelligence overlap in their predictive powers of the SAT.

With respect to the measures of metacognitive awareness and performance avoidance, although Hannon and McNaughton-Cassill (2011) showed that both types of measures are predictive of either the overall SAT, SAT-V, and/or the SAT-M, the relationships between metacognitive awareness, performance avoidance, and general intelligence are unknown. Thus, it is unclear whether metacognitive awareness, performance avoidance goals, and general intelligence make unique or overlapping contributions to the SAT.

1.4. Present study

The SAT is one of the most, if not the most, important measure of academic achievement (Hannon, 2012a, pp. 816); yet, controversies about construct validity surround it. Thus, any insight about what the SAT is actually measuring is of great interest to researchers, parents, and students. In the present study I compare two views that differ about the composition of the SAT; one view that proposes measures of C + MC + S/P factors predict the SAT and a second view that proposes a general cognitive ability, also called general intelligence or ‘g’, predicts the SAT.

Structural equation models (i.e., SEMs) were created to test how well each view explains the overall SAT, SAT-V, and SAT-M. The observed variables in each SEM were measures that are both reliable and widely-used: Turner and Engle’s (1989) operation span task (i.e., a measure of working memory), Hannon and Daneman (2001a, 2001b); Hannon & Daneman, 2006, 2009) knowledge integration measure, which was created to assess integration as a reader comprehends text, Raven’s Advanced Progressive Matrices (Raven, Court, & Raven, 1988), Cattell’s Culture Free Intelligence Test (Cattell, 1949, 1971; Cattell, Krug, & Barton, 1973), a variation of Schommer’s (1990) measure of epistemic belief of learning (i.e., a measure of metacognitive awareness), Sarason’s (1978) test anxiety measure, and the performance avoidance subtest of Elliot and Church’s (1997) achievement motivation measure.

Three SEMs were developed and compared for each SAT measure (i.e., the SAT, the SAT-V, and the SAT-M). The first SEM, called the General Intelligence + Non-general Intelligence SEM (i.e., GI + NONGI SEM) determined whether multiple latent variables (e.g., general intelligence, metacognitive awareness, performance avoidance, and test anxiety measures/factors) simultaneously explained SAT, SAT-V, and SAT-M performance. The second SEM, called the General Intelligence SEM, determined whether a single General Intelligence latent variable (i.e., metacognitive awareness and performance avoidance-test anxiety measures/factors were not predictors) explained SAT, SAT-V, and SAT-M performance. The third SEM, called the Non-general Intelligence SEM, determined whether metacognitive awareness and performance avoidance, test anxiety factors (i.e., general intelligence factor was not a predictor) simultaneously explained SAT, SAT-V, and SAT-M performance.

Based on the results of previous studies, it is expected that there will be overlap in the predictive powers among a number of the cognitive measures (e.g., Hannon & Daneman, 2014; Hannon & McNaugton-Cassill, 2011) and perhaps even between the measures of test anxiety and intelligence (Cassady & Johnson, 2002). For this reason a factor analysis will be completed first in order to identify the unique factors or underlying latent variables among the predictors. Given that Hannon and McNaughton-Cassill (2011) observed that measures of both cognitive/metacognitive and social/personality factors were unique predictors of SAT performance, it is expected that at least two separate factors will emerge from the factor analysis: a general cognitive ability or General Intelligence factor and a Non-general Intelligence factor. Moreover, because Hannon and McNaughton-Cassill (2011) observed that measures of both cognitive and non-cognitive abilities accounted for more unique variance in SAT, SAT-V, and SAT-M performance than just measures of cognitive or just measures of social/personality factors, it is predicted that a SEM that includes multiple factors, such as the General Intelligence + Non-general Intelligence (i.e., GI + NOGI) SEM, will be better at explaining the data than is a SEM that includes just a cognitive factor (i.e., General Intelligence) or just non-cognitive factors (i.e., performance avoidance and test anxiety).

2. Methods

2.1. Participants

The 171 university students received $70 for participating. Each student was 18 to 26 years old and was pre-screened in order to ensure that he/she did not suffer from a learning disability and that he/she was a monolingual, native English speaker who spoke few words in another language. Seventy-five of the students were male while 96 of the students were female.

2.2. Design

The measures were administered in two sessions: session one was individually run while session two included one to three students. In session one the following measures were administered in the following order: (i) Cattell’s Culture Fair Test, (ii) epistemic belief of learning, and (iii) the operation span. In session two the following measures were administered in the following order: (i) the component processes task, (ii) the reduced Raven’s Advanced Progressive Matrices, (iii) the measure of test anxiety, and (iii) the measure of performance avoidance goals.³

2.3. SAT scores

SAT scores, SAT-V and SAT-M scores were obtained from university records once students consented to their release and had completed the study. The SAT scores were used as part of the admissions process for the university. An overall SAT score was the sum of the SAT-V and SAT-M scores. All SAT scores were completed after 2008 and before 2011.

2.4. Measures of intelligence

The first measure of intelligence was a reduced version (Bors & Stokes, 1998) of the Raven’s Advanced Progressive Matrices Test (e.g., Raven et al., 1988). This shorter version of Raven’s Matrices has the same concurrent validity and predictive power as do both the shorter version of Raven’s Matrices developed by Arthur and Day (1994) and the original full version (see Bors & Stokes, 1998 for a discussion). However, unlike the full version which takes 40–60 min to administer, this reduced version takes about 10 min.

In the reduced Raven’s Matrices students complete, at their own pace, 12 items of Raven’s Advanced Progressive Matrices Test, namely items 3, 10, 12, 15, 16, 18, 21, 22, 28, 30, and 31. For each item, students identify the missing element that completes a pattern presented as a 3 × 3 matrix. The dependent measure is the total number of items answered correctly. Cronbach’s alpha was 0.74.

The second measure of intelligence was form A of Cattell’s Culture Fair Test. Form A includes four non-verbal subtests. Subtest one is a 3-minute test that includes 13 items which require students to select the next picture in a series. Subtest two is a 4-minute test that includes 14 items. Each item consists of five pictures that require students to select the two items that are the most different. Subtest three is a 3-minute, 13 item test that is similar to Subtest one except that in Subtest three students need to consider information in both the same row and the same column from the preceding items. Subtest four is a 2.5 min 10-item test. Each item consists of an example composed of multiple geometric shapes and a dot that requires students to select the answer choice that had a dot located in a position relative to the geometric shapes that is identical to the original example. The dependent measure is the sum of the items answered correctly on the four subtests (maximum = 50). Cronbach’s alpha was 0.71.

2.5. Measure of working memory

Students completed one measure of working memory, namely the operation span (Turner & Engle, 1989). This measure is only briefly described here because it is described in detail elsewhere (e.g., Daneman & Hannon, 2001, 2007; Turner & Engle, 1989). The operation span presents increasing longer sets of equations followed by words. For each set students read aloud each math equation and its accompanying word, make decisions about the truthfulness of each math equation, and then at the end of the set, recall the words accompanying each math equation (Hannon, 2012a, 2012b). For example, students might: (i) read: (4 × 2) − 1 = 5 fable, (ii) respond ‘no’, (iii) read (8/4) + 3 = 5 donkey and then (iv) respond ‘yes.’ At the end of this two-equation set, students recall fable and donkey. The dependent measure is the total number of correctly recalled words. Cronbach’s alpha was 0.86.

2.6. Measures of cognitive and metacognitive factors

The measure of knowledge integration was one component of a multi-component task called the component processes task (Hannon, 2012a, 2012b, 2013, 2014; Hannon & Daneman, 2001a, 2001b, 2006, 2009). Because the component processes task has been explained in detail in many other papers, the description below is a paraphrase of a number of papers (e.g., Hannon, 2012a, 2012b, 2013, 2014; Hannon & Daneman, 2001a, 2001b, 2006, 2009).

In the component processes task, students read seven short passages, for example: A NORT resembles a JET but is faster and weighs more; A BERL resembles a CAR but is slower and weighs more; A SAMP resembles a BERL but is slower and weighs more. After studying a paragraph students answer true-false statements that assess different component processes, such as text memory, text inferencing, and knowledge integration. The knowledge integration statements, which were of primary interest to the present study, assessed a student’s ability to integrate semantic information from long-term memory with new, text-based information. For example, for the above vehicle paragraph the knowledge integration statement “Like MOTORCYLCES, BERLS travel across the land” requires students to access their semantic information from long-term memory (e.g., that motorcycles travel across the land) and integrate this knowledge with new text-based information (e.g., that BERLS resemble CARS and therefore travel across the land). Each knowledge integration statement included a nonsense term (e.g., BERLS) that appeared in the paragraph and a real term (e.g., MOTORCYCLES) and semantic feature (e.g., travels across land) that did not appear in the paragraph. Each paragraph included three true and three false knowledge integration statements and in total there were 36 knowledge integration statements. Cronbach’s alpha was 0.74.

The measure of metacognitive awareness was an epistemic belief of learning questionnaire that included 12 items picked from two subsets of Schommer’s (1990) epistemology questionnaire; see Rukavina and Daneman (1996) for an identical questionnaire and administration (Hannon & McNaughton-Cassill, 2011). For the purposes of the present study this task is called a measure of metacognitive awareness. For each sample item (e.g., Things are simpler than most teachers would have you believe.) students select their agreement level using a 5-point Likert scale. High scores indicate naive beliefs about learning whereas lower scores indicate mature beliefs. Cronbach’s alpha was 0.67.

2.7. Measures of social/personality factors

The measure of test anxiety was Sarason’s (1978) test anxiety scale, a measure that includes 37 true-false statements. A sample item is Thoughts of doing poorly interfere with my performance on tests. Lower scores indicate greater test anxiety. Cronbach’s alpha was 0.88.

The measure of performance avoidance was a 6-item subscale taken from Elliot and Church’s (1997) measure of achievement motivation, for example, I just want to avoid doing poorly in this class. Students choose their response for an item using a 7-point Likert scale. High scores on the performance avoidance subscale indicate a greater propensity towards avoidance. Cronbach’s alpha was 0.86.

2.8. Data analysis: factor analysis and SEM fitting

This section includes: (i) a factor analysis, (ii) information about the structure of the SEMs that were tested, and (iii) a description of the statistics that were used to evaluate the SEMs. The results of the factor analysis were reported here because its results were used to create the latent variables used in the SEMs that are described below.

2.8.1. Factor analysis

In order to determine whether the predictors in the present study (i.e., the two measures of intelligence, knowledge integration, working memory, metacognitive awareness, performance avoidance, and test anxiety) form separate latent variables, a factor analysis was completed using the PROC FACTOR procedure in SAS. An orthogonal rotation (i.e., VARIMAX rotation) was selected because the goal of a VARIMAX rotation is to minimize the complexity of the components, which was important for the present study. The number of factors that were selected was based on: (i) the scree test, (ii) the magnitude of the eigenvalue, (iii) the amount of variance explained and, of course, (iv) interpretability. The results of the factor analysis, which are reported in Table 1, revealed three factors accounting for 69.15% of the variance; factor one accounted for 36.11% of the variance (eigenvalue = 2.53), factor two accounted for 19.43% of the variance (eigenvalue = 1.36), and factor three accounted for 13.61% of the variance (eigenvalue = 0.95). As Table 1 shows the four cognitive measures (i.e., operation span, knowledge integration, Reduced Raven’s Matrices, and Cattell’s Culture Fair Test) all loaded on factor one, range of loadings = 0.65366 to 0.76594, but the other three measures (i.e., epistemic belief of learning, performance avoidance, and test anxiety) did not, range of loadings = −0.17549 to −0.02616. On the other hand, the social-personality measures of performance avoidance and test anxiety loaded on factor two, range of loadings = 0.90416 and 0.83243 respectively, but the other five measures did not, range of loadings = −0.19483 to 0.11379. Finally, the measures of epistemic belief of learning and Cattell’s Culture Fair Test loaded on factor three, factor loadings = 0.91237 and −0.41278 respectively, but the other six measures did not, range of loadings = −0.21408 to 0.25610. Because factor one was composed of a common or ‘general’ factor among cognitive measures, for the purposes of this paper this factor is labelled as General Intelligence.⁴ Because factor two was composed of a common factor underlying performance avoidance and test anxiety, it is assumed that this factor is performance avoidance-test anxiety. Finally because factor three was composed of epistemic belief of learning as well as Cattell’s Culture Fair Test it is assumed that this factor is measuring metacognitive awareness.⁵

Table 1.

Factor loadings for factor analysis using operation span, knowledge integration, Raven’s Matrices, Cattell’s Culture Fair Test, Epistemic Belief of Learning, Performance Avoidance, and Test Anxiety (n = 171).

	Factor one	Factor two	Factor three
Operation span	0.73531	−0.01400	0.25160
Knowledge integration	0.73029	−0.19483	−0.06842
Reduced Raven’s Matrices	0.76594	−0.02520	−0.21408
Cattell’s culture fair test	0.65366	−0.11183	−0.41278
Epistemic belief of learning	−0.07070	0.11379	0.91237
Performance avoidance	−0.02616	0.90416	0.01035
Test anxiety	−0.17549	0.83243	0.15806
Eigenvalue	2.53	1.36	0.95
% variance for factor	36.11%	19.43%	13.61%

Note. Factor loadings that are bolded and italicized represent the major components. Operations span is the measure of working memory and epistemic belief of learning is the measure of metacognitive awareness. Measures with factor loadings <0.30000 were not considered to be me Engle et al., 1999asures of that factor because these loadings are too low to be substantive (see for a similar approach).

2.8.2. Structural models and statistics used to evaluate them

LISREL 9.10 (JÖreskog & SÖrbom, 2013) and maximum likelihood estimation were used for data analysis of the raw data and fitting the Structural Equation Models (i.e., SEMs).

Nine SEMs were tested. All nine SEMs included the same “predictor” latent variables, however, not all predictor latent variables were predictors in every SEM (i.e., in some SEMs the path was missing between a predictor latent variable and the SAT latent variable). The first three SEMs were the multi-factor SEMs that included both general intelligence and non-general intelligence latent variables as predictors, namely: (i) the GI + NONGI SAT SEM, (ii) the GI + NONGI SAT-V SEM, and (iii) the GI + NONGI SAT-M SEM. The next three SEMs were the General Intelligence SEMs, which included only General Intelligence as a predictor: (i) the General Intelligence SAT SEM, (ii) the General Intelligence SAT-V SEM, and (iii) the General Intelligence SAT-M SEM. The final three SEMs were the Non-general Intelligence SEMs that included only metacognitive awareness and performance avoidance-test anxiety as predictors, specifically: (i) the Non-general Intelligence SAT SEM, (ii) the Non-general Intelligence SAT-V SEM, and (iii) the Non-general Intelligence SEM.

With respect to the multi-factor SEMs, as Fig. 1a shows, the GI + NONGI SAT SEM included four latent variables: (i) a latent variable called General Intelligence that was measured by four observed variables: the operation span, knowledge integration, Reduced Raven’s Matrices, and Cattell’s Culture Fair Test, (ii) a latent variable called metacognitive awareness that was measured by the observed variables epistemic belief of learning and Cattel’s Culture Fair Test, (iii) a latent variable called performance avoidance-anxiety that was measured by the two observed variables performance avoidance and Sarason’s test anxiety scores, and (iv) a latent variable called SAT that was measured by the observed variable SAT scores. As Fig. 1a shows, the GI + NONGI SAT SEM also included paths leading from the latent variables General Intelligence, performance avoidance-anxiety, and metacognitive awareness to the latent variable SAT. As noted by Jöreskog and Sörbom (2002) the practice of using a single observed variable for a latent variable is acceptable, although it is not recommended. The reason why is because when a latent variable has a single observed variable the SEM assumes that that observed variable is a perfect measure of the latent variable. For this reason, the present study followed the recommendations of Schumacker and Lomax (1996) and Jöreskog and Sörbom (2002) by setting the variance of the single observed variables using the formula (1.00 – reliability) * variance. The single observed variables in the present study were the observed variables: SAT, SAT-V, and SAT-M scores. The reliabilities for the SAT, SAT-V, and SAT-M, which are reported by the College Board, are 0.91, 0.91, and 0.91 respectively.

Fig. 1.

a. Path diagram of GI + NONGI SAT model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. b. Path diagram of General Intelligence SAT model. OS = Operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. c. Path diagram of Non-general Intelligence SAT model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores.

As Fig. 2a shows the GI + NONGI SAT-V SEM was identical to the GI + NONGI SAT SEM except that the latent variable SAT and the observed variable SAT scores were replaced with the latent variable SAT-V and the observed variable SAT-V scores. Finally, as Fig. 3a shows the GI + NONGI SAT-M SEM was identical to the GI + NONGI SAT SEM except that the latent variable SAT and the observed variable SAT scores were replaced with the latent variable SAT-M and the observed variable SAT-M scores.

Fig. 2.

a. Path diagram of GI + NONGI SAT-V model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. b. Path diagram of General Intelligence SAT-V model. OS = Operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. c. Path diagram of Non-general Intelligence SAT-V model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores.

Fig. 3.

a. Path diagram of GI + NONGI SAT-M model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. b. Path diagram of General Intelligence SAT-M model. OS = Operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores. c. Path diagram of Non-general Intelligence SAT-M model. OS = operation span, KI = knowledge integration, R = Reduced Raven’s Matrices, C = Cattell’s Culture Fair Test, EB = epistemic belief of learning, PA = performance avoidance, S = Sarason’s test anxiety scores, and sat = SAT scores.

With respect to the General Intelligence SEMs, which included only the latent variable General Intelligence as a predictor, as Fig. 1b shows the General Intelligence SAT SEM was identical to the GI + NONGI SAT SEM except that this SEM included only the path leading from General Intelligence to SAT; the paths leading from performance avoidance-test anxiety and metacognitive awareness to SAT were excluded. As Figs 2b and 3b show, the General Intelligence SAT-V and General Intelligence SAT-M SEMs were identical to the General Intelligence SAT SEM except SAT was replaced with SAT-V and SAT-M respectively.

With respect to the Non-general Intelligence SEMs, which included only metacognitive awareness and performance avoidance-test anxiety as predictors, as Fig. 1c shows the Non-general Intelligence SAT SEM was identical to the GI + NONGI SAT SEM except that the Non-general Intelligence SEM included only the paths leading from performance avoidance-test anxiety and metacognitive awareness to SAT; the path leading from General Intelligence was excluded. As Figs 2c and 3c show, the Non-general Intelligence SAT-V and the Non-general Intelligence SAT-M SEMs were identical to the Non-general Intelligence SAT SEM except SAT was replaced with SAT-V and SAT-M respectively.

For all of the SEMs, a latent variable was considered to exert influence on another latent variable when the path coefficient between the latent variables was significantly different from 0.00 (Hannon & Daneman, 2014, p. 183). Path statistical significance was determined using two-tailed t-tests set with a p < 0.05; however where relevant, marginal p-values and one-tailed t-tests were noted and considered. Finally, a factor loading was considered to be statistically significant when the coefficient was significantly different from 0.00 (Hannon & Daneman, 2014, p. 183). In all figures sold lines represented statistically significant paths and dashed lines represented non-statistically significant paths.

Because the primary goal of this study was to determine which theoretical view was most suitable for explaining the SAT, SAT-V, and SAT-M, χ²-difference tests were computed among the SEMs; see Hannon (2012b) for more about χ²-difference tests. If a χ² difference test between two SEMs was statistically significant (i.e., p < 0.05) then it was concluded that one of the SEMs was significantly better at explaining the data.

Finally, SEM fits were evaluated using the Goodness-of-fit Index (GFI), the Comparative Fit Index (CFI), and the Root Mean Square Error of Approximation (RMSEA). The GFI ranges from 0 to 1 and the guideline is that good-fitting models have values of ≥0.90. The CFI estimates the improvement in fit of the specified model compared to the independence model, which assumes zero covariances among the observed variables. The CFI statistic ranges from 0 to 1 with higher values indicating a better fit. Hu and Bentler (1999) advocate a CFI cutoff of 0.95 as an indication of a good fit, although 0.90 is also commonly used. The RMSEA statistic estimates the error of approximation for the specified model and independence model, adjusting for degrees of freedom; RMSEA values ≤0.05 suggest close fit, RMSEA values between 0.05 and 0.08 suggest a reasonable fit, and > than 0.10 suggest a poor fit (Browne & Cudeck, 1993).

3. Results

The results include three sections: (i) data screening, (ii) descriptive statistics and correlational analysis, and (iii) structural equation modelling. All t-tests and z-tests were two-tailed tests unless stated otherwise.

3.1. Data screening

The data were screened for (i) outliers (studentized residuals, DFITTS, DFBETAS, and Cook’s D), (ii) data points that exerted excessive leverage (hat-values), (iii) linearity (bivariate scatterplots), (iv) normality (normal probability plots), and (v) multicollinearity (tolerance tests). Data screening analyses, which included all of the measures, indicated that no single data point was an outlier exerting excessive leverage. Further, examinations of the statistics for linearity, normality, and multcollinearity revealed no abnormalities. Indeed Mardia’s PK was 0.98, a value that indicated that the coefficient of multivariate kurtosis was not significantly different from zero (0). Finally, the statistics for multivariate skewness and multivariate skewness + kurtosis were all below critical thresholds, z = 1.486, p = 0.137 and χ² = 2.27, p = 0.322 respectively, which indicated no evidence of multivariate skewness or multivariate kurtosis.

3.2. Descriptive statistics and correlations

Table 2 reports the descriptive statistics: maximum scores, means, standard deviations, ranges, skews, and kurtosis whereas Table 3 reports the correlations. As Table 2 shows, nearly all of the measures had large ranges–scores ranging from chance-level to a high-level of performance–including the measures of the SAT-V and SAT-M. Indeed, even though the participants in the present study were university students and thus one might think that the ranges for the SAT measures were restricted, this assumption is false. Rather, based on the SAT norms reported by the College Board, the range of the SAT-M scores reported in the present study was from the 4th to 97th percentiles and the range of the SAT-V scores was from the 5th to 98th percentiles. Finally, the statistics for skew and kurtosis indicated that the univariate distributions for the measures were normal (i.e., all values under ±3).

Table 2.

Means, standard deviations, ranges, skew, and kurtosis for SAT, SAT-V, SAT-M, measures of intelligence, knowledge integration, metacognitive awareness, social/personality factors, and working memory (n = 171).

	M	SD	Range	Skew	Kurtosis
Measures of academic achievement
SAT (max = 1600)	1066.78	142.30	690–1360	−0.06	−0.48
SAT-V (max = 800)	537.43	76.75	320–730	−0.11	−0.13
SAT-M (max = 800)	530.18	82.30	350–750	0.18	−0.60
Measures of intelligence
Reduced ravens advanced matrices (max = 12)	7.54	2.77	2–12	−0.08	−0.38
Cattell’s culture fair test (max = 50)	27.81	3.74	17–35	−0.47	0.32
Knowledge integration (max = 36)	25.57	5.57	9–36	−0.33	−0.53
Measure of metacognitive awareness
Epistemic belief of learning (max = 60)	33.26	5.12	20–45	0.01	−0.21
Measures of social/personality factors
Test anxiety	15.47	7.17	2–32	0.28	−0.92
Performance-avoidance goals (max = 7)	4.58	1.06	1.83–6.83	−0.53	−0.08
Measure of working memory
Operations span (max = 100)	75.70	10.27	54–96	0.09	−0.73

Table 3.

Correlations among SAT, SAT-V, SAT-M, measures of intelligence, knowledge integration, epistemic belief of learning (i.e., metacognitive awareness), test anxiety, performance-avoidance goals, and operation span (i.e., working memory) (n = 171).

	1	2	3	4	5	6	7	8	9	10
1. SAT	-	0.89*	0.91*	0.32*	0.47*	0.46*	−0.26*	−0.33*	−0.27*	0.29*
2. SAT-V		-	0.63*	0.33*	0.49*	0.48*	−0.21*	−0.28*	−0.27*	0.27*
3. SAT-M			-	0.24*	0.36*	0.41*	−0.27*	−0.32*	−0.22*	0.25*
4. Reduced Raven’s advanced matrices				-	0.49*	0.46*	−0.18*	−0.21*	−0.07	0.35*
5. Cattell’s culture fair test					-	0.41*	−0.27*	−0.25*	−0.14	0.41*
6. Knowledge integration						-	−0.16*	−0.20*	−0.22*	0.36*
7. Epistemic belief of learning							-	0.23*	0.13	0.01
8. Test anxiety								-	0.55*	−0.15
9. Performance-avoidance goals									-	−0.01
10. Operation span										-

Note. For r < 0.16, p > 0.05.

^*denotes significance.

As reported in Table 3, all the predictors–the measures of intelligence, working memory (i.e., operation span), knowledge integration, metacognitive awareness (i.e., epistemic belief of learning), test anxiety, and performance avoidance goals)–significantly correlated with the three SAT measures (i.e., overall SAT, SAT-V, and SAT-M). The correlations between the three SAT measures and the two measures of intelligence (i.e., Reduced Raven’s Matrices, Cattell’s Culture Fair test), range of r = 0.24 to 0.49, were also consistent with analogous correlations in Beaujean et al. (2006) and Rohde and Thompson (2007), range of r = 0.389 to 0.423, all z-scores ≤ 0.89, all p’s > 0.18. As well, the correlations between the three SAT measures and the five C + MC + S/P measures were, for the most part, consistent with analogous correlations in Hannon and McNaughton-Cassill (2011). The only exception was the epistemic belief of learning-SAT-V correlation, which was smaller than the one reported by Hannon and McNaughton-Cassill, z = 1.98, p = 0.05; although the epistemic belief of learning-SAT-V correlation reported in the present study was the same size as the one reported by Hannon (2012a) who used the same measures, z = 1.72, p = 0.09. Also consistent with previous research were the correlations between the measures of intelligence and working memory, range of r = 0.35 to 0.41, and the analogous correlations in Engle et al. (1999) and Hannon and Daneman (2014) using the same measures, range of r = 0.26 to 0.34, all z’s < 1.27, p = 0.20 (although see Gignac, 2014 who suggests these correlations should be higher). Finally the correlations between the measures of intelligence and knowledge integration in the present study, range of r = 0.41 to 0.46, were consistent with analogous correlations using the same measures in Hannon and Daneman (2014), range of r = 0.47 to 0.59, all z’s < 1.46, p = 0.14.

3.3. Structural equation models

As noted in the Section 2, all SEMs were assessed using path coefficients, fit statistics, and χ²-difference tests. Of particular interest were the χ²-difference tests because the presence of statistically significant χ²-difference tests suggests that one of the SEMs was statistically better at explaining the data. On the other hand, the absence of statistically significant χ²-difference tests indicated that no one SEM was statistically better than another at explaining the data.

As the results below report, the GI + NONGI SEMs, which included General Intelligence, metacognitive awareness, and performance avoidance-anxiety latent variables as predictors of the SAT, SAT-V, or SAT-M, were good models for explaining the SAT, SAT-V, and SAT-M data. However the statistical significance of the paths between metacognitive awareness and the SAT, SAT-V, and SAT-M in the GI + NONGI SEMs varied as a function of type of SAT measure. Specifically, although metacognitive awareness was a statistically significant predictor of SAT-M in the GI + NONGI SAT-M SEM; for the SAT metacognitive awareness was only a marginally statistically significant predictor and for the SAT-V metacognitive awareness was not a statistically significant predictor. Finally although the GI-NONGI SEM was suitable for explaining the SAT-V, the General Intelligence SEM was the best SEM for explaining the SAT-V because it was more parsimonious.

3.3.1. Overall SAT scores

Fig. 1a depicts the GI + NONGI SAT SEM, Table 4 reports the fit statistics for this model, and Table 5 reports the correlations among the exogenous latent variables. As Table 4 shows the GI + NONGI SAT SEM fit the data well as all fit statistics were well within acceptable limits. Moreover, as Fig. 1a shows, both general intelligence and performance avoidance-anxiety exerted statistically significant influences on the construct of interest, the SAT. however, the influence that metacognitive awareness exerted on the SAT was not statistically significant using a two-tailed test; rather it was only statistically significant using a one-tailed test, t (170) = 1.64, p = 0.05. These significant and marginally significant findings are consistent with previous research which have shown that measures of general intelligence, performance avoidance, test anxiety, and metacognitive awareness correlate with SAT performance (e.g., Frey & Detterman, 2004; Hannon & McNaughton-Cassill, 2011). Indeed the 0.469 total variance in SAT scores that was accounted for by general intelligence, performance avoidance + test anxiety, and metacognitive awareness was nearly identical to the 0.433 total variance in SAT scores that was reported by Hannon and McNaughton-Cassill (2011), who used a slightly different subset of cognitive and social-personality measures

Table 4.

Fit statistics for Structural Equation Models of SAT, SAT-V, or SAT-M scores (n = 171).

Models	χ2	df	p-exact	p-close	GFI	RMSEA	CFI
SAT Structural Equation Models
GI + NONGIa	20.58	15	0.1506	0.50	0.97	0.05	0.99
General Intelligence	28.90	17	0.0354	0.26	0.96	0.06	0.97
Non-general Intelligence	53.57	16	0.0001	0.00	0.93	0.12	0.91
SAT-V Structural Equation Models
GI + NONGIb	21.53	15	0.1207	0.45	0.97	0.05	0.98
General Intelligencec	25.19	17	0.0905	0.41	0.97	0.05	0.98
Non-general Intelligence	55.24	16	0.0000	0.01	0.93	0.12	0.90
SAT-M Structural Equation Models
GI + NONGId	18.94	15	0.2166	0.59	0.97	0.04	0.99
General Intelligence	28.96	17	0.0349	0.26	0.96	0.06	0.97
Non-general Intelligence	36.65	16	0.0024	0.05	0.95	0.09	0.94

Note. p-close tests the alternative model that the RMSEA is > 0.05. If value for p-close is > 0.05 then it is concluded that the fit of the model is close (Kline, 2011). Although all models include all latent variables, not all latent variables are predictors in every model. More specifically, all GI + NONGI models include General Intelligence, performance avoidance-test anxiety, and metacognitive awareness latent variables as predictors, all General Intelligence models include a General Intelligence latent variable as a predictor and all Non-general Intelligence models include the metacognitive awareness and performance avoidance-test anxiety latent variables as predictors.

^amodel is significantly better than other two SAT models.

^bmodel is significantly better than non-G SAT-V model

^cmodel is significantly better than non-G SAT-V and GI + NONGI models

^dmodel is significantly better than other two SAT-M models.

Table 5.

Correlations among Latent Variables in SAT, SAT-V, and SAT-M SEMs.

Correlations between exogenous latent variables
	G and perform avoid-anxiety	G and metacognitive awareness	Perform avoid-anxiety and metacognitive awareness
SAT Structural Equation Models
GI + NONGI	−0.34	−0.26	0.31
General Intelligence	−0.39	−0.33	0.30
Non-general Intelligence	−0.42	−0.32	0.31
SAT-V Structural Equation Models
GI + NONGI	−0.35	−0.26	0.31
General Intelligence	−0.31	−0.27	0.30
Non-general Intelligence	−0.41	−0.31	0.31
SAT-M Structural Equation Models
GI + NONGI	−0.33	−0.26	0.30
General Intelligence	−0.37	−0.32	0.29
Non-general Intelligence	−0.37	−0.31	0.31

Of course it is always possible that a SEM that includes just a General Intelligence latent variable as a predictor but no performance avoidance-anxiety or metacognitive awareness latent variables as predictors (i.e., the General Intelligence SEM) might be just as suitable for explaining the SAT as is a SEM that includes all three of these latent variables as predictors (i.e., the GI + NONGI SAT SEM). Fig. 1b depicts this SEM. In addition, it is also quite possible that a SEM that includes just performance avoidance-anxiety and metacognitive awareness latent variables as predictors but no General Intelligence latent variable as a predictor (i.e., the Non-general Intelligence SEM) might be just as suitable for explaining the SAT as is a SEM that includes all three of these latent variables as predictors (i.e., the GI + NONGI SAT SEM). Fig. 1c depicts this SEM. As Figs 1b and c show, all the paths in the General Intelligence and Non-general Intelligence SEMs were statistically significant. However, as Table 4 shows the results of the RMSEA statistic suggests that the Non-general Intelligence SEM was a poor fit for the data.

In order to determine which SEM (i.e., the GI + NONGI SEM, General Intelligence SEM, or the Non-general Intelligence SEM) was the best model for explaining the SAT data, comparisons between the models were made using χ²-difference tests. The results of the χ²-difference tests suggested that the GI + NONGI SEM was significantly better at explaining the SAT data than both the General Intelligence and Non-general Intelligence SEMs, χ²-difference (2) = 8.32, p < 0.05 and χ²-difference (1) = 32.99, p < 0.05 respectively. These results suggest that a SEM that includes multiple C + MC + S/P factors as predictors (i.e., GI + NONGI SEM) is better for explaining the overall SAT data than are SEMs that do not include all of the C + MC and S/P factors as predictors (i.e., General Intelligence and Non-general Intelligence SEMs).

3.3.2. SAT-V scores

Fig. 2a depicts the multiple GI + NONGI SAT-V SEM, Fig. 2b depicts the general intelligence SAT-V SEM (which includes just a general intelligence latent variable as a predictor), Fig. 2c depicts the non-general intelligence SAT-V SEM (which includes just performance avoidance-anxiety and metacognitive awareness latent variables as predictors), Table 4 reports the fit statistics for these models, and Table 5 reports the correlations among their exogenous latent variables. As Table 4 shows the multiple GI + NONGI SAT-V SEM fit the data well as all the fit statistics were well within acceptable thresholds. Moreover, as Fig. 2a shows, general intelligence exerted a statistically significant influence on the construct of interest, namely the SAT-V. However as Fig. 2a also shows, the influences that performance avoidance + anxiety and metacognitive awareness exerted on the SAT-V were not statistically significant. Despite this lack of significance for the paths between SAT-V performance and performance avoidance + anxiety and metacognitive awareness, the 0.428 total variance in SAT-V scores that was accounted for by general intelligence, performance avoidance + anxiety, and metacognitive awareness in the present study was, nevertheless, nearly identical to the 0.446 total variance in SAT-V scores reported by Hannon and McNaughton-Cassill (2011), who used a slightly different subset of cognitive and social-personality measures. Finally, as Figs 2b and c show, all the paths in the general intelligence and non-general intelligence SAT-V SEMs were statistically significant. However, as Table 4 shows the results of the RMSEA statistic suggests the non-intelligence SAT-V SEM was a poor fit for the data

In order to determine which SEM (i.e., the GI + NONGI, General Intelligence, or Non-general Intelligence SEM) was the best model for explaining the SAT-V data, comparisons between the models were made using χ²-difference tests. The results of the χ²-difference tests suggested that the GI + NONGI SEM was significantly better at explaining the SAT-V data than the Non-general Intelligence SEM, χ²-difference (1) = 33.71, p < 0.05. However the GI + NONGI SEM was not better at explaining the SAT-V data than was the General Intelligence SEM, χ²-difference (2) = 3.66, p = 0.16. Because the General Intelligence SEM is the more parsimonious SEM, which is typically considered to be the best choice, these findings suggest that a SEM that includes a single factor, General Intelligence, is better for explaining the SAT-V data than is a SEM that includes all the factors (i.e., the GI + NONGI SEM) as predictors or just the MC + S/P factors as predictors (i.e., the NONGI SEM).

3.3.3. SAT-M scores

Fig. 3a depicts the GI + NONGI SAT-M SEM, Fig. 3b depicts the general intelligence SAT-M SEM (which includes just a general intelligence latent variable as a predictor), Fig. 3c depicts the non-general intelligence SAT-M SEM (which includes just performance avoidance-anxiety and metacognitive awareness latent variables as predictors), Table 4 reports the fit statistics for these models, and Table 5 reports the correlations among their exogenous latent variables. As Table 4 shows the GI + NONGI SAT-M SEM fits the data well as all the fit statistics were well within acceptable thresholds. Moreover, as Fig. 3a shows, general intelligence, metacognitive awareness, and performance avoidance-anxiety all exerted significant influences on the construct of interest, the SAT-M. Indeed, the 0.336 total variance in SAT-M scores that was accounted for by general intelligence, performance avoidance + anxiety, and metacognitive awareness in the present study was nearly identical to the 0.280 total variance in SAT-M scores reported by Hannon and McNaughton-Cassill (2011), who used a slightly different subset of cognitive and social-personality measures. Finally, as Figs 3b and c show, all the paths were statistically significant in these two SEMs. However, as Table 4 shows the results of the RMSEA statistic suggests the Non-general intelligence SAT-M SEM has a poor fit for the data

In order to determine which SEM (i.e., the GI + NONGI, General Intelligence, or Non-general Intelligence SEM) was the best model for explaining the SAT-M data, comparisons between the models were made using χ²-difference tests. The results of the χ²-difference tests suggested that the GI + NONGI SEM was significantly better at explaining the SAT-M data than both the General Intelligence and Non-general Intelligence SEMs, χ²-difference (2) = 10.02, p < 0.05 and χ²-difference (1) = 17.71, p < 0.05 respectively. These results suggest that a SEM that includes multiple C + MC and S/P factors as predictors (i.e., the GI + NONGI SEM) is better for explaining the overall SAT-M data than are SEMs that do not include all of the C + MC and S/P factors as predictors (e.g., General Intelligence and Non-general Intelligence SEMs).

4. Discussion

This study compared two views that differed about the composition of the SAT: one view that proposes cognitive, metacognitive, and social-personality factors/latent variables predict SAT, SAT-V, and SAT-M performance and a second view that proposes a general intelligence or a ‘g’ factor predicts SAT, SAT-V, and SAT-M performance. The results suggested that SEMs that included multiple factors/latent variables (i.e., General Intelligence, metacognitive awareness, and performance avoidance-anxiety) as predictors were suitable models for explaining the SAT, SAT-V, and SAT-M data. Moreover, these multi-factor SEMs (i.e., GI + NONGI SEMs) were best for explaining the SAT and SAT-M data even when they were statistically compared to SEMs that included only a General Intelligence latent variable as a predictor or only Non-general Intelligence latent variables as predictors (i.e., performance avoidance-anxiety and metacognitive awareness). However for the SAT-V, although the multi-factor SEM (i.e., GI + NONGI SEMs) was more suitable for explaining the SAT-V data than the Non-general Intelligence SEM, the General Intelligence SEM was better at explaining the SAT-V data then the multi-factor SEM.

Nevertheless, there were differences in predictive powers among the latent factors within SEMs and between SEMs. For instance, there was a consistent difference in predictive powers between the General Intelligence versus the Non-general Intelligence factors in all three of the GI + NONGI SEMs. This difference was that General Intelligence was a much stronger predictor of SAT, SAT-V, and SAT-M performance than either of the two Non-general Intelligence factors (i.e., performance avoidance-anxiety and metacognitive awareness). Additionally, the statistical significance of the paths between the measures of the metacognitive awareness latent variable and the three SAT measures varied as a function of type of SAT measure. Specifically, whereas the metacognitive awareness latent variable was a statistically significant predictor for the SAT-M, metacognitive awareness was only a marginally significant predictor for the SAT and for the SAT-V it was a non-statistically significant predictor.

But why might the statistical significance of metacognitive awareness vary as a function of the type of SAT measure? With respect to overall SAT scores, the most likely explanation why metacognitive awareness is a marginally significant predictor is because each overall SAT score is composed of both: (i) an SAT-V score for which metacognitive awareness was not a statistically significant predictor, and (ii) an SAT-M score for which metacognitive awareness was a statistically significant predictor. With respect to the SAT-M and SAT-V scores, the present study cannot provide a definitive answer as to why metacognitive awareness significantly predicts the SAT-M but not the SAT-V and consequently, it is a question for future research. However, one possible explanation might be because measures of quantitative skills, like the SAT-M, tend to require the coordination of a greater collection of separate abilities than does the SAT-V, a measure of verbal abilities. Indeed, Hannon and Daneman (2014) showed that whereas measures of math problems tapped measures of spatial abilities, knowledge integration, and text-based inferencing to an equal extent (range of r = 0.32 to 0.39), measures of reading comprehension/verbal abilities tapped measures of knowledge integration and text inferencing to a greater extent than measures of spatial abilities (i.e., range of r = 0.51 and 0.54 versus range of r = 0.26 and 0.28). Quite possibly, knowing or being metacognitively aware as to which ability to use for which question, whether it is a linear algebra, trigonometry, geometry, or a math word problem, leads to greater success on the SAT-M.

From a theoretical perspective, these findings are informative because they suggest that no single construct explains the SAT. Rather, the findings suggest that the best theoretical explanation for the SAT is that it is a complex construct that is composed of many factors, including cognitive, metacognitive, and social/personality factors. Indeed from a componential perspective, the SAT appears to be as complex of a construct as is reading comprehension (e.g., Hannon, 2012b, 2013, 2014; Hannon & Daneman, 2001a, 2006, 2009). For this reason, future research should examine whether there are different C + MC + S/P profiles of SAT test takers. For example, are the SAT scores of some test takers restricted by a cognitive factor but not non-cognitive factors or vice versa? Future research might also consider other potentially unique factors that might predict SAT performance. For example, where does socio-economic status, another factor that is known to predict the SAT (Hannon, 2015), fit in with respect to the factors used in the present study?

The present results also extend a number of previous findings that showed the influences of just general intelligence or just non-general intelligence factors on the SAT. For instance, the present findings extend those of Hannon and McNaughton-Cassill (2011) by showing that the influences their C + MC + S/P factors exerted on the SAT, the SAT-V, and the SAT-M overlapped with the influences exerted by general intelligence. The present findings extend those of Beaujean et al. (2006) by showing that general intelligence as well as other factors—metacognitive awareness and performance avoidance-text anxiety—can all simultaneously influence the SAT. Similarly, the present findings extend those of Rohde and Thompson (2007) by showing that general intelligence as well as other factors, other than working memory and processing speed, can simultaneously predict the SAT. Specifically, unlike Rohde and Thompson the present results showed that metacognitive awareness, performance avoidance goals-test anxiety can also influence the SAT. Most importantly though, the present results both replicate and extend the findings of Frey and Detterman (2004). That is, consistent with Frey and Detterman, the results showed that general intelligence exerts considerable influence on the SAT. However, the present results also showed that other MC + S/P factors, metacognitive awareness and performance avoidance goals-test anxiety, can also exert some influence on the SAT even when general intelligence is a simultaneous predictor.

One could also argue that the influences that the Performance Avoidance-Test Anxiety and metacognitive awareness latent variables/factors exerted on the SAT, SAT-V, and SAT-M were weak and that another dataset using the same measures might fail to yield similar results to the present study. The present study does not dispute this fact as this possibility is true for nearly all research studies. However, it is important to point out that, as noted in the Introduction, other studies have found that performance avoidance, test anxiety, and metacognitive awareness measures predict the SAT, SAT-V, SAT-M (e.g., Hannon & McNaughton-Cassill, 2011). So, from this perspective there is a good chance that the present findings are not simply the consequence of the present set of data.

In summary, the present study compared two views that differed about the composition of the SAT: one view that proposes C + MC + S/P factors predict the SAT and a second view that proposes general intelligence predicts the SAT. The results showed that general intelligence was not the only significant influence on the three SAT measures. Rather, the present findings revealed that the model that best explained the SAT and the SAT-M data was the model that included three factors/latent variables, namely a General Intelligence latent variable, a performance avoidance-test anxiety latent variable, and a metacognitive awareness latent variable. Additionally, for the SAT-V the present findings revealed that this three-factor model was also suitable for explaining the SAT-V data; however, the present findings also revealed that a model that included just a General Intelligence factor was the best model for explaining the SAT-V data.

The present findings are, nevertheless, limited to students at a single university and consequently, future research should seek to determine whether the present study generalizes to other universities. In addition, future research might wish to determine whether socioeconomic factors (e.g., Hannon, 2015; Zwick & Sklar, 2005), which are known to predict the SAT, influence the overall SAT, SAT-V, and SAT-M beyond the influences of the three factors tested here. Finally, given that Koenig et al. (2008) observed that measures of intelligence are highly predictive of the ACT future research might seek to ascertain the overlapping and unique influences of non-general intelligence factors versus general intelligence for influencing the ACT.