007) 83–92

Intelligence 35 (2

Predicting academic achievement with cognitive ability

Treena Eileen Rohde ⁎, Lee Anne Thompson

Case Western Reserve University, Department of Psychology, 10900 Euclid Avenue Cleveland, Ohio 44106-7123, United States

Received 25 October 2005; received in revised form 15 February 2006; accepted 27 May 2006Available online 10 July 2006

Abstract

The purpose of the present study is to explain variation in academic achievement with general cognitive ability and specificcognitive abilities. Grade point average, Wide Range Achievement Test III scores, and SAT scores represented academicachievement. The specific cognitive abilities of interest were: working memory, processing speed, and spatial ability. Generalcognitive ability was measured with the Raven's Advanced Progressive Matrices and the Mill Hill Vocabulary Scales. Whencontrolling for working memory, processing speed, and spatial ability, in a sample of 71 young adults (29 males), measures ofgeneral cognitive ability continued to add to the prediction of academic achievement, but none of the specific cognitive abilitiesaccounted for additional variance in academic achievement after controlling for general cognitive ability. However, processingspeed and spatial ability continued to account for a significant amount of additional variance when predicting scores for themathematical portion of the SAT while holding general cognitive ability constant.© 2006 Elsevier Inc. All rights reserved.

Keywords: Intelligence; Spatial ability; Academic achievement

Academic achievement scores of high school studentscorrelate between .50 and .70 with IQ scores (Jensen,1998), and performance on standardized measures ofacademic achievement can be used to accurately estimateIQ scores (Frey & Detterman, 2004). While there isempirical evidence for a strong association betweengeneral cognitive ability and academic achievement, thereis still anywhere from 51% to 75% of the variance inacademic achievement that is unaccounted for bymeasures of general cognitive ability alone. Moreover,understanding the nature of the relationship betweengeneral cognitive ability and academic achievement haswidespread implications for both practice and theory.

Several specific cognitive abilities have the potentialto further an understanding of the components of

⁎ Corresponding author. Tel.: +1 216 368 6467; fax: +1 216 368 4891.E-mail address: treena.rohde@case.edu (T.E. Rohde).

0160-2896/$ - see front matter © 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.intell.2006.05.004

general cognitive ability. Recent research focused ondelineating the structure of general cognitive ability hasattempted to identify separable constructs to explainindividual differences in psychometric ‘g’. These sameconstructs may also be relevant for understandingacademic achievement. As an example, informationprocessing theory suggests that overall mental efficien-cy can account for a large portion of the individualdifferences in ‘g’ (Vernon, 1983). Processing speed andworking memory are two cognitive processes that haveeach been used to explain what drives mental efficiencyand thus general cognitive ability.

Jensen (1992) was able to account for 40% of thevariance associated with ‘g’ using Reaction Time (RT)variables — the intraindividual median (RTmd) and thestandard deviation (RTSD). Of that 40%, 63.5% wascommon to both variables, and 17.1% was specific toRTmd, and 19.4% was specific to RTSD. In addition to

84 T.E. Rohde, L.A. Thompson / Intelligence 35 (2007) 83–92

processing speed, Jensen maintains that other “neurolog-ically independent mechanisms” are likely to be related togeneral cognitive ability (Jensen, 1992, p. 879).

Theworkingmemory system involves several cognitiveprocesses thought to be related to general cognitive ability.Some researchers believe processing speed is the bridgebetween working memory and general cognitive ability.Vernon (1983) suggests that the relationship betweenprocessing speed and general cognitive ability representsindividual differences in the limitations of the componentsof working memory. Developmental research suggests acombination of processing speed and working memory areneeded to explain the individual difference in generalcognitive ability (Fry & Hale, 1996). In addition to pro-cessing speed and working memory other specific cog-nitive abilities could also be investigated to determine theirimportance to individual differences in psychometric ‘g’.

Luo and Petrill (1999) using exploratory andconfirmatory factor analysis, selected basic cognitivetasks to test whether or not speed of informationprocessing or memory processing are intrinsic parts ofgeneral cognitive ability. Their findings revealed thatgeneral cognitive ability can be defined with a combina-tion of basic cognitive tasks and traditional psychometricmeasures of general cognitive ability without altering thenature of the relationship between ‘g’ and academicachievement. Additionally, a learning and memory factorcomposed of non-chronometric variables was highlyrelated yet independent of the general informationprocessing component. This finding led the researchersto conclude that the learning and memory factor'srelationship with general cognitive ability must tap intosome aspect of information processing andmemory that isnot related to speed of information processing.

Luo, Thompson, and Detterman (2003) tested thehypothesis that the correlation between psychometric ‘g’and academic achievement was in large part associatedwith a mental speed component. Initially, the sharedvariance between general intelligence and academicachievement was approximately 30%. However, aftercontrolling for the mental speed component, the sharedvariance between psychometric ‘g’ and academicachievement was reduced to approximately 6% (Luoet al., 2003). This finding is strong evidence that themental speed component is an important mediatorbetween psychometric ‘g’ and academic achievement.

Spatial ability is also an important construct related togeneral cognitive ability. For the purpose of this research,spatial ability was defined as a type of visual perception orsensory input involved in the mental manipulation orrotation in the orientation or position of objects or shapeswithin a given area or space (Carroll, 1993, pp. 304–310).

Stumpf (1994) found that subtypes of spatial ability are ableto predict success in accelerated mathematics coursesoffered to gifted high school students. Baddeley and Logie(1999) proposed that working memory involved severaldistinct cognitive skills including: verbal ability, spatialability, long-term memory retrieval, and of courseexecutive functioning. Logie's (1995) theoretical modelrepresents working memory, long-term memory retrieval,and sensory inputs such as spatial ability as separablecognitive processes that may individually account forunique variance in general cognitive ability. Johnson andBouchard (2005) go a step further and propose a structuralmodel of human intelligence that includes image rotation asone of the three main factors of general cognitive ability.

Spatial ability is a construct shown to add incrementalvalidity to both math and verbal sections of the SATwhenpredicting the educational choices and occupation out-comes of academically gifted individuals (Shea, Lubinski,& Benbow, 2001). Spatial ability tasks, especially thoseinvolving visualization, are able to predict which engineer-ing students will excel in the area of technical drawing(Adanez & Velasco, 2002). Spatial ability and its influenceon performance in academic interests such as mathematicsand the sciences could be very useful tools for educators toassist students in designing appropriate academic paths.

The aim of this study is to understand the role, if any,that specific cognitive abilities play when predictingacademic achievement. Three cognitive constructs mostconsistently recognized in the literature as being impor-tant components of general cognitive ability are workingmemory, processing speed, and spatial ability. The firstgoal of the study was to establish whether generalcognitive ability or a combination of specific cognitiveabilities allowed for the best prediction of academicachievement. The second task was to verify if the specificcognitive abilities could account for unique variancewhen predicting the different measures of academicachievement after controlling for general cognitive ability.In order to determine if domain specific types ofachievement are better predicted by different subsets ofspecific cognitive abilities, the SAT combined score wasbroken down into its two separate components — SATverbal scores and SAT math scores.

1. Method

1.1. Participants

Participants were undergraduate students at a privateMidwestern university and were at least 18 years of ageat the time of the study. Students enrolled in Psychology101 courses received ungraded course credit for

85T.E. Rohde, L.A. Thompson / Intelligence 35 (2007) 83–92

participating in the study. A total of 71 young adults (29males) participated; however, the sample size fluctuatedacross analyses due to missing data.

2. Materials

Participants were assessed individually on a batteryof cognitive tasks measuring working memory, proces-sing speed, spatial ability, general cognitive ability, andacademic achievement. Working memory was assessedwith the Operation Span task (Conway, Conwan,Bunting, Therriault, & Minkoff, 2002) which is acomputer administered task with a Cronbach's alpha of.64. The object of the Operation Span task is to recallunrelated words while attempting to solve simplemathematical operations. A simple math problem andan unrelated word (e.g., “IS 10 /2+2=7? DOG”) aredisplayed on the screen, and participants read the mathproblem aloud, stated whether or not the given answer tothe math problem was correct, and then read aloud theunrelated word. After a series of math problems, a recallcue consisting of three question marks (“???”) promptedthe participants to recall all of the words displayed in theseries by writing the words down on an answer sheet inthe order they were presented [See Conway et al., (2002)for a detailed description of the Operation Span task].

Processing speed was assessed using four timed-tasksrequiring only the simple ability to identify matchingvisual stimuli including shapes, letters, and numbers toarrive at the maximum number of correct answers within agiven time limit. The four paper and pencil processingspeed tasks used to create the processing speed compositescores are described below. The Finding A's task(Ekstrom, French, Harman, & Dermen, 1976) has fourcolumns of words each with 41 words. Only five of thewords in each column contain the letter “a.” The object ofthe task is to circle words containing the letter “a” asquickly as possible within a 60-second period. TheIdentical Pictures task (DeFries, Plomin, Vandenberg, &Kuse, 1981) presents a target picture and five similarpictures. The object of the task is for the participants toidentify from the five similar pictures which option mostclosely resembles the target picture. Participants weregiven 60 s to complete as many items as possible. TheHidden Patterns task (DeFries et al., 1981) is a sheet ofpatterns created from straight lines and a similar targetpattern at the top of the page. The object is to circle thepatterns that have the target pattern embedded, in its givenorientation, within the individual patterns. The participantswere given 2 min to complete as many items as possible.The Matching Letters task (DeFries et al., 1981) is a seriesof nonsense strings of characters containing a combination

of letters and numbers. There are four similar answeroptions to choose from. Only one of the four answeroptions matches the target string of characters. The objectis to circle the option matching the target string ofcharacters. Participants were given 60 s to complete asmany items as possible.

Spatial ability was assessed using three timed-taskswhich required the ability tomentallymanipulate or rotateobjects or shapes in terms of their orientation or positionwithin a given area or space (Carroll, 1993). The threepaper and pencil spatial ability tasks used to create thespatial ability composite scores are described below. Itemsfor the Spatial Relations task (DeFries et al., 1981) eachconsists of a target figure representing a portion of asquare and four multiple-choice figures. The correctresponse for each item is the multiple choice figure whichwhen fitted together with the target figure, makes acomplete square. The participants were asked to completeas many items as possible within a 2-minute period. TheCard Rotation task (DeFries et al., 1981), consists of atarget figure on the left and eight different positions of thetarget figure to the right. The eight items on the right are tobe viewed as cardboard cutouts of the target figure thathave been repositioned either by rotating the figurearound in its given orientation or by flipping the figureover and then rotating it. The object of the task is toidentify which figures have been flipped over, and whichfigures were just rotated. If the figure had been flippedover, the participant drew aminus sign (−) over the figure,and if the figure had just been rotated, the participant drewa plus sign (+) over the figure. Participants were given1.5 min to complete as many items as possible. Items onthe Paper Form Board task (DeFries et al., 1981) consistsof a line drawing of a whole shape and a line drawing ofthat shape broken into “puzzle” pieces. The object is tomentallymanipulate the “puzzle” pieces to determine howthey fit together to create the target shape. The participantsmust draw the lines in the outline of the target shape toillustrate how the “puzzle” pieces fit together to create thetarget shape. The participants were given 2 min tocomplete as many items as possible. As reported byDeFries et al. (1981), the test–retests reliabilities for thefollowing timed-tasks: Identical Pictures, Hidden Pat-terns,MatchingLetters, CardRotation, Paper FormBoardwere greater than .7, and the split-half reliabilities allexceed .8 for these timed-tasks.

General cognitive ability was assessed using theRaven's Advanced Progressive Matrices (Raven's)(Raven, Raven, & Court, 1998a) Set II. Items wereadministered un-timed and scored according to the 1998edition of the manual. The manual reported a test–retestreliability of .91 for an adult population taking the

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Raven's. The Mill Hill Vocabulary Scales (Vocabulary)(Raven, Raven, & Court, 1998b) Senior Form 2: sets Aand B were administered and scored in accordance withthe 1998 edition of the manual. The manual reportedconsistent test–retest reliabilities in excess of .90 forseveral normal adult populations. The Vocabularycomposite score was formed by summing the standard-ized residuals from the scores for Set A and Set B.

Academic achievement was assessed using the WideRange Achievement Test III (WRAT III) (Wilkinson,1993). The WRAT III was administered using the tanseries forms and scored according to the 1993 edition ofthe administration manual. Separate scores were calcu-lated for each of the sub-tests: reading, spelling, andarithmetic. The test–retest alphas are .91, .91, and .88respectively for ages 17 to 24. The sumof the standardizedresiduals formed the WRAT III composite scores.

In addition to the WRAT III, college GPA forfreshmen year, and SAT scores were also used to assessacademic achievement. College GPA and SAT scoreswere collected from the participants' school recordsafter they completed the battery of cognitive tasks.

2.1. Procedures

Each participant voluntarily signed up to be in thestudy, and participants were then contacted by theresearcher or a research assistant to schedule anappointment. Each participant individually completeda battery of cognitive tasks taking an average of 2 h tocomplete. The participants were debriefed, and theiracademic information was obtained from files in theOffice of Undergraduate Studies at a later date.

2.2. Analyses

A guessing correction was applied to the processingspeed and spatial ability tasks. The formula used to makethis correction is R− (W /n−1), where R is the number ofcorrect responses,W is the number of incorrect responses,and n is the number of response options for each item(Ekstrom et al., 1976, p. 10). All scores were corrected forage, age squared, and gender and standardized to have anM of zero and SD of one. The sum of the correctedstandardized residuals for the spatial ability tasks formedthe spatial ability composite, and the sum of the correctedstandardized residuals for the processing speed tasksformed the processing speed composite.

Three multiple regression analyses were used toindividually predict the measures of academic achieve-ment (GPA, WRAT III, SAT). The independentvariables were Raven's, Vocabulary, working memory,

processing speed, and spatial ability. For each of theregression models, the contribution of the independentvariables was assessed simultaneously using the “Enter”method available in the SPSS 11.0 for Windowsstatistical package (SPSS Inc., 1999, 2001).

A series of two-step hierarchical multiple regressionanalyses were used to individually predict the measures ofacademic achievement (GPA, WRAT III, SAT combined,SAT verbal, SAT math). The hierarchical models wereemployed to identify unique variance accounted for by therange of cognitive ability measures when predicting aca-demic achievement. The independent variables were themeasures of general cognitive ability (Raven's, Vocabu-lary) and specific cognitive abilities (working memory,processing speed, spatial ability). The independent vari-ables were entered in two steps. The contribution of theindependent variables in each step was assessed simulta-neously using the “Enter” method. Hierarchical modelscontrol for the variance associated with the independentvariables in step 1 while predicting the dependent variablewith the set of independent variables entered in step 2.

First, the measures of general cognitive ability(Raven's, Vocabulary) were controlled for in step 1before predicting the academic achievement measures(GPA,WRAT III, SATcombined, SAT verbal, SATmath)with the specific cognitive abilities (working memory,processing speed, spatial ability) in step 2. Next, the twostep hierarchical multiple regressions were performedcontrolling for the variance associated with the specificcognitive abilities measures (working memory, proces-sing speed, spatial ability) in step 1 before predicting theacademic achievement measures (GPA, WRAT III, SATcombined, SAT verbal, SAT math) with the generalcognitive ability measures (Raven's, Vocabulary) in step2. These hierarchical multiple regression models werecompared to determine if the prediction of academicachievement was influenced by the degree of overlappingvariance between the specific cognitive abilities (workingmemory, processing speed, spatial ability) and the generalcognitive ability measures (Raven's, Vocabulary).

3. Results

All of the processing speed and spatial ability tasksused to form the composite scores were administeredwith time limits. To confirm that the spatial abilitymeasures could be distinguished from the processingspeed tasks, a factor analysis was performed on thesemeasures. The primary loadings for the spatial abilitytimed tasks all loaded on a spatial factor. The primaryloadings for the processing speed timed tasks all loadedon a separate factor. The results of the factor analysis

Table 2Correlating general cognitive ability academic achievement

Academicachievement

na General cognitive ability

Raven's Vocabulary

GPA 61 .375⁎⁎ .211b

WRAT III 71 .357⁎⁎ .494⁎⁎

SAT combined 64 .389⁎⁎ .688⁎⁎

SAT verbal 64 .295⁎ .709⁎⁎

SAT math 64 .382⁎⁎ .463⁎⁎

Note: The correlations presented above were produced using scorescorrected for age, age squared, and gender. All variables werestandardized to have an M of zero and a SD of one.a The fluctuations in n were due to cases where either SAT scores

went unrecorded in the students' official files or insufficientinformation was available to calculate cumulative GPAs at the timedata analyses were performed.b The correlation between GPA and Vocabulary was not significant.

+p<.10, ⁎p<.05, and ⁎⁎p<.01.

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indicate that these measures are capturing distinctcognitive processes.

The sample consisted of 71 participants (29 males) age18 to 23 years (M=18.86 and SD=1.03). The descriptivestatistics for the academic achievement measures used inthe current study are presented in Table 1. The SATcombined score was designed to have anM of 1000 and aSD of 200, and the SAT verbal and SAT math sectionswere designed to haveMs of 500 and SDs of 100. For the2002 college-bound seniors (n=1,327,831) taking theSAT, the Ms and SDs were: SAT combined scores(M=1020, SD=209), SAT verbal scores (M=504,SD=111), and SAT math scores (M=516, SD=114)(The College Board, 2002). Due to selection, the studysample has a restricted range in academic achievement ascan be seen in the sample Ms and SDs for SAT scorespresented in Table 1. The sample Ms for the SAT scoresare elevated, and the sample SDs for the SAT scores aresmaller than those expected according to the psychomet-ric properties of the SAT and the scores reported for the2002 college-bound population. The sampleMs and SDsfor the percentile scores on the WRAT III sub-tests arealso presented in Table 1 (Wilkinson, 1993). For all of theWRAT III subtests, theMs were above the 70th percentile,and the majority of participants scored above the 75thpercentile (arithmetic computation had 58%, wordrecognition had 63%, and written spelling had 70% ofthe participants scoring above the 75th percentile).

Table 2 presents correlations between measures ofgeneral cognitive ability and academic achievement. The

Table 1Descriptive statistics for measures of general cognitive ability andacademic achievement

Variables n M SD Min Max Median

General cognitive abilityRaven's 71 26.0 5.5 11 36 26Vocabulary 71 56.3 7.0 36 75 56

GPAGPA 61 3.44 0.41 2.44 4.0 3.52

SATSAT combined 64 1355.8 149.2 970 1560 1395SAT verbal 64 662.0 88.5 420 800 680SAT math 64 693.8 83.2 470 800 710

WRAT IIIa

WRAT IIIarithmetic

71 72.8 20.4 19 98 79

WRAT III reading 71 76.6 12.7 39 94 79WRAT III spelling 71 79.8 12.4 34 99 83

Note: TheMs and SDs presented above were not corrected for age, agesquared, and gender.a The descriptive statistics for the WRAT III presented above were

produced using percentile scores uncorrected for age, age squared,and gender.

largest correlation, (r=.709 or ∼49% shared variance),was between SAT verbal and Vocabulary and accountedfor less than 50%of the variance in academic achievement.

The Raven's, Vocabulary, working memory, proces-sing speed, and spatial ability accounted for 16% to 52%of the variance associated with the three indicators ofacademic achievement. The results for three separatemultiple regressions — each predicting a measure ofacademic achievement (GPA, WRAT III, SATcombined)from the following independent variables: Raven's,Vocabulary, working memory, processing speed, andspatial ability are presented in Table 3. None of theindependent variables significantly added to the predic-tion of GPA. The results for the regression of the WRATIII composite scores on general cognitive ability andspecific cognitive abilities measures identified Vocabu-lary (β=.404, p<.05) as the only independent variablesignificantly adding to the prediction of this measure ofacademic achievement. Lastly, when predicting the SATcombined from the same independent variables, bothgeneral cognitive ability and specific cognitive abilitiesmeasures added significantly to the prediction of SATcombined scores: Raven's (β=.194, p<.05), Vocabulary(β=.618, p<.05), and processing speed (β=− .229,p<.05). The adjusted R2 for each of the three regressionsindicated that the predictors were accounting for asignificant amount of total variance in each of the threemeasures of academic achievement (GPA, WRAT III,SAT combined). Additionally, the adjusted R2 increasedin magnitude from .158, p<.05 for GPA to .205, p<.05for the WRAT III and .539, p<.05 for the SATcombined.

Three hierarchical multiple regressions were per-formed, each predicting one of the measures of academicachievement (GPA, WRAT III, SAT) with the Raven's

Table 3Regression results predicting academic achievement with generalcognitive ability and specific cognitive abilities

Independentvariables

Dependent variables

GPA WRAT III SATcombined

n β n β n β

Raven's 61 .224+ 71 .194+ 64 .194⁎

Vocabulary 61 .020 71 .404⁎ 64 .618⁎

Working memory 61 .203 71 .017 64 .081Processing speed 61 .135 71 − .023 64 − .229⁎Spatial ability 61 .137 71 .122 64 .151

Note: Fluctuations in n are due to availability of GPA and SAT scores.+p<.10, ⁎p<.05, and ⁎⁎p<.01.

Table 5Hierarchical regression results predicting SAT verbal and SAT mathwith working memory, processing speed, and spatial ability whilecontrolling for Raven's and Vocabulary

Independentvariables

Dependent variables

Change in R2:SAT verbala

Change in R2:SAT matha

Step 1Raven's .511⁎ .287⁎

VocabularyStep 2Working memoryProcessing speed .032 .132⁎

Spatial ability

Note: The independent variables were entered in two steps. In step 1,the independent variables are held constant. The change in R2 for step2 indicates the amount of unique variance accounted for by theindependent variables in step 2.+p<.10, ⁎p<.05, and ⁎⁎p<.01.a n=64.

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and Vocabulary, while controlling for working memory,processing speed, and spatial ability. When predictingGPA, Raven's, and Vocabulary did not account for anyadditional variance once working memory, processingspeed, and spatial ability were controlled for. For theprediction of the WRAT III, the Raven's and Vocabularycontributed an additional 20% (change in R2 for step2= .200, p<.05) of unique variance after controlling forworking memory, processing speed, and spatial ability.When predicting SATcombined scores while controllingfor working memory, processing speed, and spatialability, the Raven's and Vocabulary accounted for anadditional 39% (change in R2 for step 2= .386, p<.05)of unique variance. Furthermore, step 1 was alsoaccounting for a significant amount of variance (changein R2 for the step 1= .176, p<.05).

Three similar hierarchical multiple regressions wereperformed, each predicting one of the measures of aca-

Table 4Hierarchical regression results predicting SAT verbal and SAT mathwith Raven's and Vocabulary while controlling for working memory,processing speed, and spatial ability

Independentvariables

Dependent variables

Change in R2:SAT verbala

Change in R2:SAT matha

Step 1Working memoryProcessing speed .063 .272⁎

Spatial abilityStep 2Raven's .479⁎ .138⁎

Vocabulary

Note: The independent variables were entered in two steps. In step 1,the independent variables are held constant. The change in R2 for step2 indicates the amount of unique variance accounted for by theindependent variables in step 2.+p<.10, ⁎p<.05, and ⁎⁎p<.01.a n=64.

demic achievement (GPA, WRAT III, SAT combined),while controlling for the Raven's and Vocabulary. WhenpredictingGPAand theWRAT III, the unique contributionof working memory, processing speed, and spatial abilityaccounted for between 1% and 8% of the variance but didnot reach significance. When predicting SAT combinedscores, working memory, processing speed, and spatialability accounted for approximately 5% (change in R2 forstep 2=.051, p<.10) of unique variance.

When using the same hierarchical multiple regres-sion methods to individually predict SAT verbal andSAT math achievement scores, the Raven's andVocabulary continued to account for unique varianceafter controlling for working memory, processing speed,and spatial ability (See Table 4). After controlling for theRaven's and Vocabulary; no additional variance in SATverbal scores was accounted for by working memory,

Table 6Standardized coefficients for the hierarchical regression modelpredicting SAT math with working memory, processing speed, andspatial ability while controlling for Raven’s and Vocabulary

Independent variables β

Step 1Raven's .264⁎

Vocabulary .395⁎

Step 2Working memory .132Processing speed − .261⁎Spatial ability .368⁎

Note: The independent variables were entered in two steps. In step 1,the independent variables are held constant. The change in R2 for step2 indicates the amount of unique variance accounted for by theindependent variables in step 2. n=64.+p<.10, ⁎p<.05, and ⁎⁎p<.01.

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processing speed, and spatial ability. However, whenpredicting SAT math scores while controlling for theRaven's and Vocabulary, an additional 13% (change inR2 for step 2= .132, p< .05) of unique variance wasaccounted for by working memory, processing speed,and spatial ability (See Table 5).

Table 6 presents the βs for each independent variablein the hierarchical multiple regression predicting SATmath scores after controlling for the Raven's andVocabulary. The results show that processing speed(β=− .261, p<.05) and spatial ability (β=.368, p<.05)were significant predictors of SATmath scores. The posthoc power analysis estimates power to be .8861 for amedium effect size ( f 2 = .2271).

4. Discussion

Some researchers in the area of education have atendency to view ‘g’ as an irrelevant statistic and suggestthat measures of general cognitive ability simply assessschool-related achievement or acquired knowledge (Ceci,1994). Ceci's 1991 review of the education literature ongeneral intelligence attributes the relationship between IQand achievement to the circumstances encountered in thelearning environment.Much of the literature cited byCeciinvestigated varying features of education such as accessto education, age when first exposed to formal education,years of education completed, and quality of educationreceived. Because IQ scores fluctuated when changesoccurred in the educational environment, Ceci argues thatit is more accurate to view IQ measures as nothing morethan assessments of school-related achievement.

Conversely, the broad literature on ‘g’ defines generalcognitive ability and academic achievement as twostrongly related yet distinct constructs. An important factto note about the relationship between general cognitiveability and academic achievement is that they are notable to perfectly predict one another. In fact, more than50% of the variance in academic achievement cannot beaccounted for by measures of general cognitive abilityalone (Jensen, 1998). While the considerable amount ofshared variance between these constructs is well estab-lished in the literature, it may not be appropriate to as-sume that they are equivalent.

The current study examined how well specificcognitive abilities can predict academic achievement.Working memory, processing speed, and spatial abilityare specific cognitive abilities identified in the literatureas good candidates for influencing academic perfor-mance beyond general cognitive ability (Conway et al.,2002; Fry & Hale, 1996; Jensen & Munro, 1979;Lubinski, Webb, Morelock, & Benbow, 2001; Luo &

Petrill, 1999). The collective and individual contribu-tions to academic performance were assessed for thesespecific cognitive abilities. Although the measures ofgeneral cognitive ability significantly correlated withmeasures of academic achievement, general cognitiveability alone was unable to account for more than 50% ofthe variance associated with academic achievement.When predicting the measures of academic achievementfor young adults with both general and specific cognitiveabilities, the measures of general cognitive ability(Raven's, Vocabulary) were superior to the specificcognitive abilities. General cognitive ability measures(Raven's, Vocabulary) and specific cognitive abilities(working memory, processing speed, spatial ability)collectively accounted for between 16% and 54% of thevariance in academic achievement. In order to tease apartthe influence of general cognitive ability from that ofworking memory, processing speed, and spatial ability,hierarchical multiple regression techniques wereemployed. After partialling out working memory,processing speed, and spatial ability; measures of generalcognitive ability continued to add to the prediction of theacademic achievement measures. After partialling outthe measures of general cognitive ability, the specificcognitive abilities did not account for any additionalvariance in GPA or the WRAT III scores. In contrast,specific cognitive abilities were able to add significantlyto the prediction of SAT combined scores after themeasures of general cognitive ability had been partialedout.

The SAT combined score is the sum of the scores forthe verbal and arithmetic sections of the SAT. For theindividual SAT verbal and SATmath scores, the measuresof general cognitive ability accounted for unique varianceafter partialling out working memory, processing speed,and spatial ability. However, different trends emerged forthe SAT verbal and SAT math scores when predictingthese scores with the measures of general cognitive abilitypartialled out first. Measures of general cognitive abilitycontinued to be superior predictors overworkingmemory,processing speed, and spatial ability for SAT verbal. Incontrast, spatial ability and processing speed continued toaccount for a significant amount of additional variancewhen predicting SAT math scores with the measures ofgeneral cognitive ability partialled out. These resultssuggest that general cognitive ability, spatial ability, andperceptual speed each make important contributions tomathematical achievement.

The findings of the current study replicated andextended the previous findings of Luo et al. (2003) andLubinski's work with gifted populations. The recom-mendation by Luo et al. (2003) to define psychometric

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‘g’ with a combination of specific cognitive abilities andtraditional measures of general cognitive ability is to acertain extent supported by the current findings. Factorsoutside of general cognitive ability appear to beinfluencing broad areas of academic achievement. Inaddition to the specific cognitive abilities used by Luo etal. (2003), the current study was able to add spatialability tasks to the list of cognitive measures useful inaccounting for academic achievement. This type ofdetailed approach may offer the added informationneeded to identify the underlying sources of academicstrengths and weaknesses. Specifically, accounting foradditional variance in a measure of mathematicalachievement with spatial ability lends support to thebody of work by Lubinski et al. (2001). They identifiedspatial ability as uniquely important to mathematicalachievement after accounting for general cognitiveability in extremely gifted samples. While it is possiblethat these findings only apply to extremely giftedpopulations, the current study shows that the relationshipbetween mathematical achievement and spatial abilityextends to a college sample. Although the current samplealso has a restricted range in academic achievement, it isnot as highly selected as the sample studied by Lubinskiand colleagues. This suggests that the relationshipbetween mathematical achievement, general cognitiveability, and spatial ability are robust associations that canextend to samples with a wider range of mathematicalability (e.g., Lubinski et al., 2001; Shea et al., 2001).Because the current findings are based on a relativelysmall sample from a gifted population, these findingswill need to be replicated in a larger more diverse samplein order to gage the full extent of the association betweenspatial ability and mathematical achievement.

The association between spatial ability and mathe-matical achievement needs to be explored further. Thefirst step is to develop a method to identify the source ofthe relationship between mathematical achievement andspatial ability. There are some indications in the literaturethat both spatial ability and mathematical achievementare constructs that could be broken down even further. InCarroll's (1993) proposed structure of cognitive abilities,his extensive factor analysis identified a broad visualperception factor characterized by a collection of 11 sub-factors. Of these 11 factors, Carroll (1993) designated thefollowing five factors: spatial relations, closure speed,flexibility of closure, visual perceptual speed, andvisualization as the major classifications of broad visualperception because they were consistently identified inhis series of factor analyses (Carroll, 1993, pp. 308–315). Visualization and spatial relation tasks involvemental manipulation of visual stimuli. Closure speed and

flexibility of closure require the ability to fill in themissing portions of visual stimuli or identify visualstimuli that has been distorted in some manner.Perceptual speed is measured by the speed with whichvisual stimuli are matched to or compared with a targetfigure. It makes intuitive sense that these five factors maynot equally influence mathematical ability because thetasks are very different form one another and vary inrelative difficulty. The literature suggests that the mentalmanipulation of visual stimuli may be the most salientaspect of spatial ability for the prediction of both theeducational choices and occupational success of math-ematically gifted populations (Humphreys, Lubinski, &Yao, 1993; Shea et al., 2001). The remaining three spatialfactors: closure speed, flexibility of closure, andprocessing speed may also be important to mathematicalability although perhaps to a lesser degree. These factorsrely on what Carroll (1993, pp. 308–315) describes asmore basic composites of spatial abilities. For example,simply identifying or recognizing relationships in fixedvisual stimuli requires no mental manipulation, but itdoes involve a rudimentary visual assessment of thestimuli.

Carroll's (1993) model of the five spatial ability factorsallows one to test the degree to which each factor of spatialability influences mathematic ability. The same could betrue of mathematical skills. Spatial ability may be moreinfluential on somemath skills over others, but the divisionof math skills into basic components is somewhat am-biguous. An approach that may be useful is the frameworkused for the study of spatial ability and its relationship tomath disabilities. Geary (1993) has proposed several sub-types of math disability including a visuospatial subtypethat specifically identifies spatially relevant math skills. Inthe same way that reading disabilities have helped to shedlight on the array of skills involved in reading ability as awhole, the subtypes of math disabilities may also help topinpoint skills involved in overall math ability.

Acknowledgements

This research was funded by the following grants:HD07176 from the National Institute of Child Healthand Human Development, Office of Mental Retardation;a Predoctoral Fellowship for Students with Disabilities(5F31HD41926-03) from the National Institute of ChildHealth and Human Development; R01 HD046167-01;and R01 HD038075-03. Caley Schwartz and HeatherGilmore assistance in the collection of the data for thecurrent study was greatly appreciated. I also thankAndrew Conway (2002) for supplying me with theworking memory task used in the current study.

Appendix A

Table 7Correlation matrix of raw scores for the measures used in the current study

1 2 3 4 5 6 7 8 9 101. SAT combined –

n 642. SAT verbal .877⁎⁎ –

n 64 643. SAT math .860⁎⁎ .509⁎⁎ –

n 64 64 644. GPA .357⁎⁎ .270⁎ .356⁎⁎ –

n 59 59 59 615. WRAT III .577⁎⁎ .426⁎⁎ .508⁎⁎ .288⁎ –

n 64 64 64 61 716. Raven's .430⁎⁎ .299⁎ .453⁎⁎ .308⁎ .390⁎⁎ –

n 64 64 64 61 71 717. Vocabulary .668⁎⁎ .694⁎⁎ .460⁎⁎ .203 .440⁎⁎ .313⁎⁎ –

n 64 64 64 61 71 71 718. Processing speed − .030 − .020 − .032 .289⁎ .133 .122 .135 –

n 64 64 64 61 71 71 71 719. Spatial ability .270⁎ .115 .362⁎ .306⁎ .241⁎ .252⁎ .218 .416⁎⁎ –

n 64 64 64 61 71 71 71 71 7110. Working memory .235 .170 .240 .241 .120 .278⁎ .328⁎⁎ .108 .066 –

n 64 64 64 61 71 71 71 71 71 71

⁎p<.05, and ⁎⁎p<.01.

91T.E. Rohde, L.A. Thompson / Intelligence 35 (2007) 83–92

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