1

7LWOH� The assessment of spatial ability through a single computerized test 1

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Roberto Colom Mª José Contreras Pei Chun Shih José Santacreu $IILOLDWLRQ� Facultad de Psicología Universidad Autónoma de Madrid 28049 Madrid (Spain) &RUUHVSRQGLQJ�DXWKRU�

Roberto Colom Facultad de Psicología Universidad Autónoma de Madrid 28049 Madrid (Spain) Email: roberto.colom@uam.es�

Paper IN PRESS (European Journal of Psychological Assessment)

1 This research was partially supported by the project AENA-UAM/ 785001.

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Summary

Spatial cognitive ability has to do with how individuals deal with spatial information. Spatial

ability is routinely assessed to predict performance in a variety of job positions. Air Traffic

Control is an example. Spatial tests are good predictors of performance in those

occupations. One of the most valuable knowledge for psychological assessment in

personnel selection is the one about efficient ways to measure a given psychological trait.

“Efficient way” means that the measure shows high validity and low application cost. This

article reports two studies showing the high efficiency of a new measure of spatial ability:

SODT-R. This is a computer-administered test of dynamic spatial performance in which

the person is required to simultaneously orient two moving points to a given destination

that change from trial to trial. In the first study, 602 applicants for an Air Traffic Control

training course completed a battery of nine cognitive tests. In the second study, 105

University undergraduates completed a battery of eleven tests. Both batteries comprise

tests of reasoning, visualization, spatial relations, and dynamic spatial performance. SODT-

R emerges as a good measure of general spatial ability (Gv). This is especially true in the

second study, where a broader sample of spatial tests is considered. A theoretical account

based on the well-known high correlation between working memory capacity and cognitive

abilities is discussed.

Keywords

Spatial ability, Visualization, Spatial relations, Dynamic spatial performance, Working

memory, General intelligence, Personnel selection.

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INTRODUCTION

Cognitive abilities in the domain of visual perception have to do with how

individuals deal with materials presented in space. However, as it was stated by Carroll

(1993) “considerable confusion exists about the identification of factors in this domain (...)

tests do not always load consistently on distinct factors, or they load rather indiscriminately

on a number of factors” (p. 308). Most spatial tests are quite complex, requiring a variety of

processes like apprehension and encoding of spatial forms, mental manipulation of these

forms, decision making about comparisons, or still another actions.

Visualization (Vz) and Spatial Relations (SR) are two main factors of spatial ability

that usually emerge in factor-analytic studies (French, 1951; Ekstrom, French, & Harman,

1976; Lohman, 1979, 1987, 2000; Carroll, 1993). Vz refers to the ability to mentally

manipulate visual patterns, as indicated by level of difficulty and complexity in visual

material that can be handled successfully under relatively un-speeded conditions. Usual

marker tests for Vz are classified in six categories: paper form-board tasks, block tasks,

block rotation tasks, paper folding tasks, surface development tasks, and perspective tasks

(Eliot & Smith, 1983). SR refers to the speed in manipulating relatively simple visual

patterns by mentally rotating or transforming them. Speed in apprehending the stimulus

and rotating them seems critical aspects of this factor. The best markers fall under the

category “Figural Rotation Tasks” as described by Eliot and Smith (1983). SR also includes

the so-called spatial orientation (SO) tests (French, 1951; Lohman, 1987).

Several studies have identified still other spatial factors derived from dynamic

testing (Pellegrino, Hunt, Abate, & Farr, 1987; Hunt, Pellegrino, Frick, Farr, & Alderton,

1988; Law, Pellegrino, & Hunt, 1993; Contreras, Colom, Shih, Álava, & Santacreu, 2001;

Contreras, Colom, Hernández, & Santacreu, 2002). Dynamic spatial tasks test the ability to

perceive and extrapolate real motion, to predict trajectories of moving objects and to

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estimate arrival times of two or more objects. Dynamic spatial performance (DSP) is

measurable preferably in the context of computerized testing.

Spatial ability is usually measured to predict efficient performance in a variety of job

positions. Vz and SR can be measured by printed tests, while dynamic spatial performance

is preferably measured by computerized tests (Pellegrino et al., 1987; Hunt et al., 1988;

Pellegrino & Hunt, 1989; Contreras, Colom, et al., 2001). Pellegrino et al. (1987) and

Contreras, Colom, et al. (2002) heavily recommend the use of dynamic spatial tests in

addition to the static ones, because they could significantly increase predictive validity in

some occupations. Air Traffic Control (ATC) is an example. Ackerman & Kanfer (1993)

developed a test battery for predicting air traffic control training success. They assessed

several abilities like reasoning, spatial visualization, numerical ability, spatial memory, and

spatial time estimation. Spatial and reasoning tests had the highest validities. However, only

static spatial tests were considered.

Several markers of Vz, SR, and DSP are routinely considered in personnel selection.

However, Colom, Contreras, Botella, & Santacreu (2002) found that Vz, SR, and DSP

markers show high loadings in a powerful hierarchical higher-order factor designated as Gv

(general spatial ability). Their data demonstrates that a) within the spatial ability domain,

there is a strong single source of variance, and b) it is difficult to separate specific spatial

tests by construct (Vz and SR are some examples). The latter statement agrees with

Carroll’s (1993) famous survey of factor-analytic studies. The implication is noteworthy: it

could be possible to design a single measure tapping core spatial ability processes.

A valuable knowledge for psychological assessment in personnel selection is the

one about efficient ways to measure a given psychological trait. Schmidt & Hunter (1998)

reviewed 85 years of research findings in personnel selection. In their own words “ in the

pantheon of 19 personnel measures, JHQHUDO�FRJQLWLYH�DELOLW\ occupies a special place” (p. 264,

italics added). Among the reasons they gave, one is especially germane for the present

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studies: general cognitive ability has the highest validity and lowest application cost. :RUN�VDPSOH�PHDVXUHV, for instance, are slightly more valid but they are much more costly.

Moreover, work sample measures can be used only with applicants who already know the

job.

The present studies look for empirical evidence about a main question, namely,

what is a good measure of spatial ability with a low application cost. If general spatial ability

(Gv) can be measured reasonably well through a single test, then it will be less germane

(although interesting) to consider several diverse measures. This will translate into less time,

effort, and cost.

STUDY 1

METHOD�3DUWLFLSDQWV�The sample comprised 602 university graduates. They were applicants for an Air

Traffic Control Training program. The mean age was 27.79 (SD=3.88). Half of the

applicants were females. The sample was randomly selected from the total population of

applicants. It is interesting to note that the graduates come from several diverse carrers:

humanities, social sciences, sciences, and engineering.

�0HDVXUHV�DQG�3URFHGXUHV�A battery of printed and computerized tests was applied. Participants completed the

tests in two separate sessions. One of them was dedicated to the printed tests and the other

to computerized testing.

Test description is organized by construct.

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SR (Spatial Relations)

Identical figures (Manzione, 1978). The person must decide as soon as possible

which of five possible astract figures matches a given model figure.

Rotation of solid figures (Yela, 1969). Five different solid figures are presented.

Each figure display a three dimensional solid block. The person must decide which figure

matches a given model figure seen from another perspective.

Vz (Visualization)�Bricks (Manzione, 1978). A block of bricks is presented. The block represents a

three-dimensional figure. The person must compute how many bricks build up the block

choosing among five alternatives.

Printed Puzzles I and II (Yela, 1974). This test closely resembles the well-known

Paper-Form Board Test. Several black figures are displayed on the left. A white figure is

displayed on the right. The person must decide which one of the black figures must be

ignored to build up the white figure. To give the answer, the person must use rotation and

synthesis spatial processes (Lohman, 1979).

DSP (Dynamic Spatial Performance)

Spatial Orientation Dynamic Test (SODT) and Spatial Visualization Dynamic Test

(SVDT) (Santacreu & Rubio, 1998). The dynamic spatial tests were programmed in

Borland C++. The person must direct simultaneously two moving points to a given

destination. The destination changes from trial to trial and the two moving points could

come from the north, the east, or the west of the computer screen. For directing the two

moving points, the participant must use a digital compass linked to each of them (see

Figure 1). In the SODT, the participant can see the whole screen, while in the SVDT the

participant can see only the points for a few seconds before they are hidden by a black

band (the participant must ‘visualise’ the moving points after the information given by the

digital compass; see more details in Contreras et al., 2001). These computerized tests were

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applied in groups of ten people. The administration of each computerized test takes about

10 minutes of effective work. Each test consists of 10 trials.

PLEASE INSERT FIGURE 1 ABOUT HERE�Reasoning�Bonnardel Series Test (BLS-IV) (Bonnardel, 1970). This is a series test. Three

figures serve as model. They are related through a rule that the person must find. The task

is to apply the extracted rule to “ draw” the answer.

Changes (Seisdedos, 1994). Five figures are displayed. The second and the forth

one include information about the similarity between the first and the third one and

between the third and the fifth one, respectively. Thus, for instance, there will be some

“ changes” in the third figure with respect to the first one. The changes are indicated in the

second figure, but these changes could not be correct. The changes refer to the number of

sides, the size, and the background.

�$QDO\VHV The correlation matrix (see Appendix) is submitted to a hierarchical factor analysis

(Schmid-Leiman transformation, SL). The SL procedure is highly recommended within the

abilities literature (Carroll, 1993; Jensen, 1998; Loehlin, 1998). It divides common factor

variance in terms of factors with differing generality making all the factors orthogonal to

one another, both between and within levels of the hierarchy. The higher order factors are

allowed to account for as much of the correlation among the observed variables as they

can, while the lower order factors are reduced to residual factors uncorrelated with each

other and with the higher order factors. A principal axis factoring was performed, followed

by a Promax rotation.

The interpretation of the factor matrix is straightforward: the higher the loading,

the best is the measure as representative of the respective factor. We look first at the

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proportion of common variance explained by the extracted factors. Then, the measures’

factor loadings are considered. Higher loadings indicate that the measure nicely represent

the factor. Therefore, good measures must show high loadings (Carroll, 1993).

RESULTS AND DISCUSION

Table 1 shows the factor matrix. The higher-order factor explains much more

common variance than the sum of the three first-order factors. Therefore, the higher-order

factor must be considered as the most powerful source of variance.

PLEASE INSERT TABLE 1 ABOUT HERE

F1 is loaded by the dynamic spatial tests. F2 is loaded by the printed spatial tests.

Finally, F3 is loaded by the reasoning tests. Note that SR and Vz tests do not define

separate factors. Therefore, some doubts can be raised about the nature of the construct

tapped by the printed spatial tests (see Colom, Contreras, et al., 2002).

The higher-order factor can be psychologically interpreted as representative of

general spatial ability or Gv: the nine tests show salient loadings on this higher-order factor,

ranging from .366 to .696. The mean loading is .530. Although the dynamic spatial tests do

not deviate from the latter value, they do not show the highest loadings. Anyway, it must

be noted that SODT and SVDT are more efficient Gv measures than the remaining spatial

tests. Dynamic tests are efficient in the sense that they show high Gv loadings at a low

application cost.

However, we are searching for an efficient measure of spatial ability showing very

high loadings on Gv and low cost of administration. It is imperative to remember that the

application cost is crucial in personnel selection (Schmidt & Hunter, 1998). It could be

possible to find other measures with high loadings on Gv, but their application cost also

counts.

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STUDY 2

The study 2 was designed to replicate, refine, and expand the findings reported in

the study 1. The specific changes follow:

(1) The dynamic spatial tests were modified trying to increase their loadings

and, therefore, their power as measures of spatial ability. Note that the

correlation between SODT and SVDT in the study 1 was .694, which

suggest that there is a close similarity between both measures. A lower

correlation between the dynamic tests is pursued.

(2) A new battery of printed spatial tests was selected. Better-known measures

of Vz and SR were considered.

(3) Three computerized tests were included in the battery, in addition to the

modified dynamic spatial tests, to avoid the definition of factors by type of

presentation (computerized vs printed).

METHOD�3DUWLFLSDQWV�105 psychology undergraduates took part in the study 2. They were paid volunteers.

(YHU\�SDUWLFLSDQW�UHFHLYHG���� �DQG�WKH�ILYH�EHVW�VFRUHUV�UHFHLYHG�DQ�DGGLWLRQDO�UHZDUG�RI���� ��7KH�SDUWLFLSDQWV�ZHUH�LQIRUPHG�DERXW�WKH�DGGLWLRQDO�UHZDUG�IRU�SHDN�SHUIRUPHUV�����participants were females and 16 were males. The mean age was 18.79 (SD= 2.3).

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0HDVXUHV�DQG�3URFHGXUHV A battery of printed and computerized tests was applied. Participants completed all

the tests in two sessions. One was dedicated to the printed tests and the other to

computerized testing.

The tests are described by construct.

SR (Spatial Relations)

&RRUGLQDWHV (Secadas, 1960). A coordinate system is presented. Within the system,

there are some points. The person must decide about the numbers that correspond to the

axes (X and Y) that locate the points.

7UDMHFWRULHV (Germain & Pascual, 1969). Four arrows represent the curve trajectories

of four cars. 5 points are proposed as passing points of the curve trajectories that the cars

must presumably follow. The person is asked to decide which point is within the cars’

trajectories.

$UURZV (Juan-Espinosa, Abad, Colom, & Fernández-Truchaud., 2000). The person

is asked to imagine that a long arrow indicates the direction of a travel and a short arrow

(associated with the long one) indicates a deviation onto which he/ she could turn. The

person must decide, as soon as possible, whether she/ he has turned to the right or to the

left, depending on both of the arrows, the long and the short one, presented on the

computer screen.

0DSV (Juan-Espinosa, Abad, et al., 2000). The person read a route (a set of

directions) on the computer screen and then a street map with four different coloured

routes appears. Below the map, four rectangles with the route colour are shown. The

person must decide which of the coloured routes represents the route described at first.

(OLRW�'RQQHOO\�%�)�WHVW (Eliot & Donnelly, 1978). A chair is located inside a room.

There are five points located in five different places of the room (floor, back, front, and so

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forth). The person task is to decide from which point is possible to see the chair as

indicated by a chair-model presented outside of the room.

30$�6 (Thurstone, 1938). The person must decide which of six possible

alternatives are rotated or inverted versions of a given figure that serve as the model figure.

Vz (Visualization)

6XUIDFH�'HYHORSPHQW (Thurstone & Thurstone, 1949). The person must fold a piece of

paper to form a solid figure. Then, she/ he must decide the correspondence among several

numbers and letters in the unfolded and the folded pieces, respectively.

Dynamic Spatial Tests

&URVV�7UDMHFWRULHV�7HVW��&77� (Santacreu, 1999). Two moving points appear on the

computer screen coming from different places. Both points move at a constant speed.

They stop in an unpredictable moment. The person’s task is to manipulate the path of one

of the points, so it will contact the second point in a “ predicted” given destination. TCT is

also a measure of SR.

6SDWLDO�2ULHQWDWLRQ�'\QDPLF�7HVW�5HYLVHG��62'7�5��DQG�6SDWLDO�9LVXDOL]DWLRQ�'\QDPLF�7HVW�5HYLVHG��69'7�5� (Santacreu, 1999). In the revised version of these dynamic spatial

tests, the participant’s task is the same as in the original version: to simultaneously direct

two moving points to a given destination. The destination changes from trial to trial and

the two moving points could come from the north, the east, or the west of the computer

screen. However, for directing the two moving points, the person must use a digital

compass linked to each of them in the SVDT-R, but not in the SODT-R. For the latter

test, the person must direct the moving points through a box with two arrows linked to

each moving point. One arrow moves the point in a given direction, while the other arrow

moves it in the opposite direction (see Figure 2). Furthermore, in the SVDT-R the moving

points are not hidden by a black band; the points simply disappear from the computer

screen. Therefore, the digital compass still play a role in the SVDT-R, but no in the SODT-

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R. Each dynamic test comprises 10 trials. The administration of each test takes about 10

minutes of effective work.

PLEASE INSERT FIGURE 2 ABOUT HERE

Fluid intelligence (Gf)

&DWWHOO·V�&XOWXUH�)DLU�,QWHOOLJHQFH�7HVW (TEA, 1997). This is the test of fluid intelligence

(Gf) developed by R.B. Cattell. The Scale 3 was administered.

$QDO\VHV The same analyses as in the study 1 were performed. The correlation matrix is

shown in the Appendix.

RESULTS AND DISCUSION

Table 2 shows the factor matrix. As in the study 1, the higher-order factor explains

much more common variance that the sum of the first-order factors. Therefore, the higher-

order factor is the most powerful source of variance.

PLEASE INSERT TABLE 2 ABOUT HERE

The first-order factors are not psychologically interpretable. They are loaded by

tests not defining SR, Vz, or DSP spatial factors. Therefore, no more attention is paid to

these factors.

The higher-order factor is loaded by all the spatial tests, as well as by the Cattell

Culture Fair test. Therefore, the higher-order factor represents general spatial ability (Gv).

The loadings range go from .146 to .706. The mean loading is .506.

Looking at Gv, we can see that surface development and SODT-R show the

highest loadings. The Eliot-Donnelly test also shows a high loading. Surface development

is a usual Vz marker, while the Eliot-Donnelly test is a common SR marker. SODT-R

shows a Gv loading very close to that of two of the best markers of the most remarkable

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spatial abilities (Carroll, 1993; Lohman, 2000). Therefore, SODT-R could be considered a

good measure of Gv or general spatial ability.

It is noteworthy that SVDT-R shows a poor Gv loading. Thus, the changes

introduced in this dynamic spatial test had an effect contrary to the expectations.

Moreover, the correlation between SODT-R and SVDT-R is .269. Therefore, SVDT-R

cannot be used as a good measure of Gv.

In summary, the study 2 shows that SODT-R can be considered an appropriate

measure of general spatial ability. It should be remembered that it takes no more than 10

minutes of administration and that the person’s score is available in a matter of seconds.

What this means is that SODT-R seems to be a test especially appropriate to assess general

spatial ability. “ Appropriate” means highly efficient: a good vehicle to measure a central

cognitive ability in personnel selection (Schmidt & Hunter, 1998). Although the surface

development test and the B-F test also show high Gv loadings, their application cost is

considerable higher.

GENERAL DISCUSION

Spatial ability is a good predictor of performance in occupations like Air Traffic

Control. Ackerman & Kanfer (1993) demonstrated that spatial tests along with reasoning

tests show the highest validities. Therefore, a measure of spatial ability tapping the core of

general spatial cognitive ability (Gv) will be a valuable assessment tool. This value increases

if the measure takes a brief period of time to both administer it and to obtain the scores. In

other words, the preferred measure must show high validity and low application cost

(Schmidt & Hunter, 1998). This is not to say that other measures are not valuable.

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The studies reported in the present article show that SODT-R fits pretty nicely the

requirements for a good assessment tool in personnel selection:

(A) Show high loadings in a higher-order factor representing general spatial ability

(Gv).

(B) Its Gv loading is very close to the loadings of two of the best markers of the

most central spatial abilities, namely, Visualization (Vz) and Spatial relations

(SR).

(C) Given that spatial tests are good predictors of performance in occupations as

Air Traffic Control, it can be concluded that a test who behaves very closely to

traditional measures of spatial ability will be also predictive of performance in

those kind of occupations. SODT-R is such test.

(D) The administration takes no more than 10 minutes of effective work.

(E) The person’s score is available in a matter of seconds.

A reviewer of the present article states that it must be demonstrated that SODT

and SODT-R are measuring the same construct. Fortunately, 208 applicants for an Air

Traffic Control training course (110 males and 98 females) completed the SODT and the

SODT-R in two moments separated by 1 year. The correlation between both measures was

.621 (S < .01). This shows that the old and new versions of this dynamic test are measuring

close spatial facets.

Another reviewer noted the possible effect of the high number of female

participants in the second study. However, Contreras, Colom, et al. (2001) demonstrated

that spatial tests require the same cognitive ability in males and females. It is true that males

outperform females in spatial tests (Voyer, Voyer, & Bryden, 1995), but this is not

15

equivalent to say that spatial tests do not measure the same spatial ability in both sexes.

Contreras, Colom, et al. (2001) computed the congruence coefficients for several factors

representing general spatial ability, dynamic spatial performance, static spatial performance,

and reasoning. The obtained values were + .984, + .959, + .82, and +.84, respectively. Those

results demonstrated that spatial tests measure the same underlying ability irrespective of

sex. Thus, the high number of females in the second study can hardly explain the observed

results.

As can be seen in Figure 2, the SODT-R requirements are easily understood. The

person must “ orient” simultaneously two points crossing the computer screen at a constant

speed. The orientation depends on a destination point to which the moving points must be

directed. There is a keyword within the task description that must help to explain why

SODT-R shows high loadings in the higher-order factor representing general spatial ability

(Gv): simultaneously.

General cognitive ability (J) is strongly related to working memory capacity

(Kyllonen & Christal, 1990; Stauffer, Ree, & Carreta, 1996; Colom, Flores-Mendoza, &

Rebollo, in press; Colom, Palacios, Kyllonen, & Juan-Espinosa, 2001). Working memory

capacity is especially strained in dual tasks: the higher the strain imposed over the person’s

working memory, the higher the correlation with measures of J (Jensen, 1998). It is

reasonable to state that SODT-R strains the person’s working memory, and, therefore, that

SODT-R must be highly J-loaded. The requirement of simultaneously direct two moving

points to any given destination that changes from trial to trial, closely resembles a typical

dual task. SODT-R cognitive complexity requires several cognitive processes associated

with spatial performance. Given that SODT-R is highly Gv loaded, then it could be

presumed that SODT-R taps several central spatial processes.

16

The latter argument agrees with the fact that the persons’ Gv factor scores are

highly correlated with the Cattell Culture Fair test in the second study. The computed

correlation is + .6 (S<.01, see Appendix). Therefore, it can be postulated that the

performance at the SODT-R is highly Gv loaded, but also J-loaded. This is further

evidence showing that SODT-R can be an appropriate assessment tool of general spatial

ability.

In summary, SODT-R can be recommended as an assessment tool in personnel

selection. There are empirical, theoretical, and practical reasons. First, SODT-R shows

salient loadings in a higher-order factor representing general spatial ability. Second, the

loadings of this dynamic test can be interpreted as indicative of the fact that SODT-R taps

central spatial mental processes. Last, but not least, the application cost is extremely low.

However, it must be recognised that we do not have direct evidence about the SODT-R

predictive validity. Further research will complete the promising empirical evidence found

in the present studies.

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19

FIGURE 1

Spatial Orientation Dynamic Test (SODT). The person must direct simultaneously the two moving points to the destination displayed at the bottom of the computer screen. The participant must use the digital compass

displayed at the top of the computer screen.

20

�

Figure 2

Spatial Orientation Dynamic Test-Revised (SODT-R). The participant must simultaneously direct the two moving points to the destination displayed at the bottom of the computer screen. The participant must use

the box displayed at the top of the computer screen.

21

Table 1 Hierarchical factor analysis. Study 1.

Tests Gv Factor 1 Factor 2 Factor 3 h2 BLS-IV .638 .132 .103 .180 .467 Changes .696 .043 .037 .420 .663 Identical Figures .489 .013 .140 .124 .274 Solid Figures .366 .081 .305 .046 .234 Bricks .536 .064 .232 .041 .346 Puzzles I .487 .014 .225 .058 .291 Puzzles II .506 .035 .279 .002 .335 SODT .495 .608 .027 .003 .615 SDVT .560 .683 .003 .019 .779 % Variance 28.9 10.6 3.3 2.5

��

22

Table 2 Hierarchical factor analysis. Study 2.

Tests Gv Factor 1 Factor 2 Factor 3 h2 Cattell .560 .692 .136 .0 .810 B-F .636 .229 .128 .119 .486 PMA-S .518 .353 .031 .026 .394 Coordinates .475 .0 .041 .545 .524 Trajectories .146 .022 .093 .516 .296 Surface development .706 .175 .186 .143 .583 SODT-R .667 .067 .270 .030 .522 SVDT-R .309 .133 .252 .075 .276 CTT .516 .228 .180 .195 .388 Arrows .494 .0 .170 .177 .304 Maps .540 .143 .223 .142 .381 % Variance 27.9 7.1 3 6.27

23

Appendix

Study 1. The correlation matrix is shown above the diagonal. Reliabilities at the diagonal (a:

Cronbach DOSKD; b: split-half; c: test-retest). The covariance matrix is shown below the diagonal.

Tests SODT SVDT BLS-IV Changes Id. Figures Bricks Solid Fig. Puzzles I Puzzles II SODT .92a .694 .384 .320 .256 .323 .122 .237 .236 SVDT 228.412 .84a .457 .355 .270 323 .147 .252 .332 BLS-IV 32.512 30.696 .90a .517 .341 .377 ..255 .342 .357 Changes 33.811 29.638 11.126 .87a .390 .375 .228 .359 .338 Id.Figures 12.087 10.105 3.286 4.679 .75c .319 .198 .264 .306 Bricks 18.025 14.267 4.294 5.317 2.025 .75c .262 .322 .326 Solid Fig. 11.364 10.884 4.859 5.416 2.106 3.285 .87b 249 .268 Puzzles I 10.444 8.785 3.078 4.021 1.326 1.902 2.470 .72b .307 Puzzles II 10.686 11.900 3.294 3.882 1.572 1.980 2.723 1.474 .72b

24

Study 2.

The correlation matrix is shown above the diagonal. Reliabilities at the diagonal (a: Cronbach’s DOSKD; b: split-half; c: test-retest; d: test communality as a lower-bound estimate

of its reliability (Nyborg & Jensen, 2000). The covariance matrix is shown below the diagonal.

7HVWV�

Cattell

B-F Arrows Maps PMA-S Surface dev.

CTT SODT-R

SVDT-R

Coord.

Traj.

Cattel .75b .501 .241 .393 .520 .523 .402 .383 .027 .270 .048 B-F 9.473 .48d .386 .339 .406 .520 .393 .538 .160 .350 .139 Arrows 62.84

5 107.57

7 .99a .307 .219 .465 .283 .345 .130 .318 .165

Maps 9.135 8.451 105.275

.92a .334 .440 .368 .411 .217 .245 .082

PMA-S 25.528

21.305 158.558

21.573

.73c .467 .418 .332 .156 .258 .129

Surface dev. 32.507

34.642 426.566

36.068

80.735 .97b .331 .487 .308 .411 .136

CTT 57.228

59.818 593.955

69.083

165.528

166.070

.95a .471 .173 .083 .015

SODT-R 53.360

80.204 708.579

75.407

128.645

238.789

529.408

.85a .255 .391 .075

SVDT-R 2.838 17.843 200.611

29.890

45.251 113.072

145.505

210.220

.74a .107 .007

Coord. 15.175

21.031 262.855

18.156

40.239 81.230 37.651 173.428

35.499 .52d .352

Traj. 1.592 4.935 80.639 3.579 11.866 15.968 4.148 19.678 1.355 37.150 .29b

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