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1
7LWOH� The assessment of spatial ability through a single computerized test 1
$XWKRUV��
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: [email protected]�
Paper IN PRESS (European Journal of Psychological Assessment)
1 This research was partially supported by the project AENA-UAM/ 785001.
2
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.
�
3
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
4
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
5
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.
6
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
7
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
8
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.
�
9
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).
10
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.
$UURZV (Juan-Espinosa, Abad, Colom, & Fernández-Truchaud., 2000). The person
is asked to imagine that a long arrow indicates the direction of a travel and a short arrow
(associated with the long one) indicates a deviation onto which he/ she could turn. The
person must decide, as soon as possible, whether she/ he has turned to the right or to the
left, depending on both of the arrows, the long and the short one, presented on the
computer screen.
0DSV (Juan-Espinosa, Abad, et al., 2000). The person read a route (a set of
directions) on the computer screen and then a street map with four different coloured
routes appears. Below the map, four rectangles with the route colour are shown. The
person must decide which of the coloured routes represents the route described at first.
(OLRW�'RQQHOO\�%�)�WHVW (Eliot & Donnelly, 1978). A chair is located inside a room.
There are five points located in five different places of the room (floor, back, front, and so
11
forth). The person task is to decide from which point is possible to see the chair as
indicated by a chair-model presented outside of the room.
30$�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-
12
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
13
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.
14
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.
17
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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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