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2010-04-26T01:32:00.000-07:00

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Principal Components Factor analysis for the JCTI and SAT relationship

2010-04-16T08:35:00.000-07:00

A principal components factor analysis has been performed with the data collected from 85 out of 119 persons, takers of the Jouve-Cerebrals Test of Induction (JCTI), whom reported previously obtained Scholastic Assessment Test-Recentered (SAT-I) scores. Individuals with perfect scores on the Mathematical and/or the Verbal part of the SAT-I were discarded in order to avoid ceiling effects. The SAT-I is often described as an objective, standardized, three-hour test that measures verbal and mathematical reasoning abilities that students develop over time, both in and out of school. Many US colleges and universities use the SAT for admission purposes because it is purported to predict successful performance in college. The recentered SAT, used between 1995 and 2005, was divided into two sections, (i) a verbal part with emphasis on critical reading in which vocabulary was tested in the context of reading passages and in analogy and sentence-completion questions and (ii) a mathematical part with emphasis on data interpretation and applied math questions in which calculators were permitted but not required.

Long-time evidence exists to suggest that the SAT is closely related to g. Prepared originally to be an IQ test for the US Army (Lemann, 1999) and despite of its revisions over the years, the SAT is still highly correlated with intelligence tests. Frey and Detterman (2003) reported a correlation of .72 between the SAT-I and the Advanced Progressive Matrices (APM) by Raven (1998). Additionally, these authors indicated that the pre-recentered SAT correlated from .56 to .82 with intelligence measures, with most correlations being higher than .70 in magnitude. Likewise, a study conducted by Raz, Willerman, Ingmundson, and Hanlon (1983) resulted in a correlation between the SAT and the Culture Fair Intelligence Test (Cattell, Krug, & Barton, 1973) of .81.

Factor analysis is a common method of examining the patterns of relationships among a set of variables and is a commonly recommended analytical approach in order to evaluate the presence and structure of any latent constructs among a set of items, or tests (Cronbach, 1990; Kamphaus, 2001). For exploring the presence of a general latent trait among the JCTI and the two subscales of the SAT-I, the method of principal factor was chosen. Although the method known as principal components might have been justified on the basis of the high reliability of scores from these tests, this method begins with the assumption of perfect reliability, with a guessed communality of 1 for each variable. The principal factor method does not make such assumption beginning with r2 (the squared correlation of all the other subtest scores with the one being considered) in the diagonal and then estimating the communality of each variable through an iterative process until h2 (the maximal communality estimate) is reached. That estimate is then placed into the diagonal of the matrix for the final factor extraction. In such analyses the first unrotated factor to be extracted is commonly interpreted as g. However, the nature of this first axis relatively represents the nature of each variable which served in the analysis. The correlations of each test with this factor, in other words, the factor loadings, are indicators of the degree to which each subtest is a measure of ability as a whole as opposed to more specific components of ability.

Results

In this study, a first unrotated factor was extracted with an eigenvalue of 2 and accounted for 70% of the variance of scores. As shown in Table 1, the highest loading was observed for the Mathematical SAT-I which correlated at .94 with this first axis. The reasoning index of the JCTI was also very highly saturated, with a factor loading of .88, and the Verbal subscale of the SAT-I shown a significantly lower loading at .67. Even though the scholastic assessment requires knowledge, these two parts of the SAT-I are indeed called reasoning tests and this latent trait is a probable representation of general reasoning. This factor is noted as gθ or general ability for a reasonable but singular representation.

References.

Cattell, R. B., Krug, S. E., & Barton, K. (1973). Technical Supplement for the Culture Fair Intelligence Tests, Scales 2 and 3. Champaign, IL: Institute for Personality and Ability Testing.
Cronbach, L. J. (1990). Essentials of psychological testing (5th ed.). Boston, MA: Addison-Wesley.
Frey, M. C., & Detterman, D. K. (2003). Scholastic Assessment or g? The Relationship Between the Scholastic Assessment Test and General Cognitive Ability. Psychological Science, 15 (6), 373-378.
Kamphaus, R. W. (2001). Clinical assessment of child and adolescent intelligence (2nd ed.). Needham Heights, MA: Allyn & Bacon.
Lemann, N. (1999). The big test: The secret history of the American meritocracy. New York City, NY: Farrar, Straus, & Giroux.
Raz, N., Willerman, L., Ingmundson, P., & Hanlon, M. (1983). Aptitude-related differences in auditory recognition masking. Intelligence, 7 (2), 71-90.
Raven, J., Raven, J. C., & Court, J. H. (1998). Raven Manual: Sec. 4. Advanced Progressive Matrices (1998 ed.). Oxford: Oxford Psychologists Press.

2-Parameters Logistic Model Item Characteristic Curves for the Cerebrals Contest 2009

2010-03-31T05:42:00.000-07:00

I've finally found the time today to report the characteristic curves for the Cerebrals Contest 2009 using the 2-Parameters Logistic Model.

Which Word? questions number 2, 4 and 7 didn't show an appropriate response function.

Download here (pdf)

Hierarchical Ascendant Classification of the EPC and the Scholastic Assessment Test-Recentered reasoning scales

2010-02-17T05:57:00.000-08:00

I've focused my energy on the JCCES - RIAS relationship those days. By the way, I'm still in the process of arranging research data on the revision of the Epreuve de Performance Cognitive (EPC) for completing the submission of this project to the test publisher.

In order to study the relationship between the EPC-Revised and the Scholastic Assessment Test-Recentered (SAT-I) used by the College Board during the 1985 to 2005 period, I've performed some Hierarchical Ascendant Classification (HAC) analyses (N = 95). Basically, I've considered two different approaches for applying the HAC: (1) the Ward's method using Euclidian distances, and the (2) Ward's method using Chebyshev's distances. The findings for both cluster analyses were different and yield to complementary evidences. On one hand, the dichotomy shown by the dendogram indicated that both the EPC-R and the SAT-I Math were linked by nonverbal reasoning, and possibly numerical content --the EPC being prepared with numerical sequences--, as opposed to the verbal reasoning and knowledge of the SAT-I Verbal. On the other hand, the measures were grouped in such manner that the two SAT-I scales appeared with a common link to scholastic reasoning and knowledge while the EPC-R being related to the former by reasoning only.

Participants. The sample of participants consisted in 95 individuals. Of these, 20 (21.05%) were females, 75 (78.95%) were males and all of them indicated to have eventually studied in college. The average age of the sample was 20.73 (SD = 3.01).

Correlations. All three measures were observed to significantly correlate. The correlation between the EPC-R and the SAT-I V was the lowest at .49. The EPC-R and SAT-I V showed a closer relationship with a correlation of .60. Furthermore, the composite SAT-I and the EPC-R correlated at .68.

HAC.

On the relationship between the JCCES and the Reynolds Intellectual Assessment Verbal Scale (Part 4)

2010-02-16T09:57:00.000-08:00

Here are the results of a Hierarchical Ascendant Classification (HAC) analysis for the T-scores of the JCCES subtests and the RIAS verbal subtests.

This cluster analysis used the Ward's method based on Chebyshev's distance. As shown in Figure 1, the dendogram revealed two distinct groups into the principal one: (1) a group with emphasis on reasoning related abilities in which we could see a subpart gathering verbal reasoning measures, (2) and another that links the tasks of verbal knowledge.

References. (parts 1 - 4)

Cronbach, L. J. (1990). Essentials of psychological testing (5th ed.). Boston, MA: Addison-Wesley.

Evans, M. G. (1999). On the asymmetry of g. Psychological Reports, 85, pp 1059-1069.

Evans, M. G. (2000). Implications of the Asymmetry of g for predictive validity. Poster Session at the APA Conference on Models of Intelligence for the New Millenium. Yale University, June.

Jensen, A. R. (1980). Bias in Mental Testing. New York city, NY: Free Press.

Kamphaus, R. W. (2001). Clinical assessment of child and adolescent intelligence (2nd ed.). Needham Heights, MA: Allyn & Bacon.

Reynolds, C. R., Kamphaus, R. W. (2003). RIAS, Reynolds Intellectual Assessment Scales and the RIST, Reynolds Intellectual Screening Test, Professional Manual. Lutz, FL: Psychological Assessment Ressources, Inc.

Tellegen, A., & Briggs, P. (1967). Old wine in new skins: Grouping Wechsler subtests into new scales. Journal of Consulting Psychology, 31, pp 499-506.

Weiss, L. G., Saklofske, D. H., Prifitera, A. & Holdnack, J. A. (2006). WISC-IV, Advanced Clinical Interpretation. Burlington, MA: Elsevier Academic Press.

Correlations between the JCCES and other measures

2010-02-14T07:27:00.000-08:00

Here are the correlations that were observed between the Jouve-Cerebrals Crystallized Educational Scale (JCCES) and other measures of cognitive abilities or achievement.

Be aware that the correlations related to the RIAS GWH and VRZ are not comparable to those provided in the JCCES - RIAS relationship posts which were not corrected for restriction of range. Moreover, these values of Pearson's coefficient are not equivalent to those that I shared in both the Institute for Applied Psychometrics (IAP) and the National Association of School Psychologists (NASP) discussion lists in response to Professor Cecil Reynolds' question on the JCCES because the scoring method of the JCCES has been recently changed -cf. post on the revision of the CCAT-. Actual values are to be taken to replace the previous ones.

Table 1 is split into 2 parts.

On the relationship between the JCCES and the Reynolds Intellectual Assessment Verbal Scale (Part 3)

2010-02-14T03:23:00.000-08:00

Mean and SD for the JCCES and RIAS scores are given in the table below.

As can be seen in Figures 1, 2, 3 and 4, the examination of observed correspondences between JCCES and RIAS scores indicate a high degree of similarity in ability levels up to approximately 1.5 SD above the general population average. The JCCES and the verbal RIAS were not longer comparable above this level.

On the relationship between the JCCES and the Reynolds Intellectual Assessment Verbal Scale (Part 2)

2010-02-13T14:12:00.000-08:00

Both the JCCES and the verbal RIAS have been observed to yield very closely related measures. However, although the two batteries gave comparable scores within an interval from about 1 SD below the mean to about 1.5 SD above, the results no longer compare appropriately in adult examinees with high abilities. The RIAS Verbal Intelligence Index (VIX) did not show sufficient top to assess among gifted adults: a ceiling effect appeared over 125 VIX. Nevertheless, despite of the small number of young participants, such a phenomenon was not observed in adolescents under the age of 16.

For the need of this research the JCCES was scored in using an original 4th order polynomial transformation for the Tellegen & Briggs' formula 4 (1967) to convert the sum of the Verbal Analogies (VA), the Mathematical Problems (MP) and the General Knowledge (GK) age-referenced T-scores. Initially, the formula proposed by Tellegen & Briggs was intended to estimate a WAIS FSIQ based on alternatively grouped subtests. Even though studies showed no statistically significant difference between actual FSIQ and estimated FSIQ as computed with the Tellegen &; Briggs' method, the formula provides with scores that are increasingly incorrectly estimated in both tails of the IQ spectrum (Weiss, Saklofske, Prifitera & Holdnack, 2006). Furthermore, average IQs are slightly over estimated. In fact, this formula is based on the assumption that the spectrum can be represented as identically linear at each IQ level. In other words, the formula implies a constant loading in g over the ability levels. In fact, the formula 4 was developed to estimate FSIQ based on subtests' inter-correlations. However, according to Evans (1999, 2000), g is asymmetrical; this means that the probability of scores is not equivalent for different ability levels, and that correlations between tests are not similar at every ability levels. For appropriately scoring the JCCES, a polynomial transformation was developed for the Tellegen & Briggs formula. Applying this original formula allows making the estimated VIQ to fit almost perfectly with the actual WAIS VIQ along the spectrum. This 4th order polynomial transformation is probably not perfect because the changes in g loading depend on the tasks that are involved and their own changes in relationship over the ability spectrum. The polynomial equation is as follows

where EIQ is the estimated IQ and a is the result calculated with the Tellegen & Briggs' formula 4.

Results. As expected, both the VAI and CEI were highly correlated with the VIX. Pearson's coefficients -corrected for restriction of range (McNemar, 1949; Jensen, 1980)- were .87 (p < .0001) between the CEI and the VIX, and .88 (p < .0001) between the VAI and the VIX. This indicates that the JCCES and the verbal RIAS shared approximately 76% of variance of scores. Correlations between JCCES scores and RIAS scores are given in Table 1. The mean CEI was 125.22 (SD = 17.10), the mean VAI was 125.73 (SD = 17.83) and the mean VIX was 122.23 (SD = 12.27). For the subtests, the mean VA T-score was 67.53 (SD = 8.98), the mean MP T-score was 62.96 (SD = 10.72), the mean GK T-score was 63.93 (SD = 13.24), the mean GWH T-score was 60.00 (SD = 8.61) and the mean VRZ T-score was 64.71 (SD = 6.60).

Understanding Wechsler IQ score differences

2010-02-11T11:09:00.000-08:00

An excellent read.

AP101 Brief #6: Understanding Wechsler IQ score differences--the CHC evolution of the Wechsler FS IQ score

On the relationship between the JCCES and the Reynolds Intellectual Assessment Verbal Scale (Part 1)

2010-02-04T08:38:00.000-08:00

The relationship between the JCCES and the two-subtest verbal part of the Reynolds Intellectual Assessment Scale (RIAS) has been analyzed in order to investigate the criterion-related validity of the JCCES. A group of 119 examinees have participated. In this first part of the study, a principal components factor analysis conducted on the three subtests of the JCCES and the two subtests of the RIAS revealed very high loadings on Gc of every measures (ranged from .70 to .89). A quantitative knowledge - reasoning factor was found on a two-factor solution in which the Mathematical Problems of the JCCES showed strong loading (.95). Moreover, the verbal analogies of the JCCES were seen to be moderately saturated by this factor (.49).

"The RIAS is an individually administered test of intelligence appropriate for ages 3 through 94 years, which includes a co-normed, supplemental measure of memory. The RIAS includes a two-subtest Verbal Intelligence Index (VIX), a two-subtest Nonverbal Intelligence Index (NIX), and a Composite Intelligence Index (CIX). The VIX assesses verbal intelligence by measuring verbal problem solving and verbal reasoning where acquired knowledge and skills are important. Administration of the four intelligence subtests by a trained, experienced examiner requires approximately 20 to 25 minutes". (Reynolds & Kamphaus, 2003)

Reliability of scores yielded by the RIAS is seen as excellent with Cronbach's alphas ranged from .90 to .94 for the subtests, and from .94 to .96 for the Indexes (N = 2,438). The subtests' raw scores are converted to age-referenced T-scores (M = 50; SD = 10). Then, these T-scores are summed in order to obtain the indexes by comparison with the manual norm tables. The RIAS indexes use the same metric than most of the contemporary cognitive ability batteries, with a mean of 100 and 15 points per standard deviation. This makes them relatively comparable to IQ or other indexes from the Wechsler's scales or the most recent Stanford-Binet revisions. According to Reynolds & Kamphaus, the RIAS VIX correlated at .86 and at .78 with the WISC-III VIQ and FSIQ respectively (N = 54). These authors also reported correlations of .71 and .70 between the VIX and both the VIQ and the FSIQ (N = 31). In both the WISC and the WAIS samples, the means and SDs of the VIX are respectively lower and tighter than those of the Wechsler's scales. The significantly lower correlations observed in adults between the VIX and the WAIS IQs could be a relative consequence of unexpected answers to verbal problems. Although the keys given by the manual are fairly appropriate in adolescents even in gifted subjects, these expected solutions could appear insufficient in gifted adults, requiring the examiner to perform researches. The authors encourage psychologists who are used to administer the RIAS to consult reference materials to decide on the scoring of unusual responses.

Participants. The sample of participants consisted in 119 individuals. Of these, 42 (35.29%) were females, 77 (64.71%) were males and 95 (79.83%) of them indicated to have completed at least one college degree. The average age of the sample was 33.82 (SD = 12.56),

Factor analysis. Factor analysis is a common method of examining the patterns of relationships among a set of variables and is a widely used analytical approach in order to evaluate the existence and the structure of any latent constructs among a set of items, or tests (Cronbach, 1990; Kamphaus, 2001). For exploring the presence of latent traits among the JCCES and the RIAS verbal subtests, the method of principal components was chosen, with a varimax rotation (Kaiser's normalization) for interpreting the results. The first unrotated factor has an engeinvalue of 3.54 and accounted for 70.73% of trace. This trait is usually interpreted as g by researchers. However, the nature of any latent trait is determined by the nature of the clusters involved in the study. In this analysis, the variables only represent cognitive abilities that are related to knowledge and its usage. Consequently, this general factor is believed to be an enlightenment of general crystallized intelligence, i.e. Gc, rather than pure g. Loadings on Gc were all very similar for the verbal measures and ranged from .86 to .89. The only variable to show a lower saturation was the Mathematical Problems (MP) subtest of the JCCES at .70. However, this value is high. A two factors solution was then investigated. The second factor accounted for 12.60% of the trace and its engeinvalue was .63. As can be seen in Table 1, in this solution the first factor could be reasonably interpreted as language development (LD). The two subtests, General Knowledge (GK; .88) and Guess What (GWH; .89), which are prepared with information content are the more loaded. The second factor, very strongly appearing in the MP questionnaire (.95), could possibly be seen as quantitative knowledge, but with a significant relationship to reasoning. In fact, the items of the Verbal Analogies (VA) subtest loaded at .49 on this factor. The RIAS Verbal Reasoning (VRZ) subtest, also made with analogies, didn't show clear loading on this factor. A value of .38 indicates little less than a moderate correlation. However, as the VRZ loading on LD factor was .78, a possible explanation is that the RIAS analogies are more dependent on knowledge than the ones of the JCCES.

Principal Components Factor analysis for the items of the JCCES Verbal Ability part

2010-01-29T03:59:00.000-08:00

In an attempt to study the structure of the Verbal Ability scale of the JCCES, I've factor analyzed the items of both the Verbal Analogies (VA) subtest and the General Knowledge (GK) subtest all at once. Factor analysis is a common method of examining the patterns of relationships among a set of variables and is a widely used analytical approach in order to evaluate the existence and the structure of any latent constructs among a set of items, or tests (Cronbach, 1990; Kamphaus, 2001). For exploring the presence of latent traits among the items of the JCCES verbal subscale the method of principal components was chosen, with a varimax rotation (Kaiser's normalization) for interpreting the results. For better interpretability, two factors were retained. The first one has an engeinvalue of 21.62, and the second one has an engeinvalue of 5.86.
The results are given in Figure 1. As it can be seen, the items of both subtests are relatively well arranged in ascending order of difficulty, and share pretty much the same space in the low to middle range of ability. However, the half-circle is split into two distinct curves when it comes to a certain level of examinees' performance. One can easily notice that although the easier items of both questionnaires are relatively grouped all together on the left side of the figure, the harder problems on the right side of the figure are getting farther and farther according to difficulty level.
These findings suggest that even though the items' sensitivity to ability is relatively homogeneous up to a certain level of performance, it appears to be heterogeneous in the high range of cognitive abilities. The difference in the representation of latent constructs is here somewhat negligible in persons' with low to superior ability in comparison to the way it appears for instance in intellectually gifted individuals. Such a phenomenon is seen as close to the asymmetry of g describes by Evans (1999, 2000). This author observed that scales are more highly intercorrelated at the bottom end of the spectrum of g than at the top end.

References.
Cronbach, L. J. (1990). Essentials of psychological testing (5th ed.). Boston, MA: Addison-Wesley.
Evans, M. G. (1999). On the asymmetry of g. Psychological Reports, 85, pp 1059-1069.
Evans, M. G. (2000). Implications of the Asymmetry of g for predictive validity. American Psychological Association / Yale University Conference on Intelligence.
Kamphaus, R. W. (2001). Clinical assessment of child and adolescent intelligence (2nd ed.). Needham Heights, MA: Allyn & Bacon.

Two-dimensional scaling for the Mathematical Problems (MP) subtest of the JCCES

2010-01-28T07:52:00.000-08:00

I've performed couple of multidimensional scaling analysis for the items of the Mathematical Problems questionnaire used as a subtest in the JCCES. I was looking for the one-dimensionality to be shown by variables' coordinates in two-dimensional Euclidian distances and a generated Guttman effect (1955): the so-called horseshoe shape. However, I had to try different measurement levels in order to achieve such phenomenon. Although both the nominal and the ordinal levels produced a shy half-circle (which indeed has an interpretative interest), the figure wasn't satisfactory with a grape of items in the middle. Finally, the horseshoe appeared in a clearer aspect with the use the ratio measurement level.

According to Steven (1951), the ratio-scale is an interval-scale with a rational origin. The interval-scale provides with relative relationships between points and the ratio-scale shows the determinate distances from a fixed origin.

References.

Guttman, L (1955). A generalized simplex for factor analysis. Psychometrika, 20, pp 173-192.

Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1-49). New York: Wiley.

Interactive effects of educational level and gender on the JCTI

2010-01-27T10:47:00.000-08:00

I've performed an analysis on raw score differences observed on the JCTI according to both the gender and the education of participants. The sample gathered 251 persons of ages 10 to 26 years. 172 were males and 79 were females. On one hand, a first group of 66 adolescents, males, and students in middle or high-school was compared to another of 37 examinees, females and students at the same educational levels. On the other hand a sample gathering 106 males studying in college was compared to 42 female college students.

The average raw score for females was 21.68 (SD=12.34) in the middle school - high school group, and 28.10 (SD=10.76) in the college sample. The mean for the males' raw score was 26.36 (SD=11.53) in adolescents, and 34.40 (SD=10.11) in young adults. It was noticeable that both gender significantly improved their performance with age, with a tendency for a slightly better gain in males than in females. In fact, the males' average was improved by 8 and that of the females' was increased by 6.42. Additionally, it was interesting to note that the standard deviation for the two samples of females was larger by a bit than male counterparts. The graphical illustration of these results is given in the figure below.

Reliability coefficients and standard errors of measurement for raw scores on the JCTI

2010-01-25T05:37:00.000-08:00

Yesterday evening, after having split the data into different samples according to examinees' age, I've computed the value for the Cronbach's Alpha coefficient of raw scores on the JCTI. Then, using both the obtained alpha and the sample standard deviation, I've calculated the standard errors of measurement (SEm).

Results are given in the table below. Alpha values ranged from .92 to .96 with .95 in the entire sample that gathered 1,020 test takers. The derived SEm fall within 2.57 to 2.74; the SEm for the sample as a whole was 2.63. These observations are seen as appropriate for the use of the JCTI as a reliable measure in individual diagnosis with a strong confidence in the scores yielded by the test. Reliability of scores are considered satisfactory at .80; and a value at or above .90 in magnitude is highly recommended for a use in cognitive assessment (Aiken, 2000; Nunnally & Bernstein, 1994).

The internal consistency coefficients compare the JCTI favorably with other assessments of this kind, such as the Advanced Progressive Matrices (APM) by Raven (1998).

References.
   Aiken, L. R. (2000). Psychological testing and assessment (10th ed.). Needham Heights, MA: Allyn & Bacon.
   Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill.
   Raven, J., Raven, J. C., & Court, J. H. (1998). Raven Manual: Sec. 4. Advanced Progressive Matrices (1998 ed.). Oxford: Oxford Psychologists Press.

Validity and reliability evidence for the scores on the Jouve-Cerebrals Test of Induction

2010-01-23T07:05:00.000-08:00

I'm floating over a revised-everything period and I've revised the Test of Inductive Reasoning (TRI52). I've added the 5 consecutive misses’ rule for stopping the scoring, and performed couple of analyses on both reliability and validity of scores. I'm writing an article on this.

Here's the abstract (subject to change):

The aim of this research is to examine both the validity and the reliability of scores yielded by the Jouve-Cerebrals Test of Induction (JCTI). The main analysis was conducted on the data gathered from 1,020 examinees, most of them having taken voluntarily the JCTI as an online assessment. In this study, construct validity, internal consistency and item analysis of the scale were examined. As a result of factor analysis for construct validity, the JCTI showed to be very highly loaded on the general ability factor (.88) latently linking it with the subscales of the Scholastic Assessment Test-Recentered (SAT-I) and proved to be the most loaded in inductive reasoning (.96). The reliability coefficients as calculated with different methods and on different groups of test-takers showed on a general point of view a very satisfactory level up to .96. Analyses also demonstrated that the correlations with other measures of cognitive ability were within the expectations and higher magnitudes of Pearson’s coefficient were observed with nonverbal tasks. As an example, the JCTI Reasoning Index (RIX) and the Performance IQ of the Wechsler Adult Intelligence Scale (WAIS) were correlated at .80. The mean obtained with JCTI RIX did not significantly differ from others yielded by nonverbal measurements. Furthermore, the JCTI RIX was seen to be very closely related to the mathematical scale of the SAT-I at .84. Significant correlations were also observed with general and crystallized intelligence measures. According to these findings the JCTI RIX can be regarded as a valid and reliable measure that could be used in the field of education and psychology.

Revision for the Epreuve de Performance Cognitive (EPC)

2010-01-23T06:01:00.000-08:00

The Epreuve de Performance Cognitive (EPC), a title that could be translated by Cognitive Performance Examination, is a nonverbal, sequential reasoning test aiming at assessing one's problem solving ability in both timed and liberally timed conditions. The EPC is suitable for persons of average ability as well as for gifted adults thanks to items of very high difficulty. The EPC is published by the ECPA in France. Availability is restricted to graduated psychologists.

During the last 2 days I've worked on the data collected from 1,764 test takers with the goal of revising the EPC. Like I did for the revision of the CCAT, I've added to the scoring process of the test a requirement for stopping after 5 consecutive misses by the examinee. A fully computerized version should be prepared very soon.

Psychometric properties weren't altered by this new rule. The reliability of the scores yielded by the EPC was observed to be .94 as estimated with the Spearman-Brown corrected Split-Half formula in the entire sample. The Cronbach's alpha was also very satisfactory at .92. The multidimensional scaling analysis confirmed the existence of a continuum in items from the easiest to the hardest. As shown in Figure 1, the two-dimensional solution appeared in a typical horsehoe shape (Stress = .14; RSQ = .92).

Figure 1. Two-dimensional scaling: a typical horseshoe shape that shows the continuum in items of the revised EPC. An inappropriate set of items would have produced a cloud figure rather than a horseshoe. Inadequacy values supported the two-dimensional solution, with a Stress of .14 and a RSQ of .92. (N = 1,764)

A principal components factor analysis performed thanks to 95 participants who reported recentered Scholastic Assessment Test (SAT-I) scores resulted in a first unrotated factor loading of .83 for the EPC. The Math reasoning scale of the SAT-I was saturated at .82, and the Verbal reasoning part at .75.

Correlations with other measures were sufficiently high. The EPC raw scores were seen to correlate at .82 with the raw scores on the Raven's Advanced Progressive Matrices (APM) in 134 subjects and at .81 with the raw scores on the Cattell's Culture-Fair Intelligence Test-3A (CFIT) in a sample of 156 observations.

Furthermore, raw scores on the EPC and FSIQ on the WAIS correlated at .85 in a highly selective sample of 23 adults with an average FSIQ of 131.70 (SD=24.35).

I've an important amount of remaining data that could be analyzed. Anyway, I've written to the test publisher to know if this new version of the EPC, as I humbly think, is interesting for another publication.

Multidimensional Scaling analysis of item response data for the JCCES General Knowledge subtest

2010-01-23T03:12:00.000-08:00

I'm in the process of revising the CCAT in an attempt to reduce the time of test taking and the test length, to what it is really required relatively to the examinee, but without limiting the time for taking the test. The revised CCAT will be called Jouve-Cerebrals Crystallized Educational Scale (JCCES).

It's a common method for administering and scoring cognitive ability tests to stop the test after a certain number of consecutive errors given by the test taker. This method is used for instance in some Wechsler subtests or in the Reynolds Intellectual Assessment Scale (RIAS).

For the CCAT, first of all I've rearranged the items accordingly to the Rasch estimates for difficulty parameters in each respective subtest (N = 588). Then, after figuring out that the use of 3 consecutive errors for stopping the test was not appropriate (too many examinees would have been significantly under-evaluated), I've chosen to limit this number at 5. The reliability of scores have slightly increased.

I've performed multidimensional scaling (MDS) analyses for each subtest and the results were indeed very interesting. In both the scores of the Verbal Analogies (VA) subtest and the General Knowledge (GK) subtest the solution for two-dimensional scaling was supported with satisfactory inadequacy values.

The GK subtest was the set of items that produced the best results. The values for inadequacy were a Kruskal's Stress of .18 and a squared correlation (RSQ) of .87. The scaling of the items showed a horseshoe shape. This is a typical figure for a continuum in which all constrains for dissimilarities have been supported.

Test of Inductive Reasoning (TRI52) 16 - 68+ years

2010-01-09T07:34:00.000-08:00

The TRI52 is a computerized nonverbal intelligence test designed with 52 figurative items which don't require acquired knowledge.

With excellent Cronbach's Alpha reliability coefficient value (.92; N = 1,019), the TRI52 raw score has demonstrated high validity.

The TRI52 Reasoning Index (RIX) has shown very high correlations with both the Scholastic Aptitude Test I (SAT I) composite score (.75), and the SAT I Mathematical reasoning test scaled score (.84).

It also very highly correlates with the IQ on traditional intelligence tests such as the Wechsler Adult Intelligence Scale III (WAIS-III) Full Scale IQ (.77) or the Slosson Intelligence Test - Revised (SIT-R3) Total Standard Score.

Thanks to the nonverbal nature of its items, this test is suitable for testing persons without cultural bias. It yields with the RIX, an age-referenced standard score equated on the SAT-I M.

-->> COMPUTERIZED VERSION on Cerebrals.org

Reliability (2008, N = 779)
Raw Score Criterion-Related-Validity (2008)
Reasoning Index Correlations with the WAIS IQs (2009)
Reasoning Index Correlation with the SAT-I Math Scale (2009)
Reasoning Index to Percentile Rank Correspondence (2008)

Cerebrals Cognitive Ability Tests (CCAT) 10:4 - 75 years

2010-01-08T15:11:00.000-08:00

The CCAT is a battery divided into three subtests: Verbal Analogies (VA), Mathematical Problems (MP) and General Knowledge (GK) of respectively 42, 38 and 56 items. Each part measures a distinct ability, and once taken as a whole, these tasks give a reasonably good estimate of general crystallized intelligence and scholastic ability.

As a psychometric tool, the CCAT shows both excellent reliability and criterion-related-validity. Reliability of the full CCAT as checked by Spearman-Brown corrected Split-Half coefficient proved to be very highly satisfactory (.97; N = 584). This ensures an acceptable measurement error (2.77 for the full scale index) and a good stability of measurement. Furthermore, the Verbal Ability scale resulting from the addition of VA and GK subtests demonstrated sufficient level of reliability for being interpreted as an individual measure (.96).

Correlations shown by the CCAT Indexes with other measures are within the expectations. Validity of both the full and the verbal scales was confirmed by very high correlations with the Reynolds Intellectual Assessment Scales (RIAS) Verbal Index (.89). Moreover, the CCAT was closely related to the Scholastic Aptitude Test I (.87), and both the Wechsler Adult Intelligence Scale III (WAIS-III) Full Scale IQ (.92) and Verbal IQ (.89). In other words, the CCAT is an appropriate measure of one's crystallized-educational processing likewise for predicting a wide range of cognitive functioning.

Norms have been established by comparing CCAT scales with RAIS VIX and WAIS-III FSIQ, VIQ (N = 160). RAIS VIX changes over years were then applied to adjust CCAT indexes and produce age-referenced norms. The CCAT is suitable for both adolescents and adults (up to 75 years old). The computerized version yields with a raw score for each subtest.

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Reliability (2009 ; N = 470)
Correlations with the SAT-Recentered (2009)
Correlations with the RIAS VIX (2009)
Crystallized-Educational Index to RIAS VIX and WAIS FSIQ Observed Correspondence (2009)
Crystallized-Educational Index Norms: Ages 10:4 -14:8 Years, Ages 14:8-75 Years (2009)
Crystallized-Educational Index Confidence Intervals (2009)
Verbal Ability Index Norms: Ages 10:4-14:8 Years, Ages 14:8-75 Years (2009)
Verbal Ability Index Index Confidence Intervals (2009)