SON-R 2.5-7 SON-R 5.5-17

Construction & Validation of the SON-R 5.5-17 Construction & Validation of the SON-R 5.5-17 A nonverbal alternative to the Wechsler scale A nonverbal alternative to the Wechsler scale Cross-cultural research with the SON-tests Cross-cultural research with the SON-tests
Is the SON-R 5.5-17 a test for learning potential? Is the SON-R 5.5-17 a test for learning potential? Cultural bias in a nonverbal intelligence test Cultural bias in a nonverbal intelligence test Bibliography SON-tests Bibliography SON-tests
The short form of the SON-R 5.5-17 The short form of the SON-R 5.5-17 The SON-test in Kenya The SON-test in Kenya The SON-test in Morocco The SON-test in Morocco
Fair Assessment of Cultural Minorities


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European Journal of Psychological Assessment, Vol 9, 1993, Issue 2, pp. 147-157
(the published text is a slightly abbreviated form of the text presented here)

The Construction and Validation of a Nonverbal Test of Intelligence:
the revision of the Snijders-Oomen tests

Peter Tellegen & Jaap Laros

Personality and Educational Psychology, University of Groningen, The Netherlands

Keywords: nonverbal intelligence test, test construction, cross-cultural testing, culture-fair test, language-free test.

For fair intelligence assessment of children of ethnic minorities and of children with hearing, speech and language problems nonverbal tests are generally indicated. For this purpose the Snijders-Oomen tests have been used since 1943. With these tests a broad spectrum of intelligence can be examined without the use of receptive or expressive language. The latest revision, here described, incorporates new features of test construction, adaptive testing, establishing of norms and estimation of ability. A summary is given of research findings related to the structure of the test, the reliability, and the validity with hearing and deaf children

Introduction

Intelligence assessment is probably the most widely used tool for the psychological diagnostic evaluation of children, with far reaching consequences for schooling, referral to special programs, and treatment of specific handicaps. Although there are good tests for general intelligence like the Wechsler scales, their dependency on language skills in test contents and instructions makes them less appropriate for the assessment of cognitive abilities of ethnic minorities and of children with problems with verbal communication, such as deaf and hearing disabled children and children with speech and language disorders. For these groups, low performance on a general intelligence test might primarily reflect poor verbal knowledge instead of limited reasoning and learning ability. Nonverbal tests for intelligence assessment like the Raven's Progressive Matrices (Raven, Court & Raven, 1983) and the TONI (Test Of Nonverbal Intelligence; Brown, Sherbenou & Johnsen, 1990) are unidimensional tests with very specific contents which do not allow generalizations to a broad area of intelligence. Because of this they are not attractive alternatives for multi-trait multi-method tests like the WISC-R (Wechsler, 1974).

In this article we will describe the latest revision of the Snijders-Oomen Nonverbal intelligence tests (SON tests). These individually administered tests examine a broad spectrum of intelligence without being dependent on language. The SON-R 5.5-17, the revision of the test for children in the age from 5.5 to 17 years was published in 1989; the SON-R 2.5-7, for younger children, will be published in 1994. A detailed description of the construction and administration of the SON-R 5.5-17, and research on the reliability and validity of the test, can be found in the manual (Snijders, Tellegen & Laros, 1989) and in the dissertation of Laros and Tellegen (1991).

In view of the ongoing economic, social and educational integration in Europe, and the growing number of migrants and bilingual children both in Europe and the United States, there will be an increasing need for language-free and culture-fair tests. A great advantage of the SON tests for this purpose and for cross-cultural and international research is that, within certain limits, the test materials can be used without modification. English, German and Dutch editions of the manuals, the scoring forms and the computer programme are available.

History of the SON tests

The first SON test was published 50 years ago by Mrs. Nan Snijders-Oomen as a result of her work with children at the Institute for the Deaf in Sint-Michielsgestel (Snijders-Oomen, 1943). She was confronted with problems of assessing the learning ability of children who were severely handicapped in their language development. For this purpose general intelligence tests were not suited due to reliance on verbal skills, while nonverbal tests at that time consisted mainly of performance tests related to spatial abilities (like mazes, form boards, mosaics).

After extensive experimentation with existing and newly developed tasks, she constructed a test series which included nonverbal subtests related to abstract and concrete reasoning. Especially the capacities for abstraction and combination were considered important for the ability to participate in the educational system (Snijders-Oomen, 1943, p. 25-28). Mental age norms were constructed for deaf children from 4 to 14 years of age.

In the subsequent revision of 1958 the test series was expanded and standardized for deaf and hearing children from 3 to 17 years (SON-'58; Snijders & Snijders-Oomen, 1970). Both deviation IQ norms and mental age norms were established. With the second revision, different series of tests were developed for younger and older children: the SON 2.5-7 for children up to seven years, also known as the preschool SON (Snijders & Snijders-Oomen, 1976), and the SSON developed by Starren (1978) for the ages of 7 to 17 years.

Research results of these SON tests with various groups of children have been published. For instance, with deaf and hearing disabled children (Backer, 1966; Stachyra, 1971; Balkay & Engelmayer, 1974; Watts, 1979; Schaukowitsch, 1981; Zwiebel & Mertens, 1985), children with speech and language disorders (Grimm, 1987), children with learning disabilities and mentally retarded children (Sarimsky, 1982; Schmitz, 1985; Eunicke-Morell, 1989), autistic children (Steinhausen, Goebel, Breinlinger & Wohlleben, 1986; Süss-Burghart, 1993), motor handicapped children (Colin, Frischmann-Rosner, Liard & Magne, 1974; Constantin, 1975), children from ethnic minority groups (de Vries & Bunjes, 1989; Eldering & Vedder, 1992), normal children (Malhotra, 1972; Harris, 1979, 1982; Ditton, 1983; Melchers, 1986 ; Wolf, 1991; van Aken, 1992) and psychiatric patients (Plaum, 1975; Plaum & Duhm, 1985)

The latest revision of the SON test for older children, the SON-R 5.5-17, was published a few years ago (Snijders, Tellegen & Laros, 1989; Laros & Tellegen, 1991). In 1991 research was started for the revision of the SON 2.5-7 (Tellegen, Wijnberg, Laros & Winkel, 1992). Standardization of the test will take place this year and after validation studies with special groups of children the SON-R 2.5-7 will be published in 1994.

The SON-R 5.5-17

Characteristics of the revision

The main reasons for the revision of the SON test for older children have been:

1. To provide adequate norms.

  • For western countries a mean rise in intelligence of 2 à 3 IQ-points per decade can be expected (Lynn & Hampson, 1986) which requires regular updating of norms.
  • The SON-R has been standardized on a representative sample of 1350 Dutch children.
  • Norms for deaf children are based on 768 subjects, almost the complete population of deaf children in the Netherlands of the relevant age.

2. To incorporate new theoretical developments on intelligence; adjust time-bound item materials; respond to criticism by users of the test.

  • In the SSON all subtests were in multiple choice form which gave few opportunities for observation. The SON-R offers the possibility of observing behaviour by allowing the subject to actively construct the solution to the given items.
  • The earlier SON tests included short-term memory tests. Because of the relatively low reliability of these tests, their low correlation with other subtests, and their relatively low validity for learning ability (Estes, 1982), memory tests are not included in the SON-R.

3. To incorporate new methods in test construction, test administration and psychometrics.

  • In the construction and selection of items use was made of "item difficulty theories", which specify the factors contributing to the difficulty of the items, and the subtests were analysed with the non-parametric item response model developed by Mokken (1971) to acquire homogeneous scales.
  • A practical method of individual adaptive testing has been developed by arranging the items in two or three parallel series. Separate research was conducted to investigate proper means of estimating the reliability.
  • Feedback is given to the child after each item. This creates a more natural situation and allows the child to change wrong response strategies.
  • For the computation of norms a mathematical model was developed in which the score distributions of the different age-samples are simultaneously fitted. Reliabilities and correlations between subtests have also been fitted as a function of age. This allowed for optimal estimation of the population characteristics relevant to the norms, and results in test norms based on the exact age of the child by means of a computer programme that is standard supplied with the test.
  • Rather unique is that the presentation of standardised test scores is based on a standardisation of true score distributions instead of observed score distributions, which allows for more sensible and interpretable estimates of ability levels. Depending on the goal of the interpretation of scores either standard errors of measurement or standard errors of estimation are taken into account.

Composition of the test

In sequence of administration the test series consists of the following 7 subtests:

  • Categories: the subject is shown three drawings of objects or situations that have something in common. The subject has to discover the concept underlying the three pictures and is required to choose, from five alternatives, the two drawings which depict the same concept. The difficulty of the items is related to the degree of abstraction of the underlying concept. For example, in an easy item the concept is 'fruit' and in one of the most difficult items the concept is 'art'.
  • Mosaics: various mosaic patterns, presented in a booklet, have to be copied by the subject using nine red/white squares. There are six different sorts of squares. With the easy items, only two sorts are used while all six sorts are used with the difficult items.
  • Hidden Pictures: a certain search object (for instance a kite) is hidden fifteen times in a drawing. The size and the position of the hidden object vary. After focusing on the search object, the subject has to indicate the places where it is hidden.
  • Patterns: in the middle of a repeating pattern of one or two lines a part is left out. The subject has to draw the missing part of the lines in such a way that the pattern is repeated in a consistent way. The difficulty of the items is related to the number of lines, the complexity of the line pattern and the size of the missing part
  • Situations: the subject is shown a concrete situation in which one or more parts are missing. The subject has to choose the correct parts from a number of alternatives in order to make the situation logically coherent.
  • Analogies: the items consist of geometrical figures with the problem format A : B = C : D. The subject is required to discover the principle behind the transformation A : B and apply it to figure C. Figure D has to be selected from four alternatives. The difficulty of the items is related to the number and the complexity of the transformations.
  • Stories: the subject is shown a number of cards that together form a story. The subject is given the cards in an incorrect sequence and is required to order them in a logical time sequence. The number of cards that is presented varies from four to seven.

The diversity in tasks and testing materials has the advantage of making the test administration attractive for the children.

Categories, Situations and Analogies are multiple choice tests, the remaining four tests are so called 'action' tests. In the action tests the solution has to be sought in an active manner which makes observation of behaviour possible. Although no observation system is provided with the SON-R, and no data regarding the reliability and validity of observations were collected, many users of the SON tests appreciate the possibilities of behaviour observation. For this reason the SON-'58 remained in use after the publication of the SSON as in the latter test all subtests were in multiple choice form.

The SON-R can be divided into four types of tests according to their contents: abstract reasoning tests (Categories and Analogies), concrete reasoning tests (Situations and Stories), spatial tests (Mosaics and Patterns) and perceptual tests (Hidden Pictures). The abstract reasoning tests are based on relationships that are not bound by time and place; a principle of order has to be derived from the presented material and applied to new material. For nonverbal testing of abstract reasoning, classification tests and analogy tests are widely used.

In the concrete reasoning tests the objective is to bring about a realistic time-space connection between objects. Emphasising either the spatial dimension or the time dimension leads to two different test types. In the so-called completion tests (Situations), the task is to bring about an imperative simultaneous connection between objects within a spatial whole. In the other test type (Stories), the object is to place different scenes of an event in the correct time sequence. The concrete reasoning tests show an affinity to tests for social intelligence in which insight in social relationships and behaviour is emphasised.

In the spatial tests a relationship between pieces or parts of an abstract figure has to be established. Mosaics is a widely known test type which was included in the earlier SON tests; the new subtest Patterns was especially developed for the SON-R.

In the perceptual test, Hidden Pictures, a certain figure hidden in an ambiguous stimulus pattern must be discovered. The subtest, which is also new for the SON tests, represents the factor 'flexibility of closure', differentiated by Thurstone.

Principal components analysis (PCA) has been performed on the subtest correlations to obtain empirical confirmation of the dimensions of the SON-R. The PCA is based on the fitted correlations of the standardisation sample (N=1350) for the ages of 6.5, 10.5 and 14.5 years. Because the focus of interest is in the dimensionality of true scores, all correlations have first been corrected for attenuation. Eigenvalues and percentages of explained variance are presented in table 1.

Table 1. Eigenvalue and percentage of explained variance
per principal component for three age groups
. 6 years 10 years 14 years
I 4.1 (59%) 4.6 (66%) 5.1 (72%)
II .8 (11%) .6 ( 9%) .5 ( 8%)
III .6 ( 9%) .5 ( 7%) .5 ( 7%)
IV .6 ( 8%) .5 ( 7%) .3 ( 5%)
V .4 ( 6%) .3 ( 4%) .2 ( 4%)
VI .3 ( 4%) .3 ( 4%) .2 ( 3%)
VII .2 ( 3%) .2 ( 3%) .2 ( 2%)
Note. PCA based on correlations corrected for attenuation.

As is clear from the eigenvalues there is a strong dominance of the first component. The percentage of explained true score variance increases from 59% at the age of six years to 72% at the age of fourteen years. The four theoretical dimensions in contents of the subtests are supported for the younger children by the loadings on the first four varimax rotated components, but in the older age groups most subtests have considerable loadings on several components (table 2). It is noteworthy that Analogies which is considered to be a test of abstract reasoning has - in the older age groups - the highest loadings on the first rotated 'spatial' component. The two-components solution gives more consistent results across the age groups with a 'reasoning' and a 'spatial' component. Analogies has similar loadings on both components, while Hidden Pictures has the highest loading on the 'reasoning' component.

Table 2a. Loadings of subtests on four varimax rotated principal components in three age groups
. 6 years 10 years 14 years
I II III IV I II III IV I II III IV
Mos. .8 .3 - - .8 .3 - .3 .8 .3 - .5
Pat. .9 - - - .9 - - - .9 .3 .3 -
Sit. .3 .8 - - .3 .7 .3 .3 .4 .7 .4 -
Sto. - .8 - .3 .3 .9 - - .3 .8 - .3
Cat. - - .9 - .3 .3 .9 - .3 .3 .9 .3
Ana. .4 .4 .6 - .6 .5 .4 - .6 .4 .4 .3
Hid. - .3 - .9 .3 .3 - .9 .3 .4 .4 .8
Note. PCA based on correlations corrected for attenuation. Correlations < .25 are not represented.

Table 2b. Loadings of subtests on two varimax rotated principal components in three age groups.
. 6 years 10 years 14 years
I II I II I II
Mos. .3 .9 .4 .8 .4 .8
Pat. .3 .9 .3 .9 .3 .9
Sit. .7 .5 .8 .3 .8 .4
Sto. .7 .4 .8 .3 .8 .4
Cat. .8 - .7 .4 .7 .4
Ana. .6 .5 .6 .6 .6 .7
Hid. .7 - .7 .4 .8 .4
Note. PCA based on correlations corrected for attenuation. Correlations < .25 are not represented.

The similarity in factor structure for different populations has been analysed for six groups:

  • native hearing children with a 'normal' school career (N=1250),
  • native hearing children from special education or with severe arrears in regular education (N=39),
  • hearing immigrant children (N=61),
  • native deaf children with no extra handicaps (N=479),
  • native deaf children who were multi handicapped or assessed as cognitively handicapped (N=150),
  • deaf immigrant children (N=140).

The analysis was based on the six correlation matrices of the standardised subtest scores. By using simultaneous component analysis for a number of data sets, we tested whether one uniform solution of component weights that was optimal across the six groups, explained considerably less of the total variance than the components that are optimal in the separate groups (Millsap & Meridith, 1988, Kiers & Ten Berge, 1989).

When only the first component was determined, the uniform solution was almost as good as the solutions that were determined per group (averaged over the six groups, the percentage of explained variance was in both cases 56%). When more components were determined, the uniform solution was only slightly less optimal. The explained variance of the specific solutions was, on the average, 1% of the total variance higher compared to the uniform solutions (with respectively two, three, or four components). The structural characteristics of the SON-R proved thus to be highly independent from the examined characteristics of the groups.

To examine the importance of the specific characteristics of the subtests, for each subtest the correlation with the sum of the other subtests and the multiple correlation with the six other subtests has been computed. These correlations which were corrected for attenuation are presented for three age groups in table 3.

Table 3.
Correlations of subtests with unweighted sum of the other tests (Rs) and multiple correlations (Rm) for three age groups
. 6 years 10 years 14 years
Rs Rm Rs Rm Rs Rm
Mos. .70 .80 .78 .82 .80 .84
Pat. .69 .80 .74 .80 .77 .82
Sit. .74 .78 .79 .81 .83 .86
Sto. .71 .76 .73 .77 .76 .80
Cat. .57 .60 .67 .68 .72 .74
Ana. .68 .70 .78 .79 .86 .86
Hid. .59 .61 .70 .71 .79 .82
mean .67 .72 .74 .77 .79 .82
Note. PCA based on correlations corrected for attenuation.

In accordance with the PCA there were relatively small differences between the multiple correlations and the subtest-rest correlations, which indicates the strong influence of a general factor in the subtests (Mosaics and Patterns are an exception since they correlate relatively strong in the youngest age groups). Both multiple correlations and subtest-rest correlations increase with age. In spite of these high correlations, the squared multiple correlations indicate that a considerable proportion of the true score variance of the subtests is specific and cannot be explained by the other subtests. The mean percentage specific true score variance is 47% at 6 years, 41% at 10 years and 32% at 14 years. Categories and Hidden Pictures are the most specific subtests, especially in the youngest age groups.

Construction of the subtests

The subtests of the SON-R were systematically constructed on the basis of a theory of item difficulty. The intention of such a theory is to cover the most important factors that contribute to the difficulty of items in a subtest. With the help of such a theory items can be ordered as subsequent, logical steps in the mastery of a specific problem type. A theory which is successful in explaining the progressive difficulty in a subtest has two important advantages. First, it creates the possibility of designing items with a certain degree of difficulty and of performing a systematic test construction. Second, one obtains a rational basis for interpreting failure at a certain level of difficulty. Especially for the subtests Mosaics, Patterns and Analogies, we succeeded in developing effective theories of item difficulties.

In the construction research extensive item sets were administered to children of varied ages and educational levels. In total 2030 subjects were involved in this phase. The non-parametric unidimensional scaling model developed by Mokken (1971) was used in selecting the items. An important characteristic of a Mokken scale is that all items measure the same latent characteristic. The ordering of persons should be independent of the subset of items, and the ordering of difficulty of the items should be independent of the subset of persons. These characteristics of sample independence also apply to the more common parametric item-response models but the last mentioned models makes extra demands on the form of the item curves that describe the relationship between the latent characteristic and the chance that an item will be answered correctly (Hambleton & Swaminathan, 1985). The extent to which a scale meets the criteria of the Mokken model is represented as the scalability coefficient H. The following interpretation is given to the value of H (Mokken & Lewis, 1982): strong scale (H > .50); moderate scale (.40 < H < .50); weak scale ( H < .40 ). The subtests Mosaics, Patterns and Stories are strong scales with H values of .73, .54 and .55. De multiple choice tests Categories, Situations and Analogies are moderate scales with H values of .48, .46 and .47.

Test Administration

Like most intelligence tests for children, the SON-R is individually administered. Group administration is less suited for nonverbal instructions and for motivating young subjects, and would exclude behaviour observation. The role of time scoring is kept to a minimum. In this sense, the SON-R is a typical power test; there is a large variation in the difficulty of the items, while allowing sufficient time for solving each item. The only exception to this is Hidden Pictures; the nature of the task in this subtest requires effective time limits. The time needed to administer the SON-R varies from 1 to 2 hours with an average of 1.5 hours.

There is a shortened version of the SON-R, consisting of four subtests: Categories, Mosaics, Situations and Analogies. The administration of this shortened version takes about three quarters of an hour.

For the subtests of the SON-R there are verbal and nonverbal instructions which were made as equivalent as possible. Nonverbal instructions form the point of departure, verbal parts are added as accompaniment and not as supplementary information. The two sets are not intended for use as two exclusive alternatives but they give, in a different form, essentially the same information. With bilingual, deaf, and hearing disabled children an intermediate form can often be used by combining the nonverbal instructions with (parts of) the verbal instructions. In practice, the choice between the two procedures is generally not a problem; the form of communication is adapted to the child.

In two important aspects the SON-R can be distinguished from traditional intelligence tests with regard to the test procedure: first by giving feedback to the child and, second, by the use of an adaptive procedure for presenting test items. Traditionally, in intelligence testing no feedback is given as to whether the subject's answer is right or wrong. This tradition is broken in the SON-R because we think that such behaviour is not natural. When no reaction is allowed following an answer, the examiner's attitude can be interpreted by a subject as indifference or, erroneously, as an indication that the answer was correct. In the SON-R, following each item the subject is told whether the answer was correct or incorrect. However, this does not include an explanation of the reason why an answer is incorrect. One advantage of giving feedback is that the subject has the opportunity to change his problem solving strategy. Another advantage is that, when a subject has interpreted the instructions incorrectly, feedback offers the opportunity to adjust.

The second important difference of the test procedure of the SON-R with common test procedures concerns adaptive testing. In intelligence tests for a population with a wide age range, the difficulty range of the test items has to be large. Presentation of all items to each subject is troublesome for a number of reasons. In the first place, this would greatly extend the duration of the test. In the second place, it is frustrating for young or less intelligent children to be required to solve many items that are too difficult. Likewise, the motivation of older and more intelligent children is reduced when they are required to solve many problems that are too easy. A practical solution, often followed, consists of presenting all items in order of difficulty and applying a discontinuation rule. However, this procedure does not result in eliminating items that are too easy for a specific subject, and the procedure has the effect that the items on which the subject fails often occur in successive order, which can be highly frustrating. In recent years, adaptive testing procedures have been developed which restrict the presentation to those items that are most suited for the specific subject. These adaptive procedures are aimed at effectively limiting the number of items to be administered with relatively little loss of reliability (Weiss, 1982). With computerised testing, these procedures can easily be implemented; with non-computerized testing, there are major practical difficulties for the examiner, both in selection and presentation of the most informative items.

The SON-R uses an effective adaptive test procedure by dividing the subtests into either two or three parallel series of about 10 items (three series are used for the multiple choice tests). The difficulty in each series increases relatively fast. Every subject starts with the easiest item of the first series. Each series is broken off after two (not necessarily successive) errors. The starting point of the next series is determined by the score on the preceding series. The score in each series equals the number of the last item presented minus the number of errors, and the first item in the next series equals this score minus one. In this way, the administration of items is determined by the subject's individual performance and the presentation is limited to the most relevant items. On the average the number of items presented is 50% of the total number of items in the subtests and the maximum number to be presented is about 60%.

For the examiner, this procedure has the advantage of presenting the items within a series in a fixed sequence. Thus, searching the test booklet for the item which has to be presented next, takes place only at the beginning of a new series. For the subject this procedure has great advantages, because after two errors much easier items are presented which he will probably be able to solve. Especially with children who become easily demotivated, this adaptive procedure will improve their performance and make the results more in accordance to their ability.

Standardisation

The standardisation of the test scores of the SON-R was based on a nation-wide sample of 1350 subjects varying in age from 6 to 14 years. Each age group was represented by a sample of 150 subjects which was stratified according to sex, educational type and demographic variables. The population was restricted to children residing in the Netherlands for at least one year and who were not suffering from severe physical or mental handicaps.

Test performance strongly increased with age; 66% of the variance of the raw total score was explained by age. To enable comparisons between subjects of different ages, a standardisation of test scores dependent on age is required. In practice, such standardizations are often performed on the separate age samples. Generally the raw scores for each sample are either linearly transformed to standardized scores, or the raw scores are standardized and normalized on basis of the cumulative proportions of each group. For the SON-R a model was developed in which the cumulative proportions of the raw scores in the nine age groups were simultaneously fitted as a higher order function of raw score and age. This model resulted, for example, for the subtest Mosaics in the following equation:

z' = p1+p2X+p3X2+p4X3 +p5Y+p6Y2+p7Y3 +p8XY+-p9X2Y+p10X3Y

Given the raw score X and the exact age Y, z' is the population value of the normalized standard score. The parameters p1 to p10 of the model are estimated by minimalisation of the squared deviations of the arcsine transformations of the observed cumulative proportions of the samples and of the corresponding model values (Novick & Jackson, 1974, p. 324).

This method yields population estimates of the score distributions which are more accurate (by combining the information of all the age groups) and more consistent (by imposing constraints on the form of the functions). As an investigation on the effectiveness of this new method of standardisation a cross-validation study of the method has been performed for four subtests. In this study we compared our method with the method of separate linear transformations within each age group (based on the mean and standard deviation and assuming normal distributions) and the method of separate non-linear transformations within each age group by directly transforming the observed cumulative proportions.

Stratified according to educational background, the nine samples of 150 subjects were divided at random into sample A and sample B (each consisting of 75 subjects). The estimated population distribution of raw scores for each age group was based on the subjects in sample A by three methods

  • assuming a normal distribution for each age group
  • assuming for each age group a population-distribution identical to the corresponding samples in A
  • by fitting simultaneously across scores and age groups, using the arcsine transformation.

Subsequently the expected population distributions were compared with the observed distributions in the nine age groups of sample B. In each age group scores were combined to have expected frequencies of 5 or more. The results of the chi-square tests are presented in table 4.

Table 4. Results of chi-square test for different methods of standardisation
subtest method X2 df p
Mosaics a. normal 91 74 .086
b. identical 137 73 .000
c. fit 65 76 .818
Situations a. normal 120 88 .014
b. identical 163 85 .000
c. fit 88 87 .450
Analogies a. normal 128 90 .006
b. identical 160 85 .000
c. fit 109 91 .101
Stories a. normal 127 78 .000
b. identical 157 73 .000
c. fit 99 77 .049

It is evident that our method of standardisation is far more effective than both other methods that are more commonly used. That the 'normal' method was superior in this study to the 'identical' method will be a consequence of the small sample sizes. As the distributions of the test scores of the SON-R were markedly not normal, it is to be expected that differences in effectiveness between the 'fit' method and the 'identical' method would diminish with increasing sample size.

Another advantage of the model is that standardised scores can be computed for any specific age; by using the model it was also possible to extrapolate the age norms to 5;6 and 17;0 years. Within this age range, the raw subtest scores are normalised and standardised, thus reflecting the relative position of an individual compared to persons of the same age. The normalised total score on the test is based on the sum of the standardised subtest scores. In the SON-R manual, norm tables for 38 age groups are presented. Even more accurate norms are obtained by using the computer programme which is supplied with the test. The programme computes norms based on the exact age of the subject.

Reliability and Generalizability

The reliability of the standardised subtest scores depends on the correlations between the item responses. Since with the adaptive procedure almost 50% of the items are not administered, the correlations between the item scores are systematically and artificially enhanced because easy items which are not administered are scored '1' and difficult items which are not administered are scored '0'. As a result, the usual formulas overestimate the reliability. In general this problem is not considered and reliabilities are computed as if the whole test had been administered (for instance in the WPPSI-R; Wechsler, 1990). For the SON-R a separate study was conducted to achieve unbiased estimates. In this study, the subtests were (almost) completely administered. Score patterns of the complete administration were compared to score patterns computed as if the adaptive procedure had been applied. It appeared that as a result of the adaptive procedure, the correlations between the subtests decreased, while the computed reliability coefficient (lambda 2; Ten Berge & Zegers, 1978) was higher compared to the reliability of the complete administration (.86 instead of .80). The correlation with the criterium (the sum of the other subtests, completely administered) dropped from .60 to .58. Assuming that the correlations of the true scores with the criterium would be the same, the reliability of the adaptive tests had to be .75. The outcome indicated that (averaged over subtests and age groups) the reliability was .11 lower than computed by traditional methods. Compared to a complete subtest administration the loss was about .05.

Based on the standardisation research, the reliability of the subtests of the SON-R (after correction) is .76 on the average. The most reliable subtests are Mosaics, Patterns and Analogies. The average reliabilities of the subtests for the different age groups are presented in table 5.

Table 5. Mean reliability (rxx) and intercorrelations (rxy) of
subtests, and reliability (αs) and generalizability (α)
of the total score for 12 age groups
age subtests total test score
rxx rxy αs s) α (α)
5 yrs .71 .35 .90 (.85) .79 (.67)
6 yrs .73 .38 .92 (.87) .81 (.70)
7 yrs .75 .40 .93 (.89) .83 (.73)
8 yrs .76 .43 .93 (.90) .84 (.76)
9 yrs .77 .45 .94 (.90) .85 (.77)
10 yrs .77 .47 .94 (.91) .86 (.79)
11 yrs .77 .48 .94 (.91) .87 (.80)
12 yrs .77 .49 .94 (.91) .87 (.80)
13 yrs .77 .50 .94 (.91) .88 (.81)
14 yrs .76 .51 .94 (.91) .88 (.81)
15 yrs .76 .52 .94 (.91) .88 (.82)
16 yrs .76 .53 .94 (.91) .89 (.82)
mean .76 .46 .93 (.90) .85 (.77)
Note. Values in brackets concern sum score of the shortened test

In classical test theory, reliability refers to the stability of hypothetic independent repeated measurements (Lord & Novick, 1968). In the theory of generalizability the items are considered to be a sample from a domain of comparable items and the internal consistency of the item scores indicates the validity of the generalisation from the outcome of the sample to the entire item domain (Cronbach, Rajaratnam & Glaser, 1963; Nunnally, 1978). For homogeneous item sets, both approaches are almost equivalent. For the total score on an intelligence test that is composed of several subtests, all partly measuring separate components, an important distinction between reliability and generalizability can be made. With the reliability of the total score (stratified alpha; Nunnally, 1978, p. 246), the possibilities for generalisation remain restricted to the specific contents of the subtests. For the interpretation of individual outcomes it is more relevant to generalise to the entire domain of comparable subtests, and to consider the subtests as a restricted sample from the domain that is important for the assessment of intelligence. In the latter case, the number of subtests and the mean correlation between the subtests determine the coefficient of generalizability. This coefficient can be computed by the usual coefficient alpha in which the subtests are the unit of analysis (Nunnally, 1978, p. 212).

For the SON-R, the reliability of the total score (alpha stratified) is .93. The generalizability of the total score (alpha) increases from .81 at six years to .88 at fourteen years, with a mean value of .85. For the shortened version of the SON-R, the reliability has a value of .90 and the generalizability is .77 on the average.

Stability through time

Test-retest research has not yet been carried out with the SON-R. In the research with the SON-R with deaf subjects, test results on earlier versions of the SON were available for 434 subjects. The mean correlation of the SON-R with earlier versions of the SON was .76, and related to the age at administration of the first test and to the lapse of time between the two administrations. For the children with a mean age of 6 years and a mean interval of 5.5 years the correlation was .67; for the children with a mean age of 9 years and an interval of 1.6 years the correlation was .79. As is the case in American research on general intelligence tests, stability increases with age and with shorter time intervals (Bayley, 1949).

Presentation and interpretation of the results

Given the above-mentioned characteristics, the total score of the SON-R provides a reliable and generalizable indication of nonverbally tested intelligence. The subtest scores add information concerning specific abilities. For the interpretation of the standardised subtest scores and the IQ scores, reliability is taken into account in two different ways, namely by representing the scores as norm scores and as latent scores. For both types of scores, the basis of the standardisation is that the distribution of true scores has a population mean of 100 and a standard deviation of 15. The norm score and the latent score are different approaches to estimating the true score and they are used for different purposes.

The norm score is defined as the sum of the standardised true score and the error of measurement. This unbiased estimate of the true score is used for hypothesis testing on basis of the standard error of measurement, research on groups and for computation of the total test score. Although the more common standard scores (with standardised observed scores instead of standardised true scores) are also unbiased estimates of their true scores, these true scores do not have a fixed distribution (as their standard deviation is dependent on the reliability) which means that for standard scores on different (sub)tests there is no sensible basis for the comparison of their true scores.

The latent score is the estimate of the true score computed by means of linear regression, which means that the estimation uses prior assumptions on the score distribution. In combination with the accompanying probability interval of the true score (based on the standard error of estimation), the latent score is best suited for individual interpretation of the test results and for intra-individual comparison of subtest scores. The latent scores are presented graphically on the scoring form. In the computation of the latent subtest scores, the correlations between the subtests are used to improve the estimates of the true scores. To predict the true score of a specific subtest, the performance on the other subtests is also entered into the multiple regression equation. This results in smaller errors of estimation and in estimates which are more close to each other. Also, a test of significance of intra-individual differences is performed. This way the problem of exaggeration of these differences in the profile is avoided.

Latent scores for the IQ are computed in two ways, denoted as specific IQ and as generalised IQ. The estimation of the specific IQ is based on the reliability of the total score; the estimation of the generalised IQ is based on the coefficient of generalizability. The latter score is the estimated performance on the entire domain of comparable intelligence tests, and is best suited for interpretation of the test result as level of intelligence.

In addition to these scores which take reliability into account, some descriptive characteristics of the test results are presented. The reference age is given for the subtests and for the total score; it represents the age at which a specific test result corresponds with a standardised score of 100. This 'mental' age facilitates interpretation from a developmental viewpoint. The total score is also presented as a standard IQ (fixed population standard deviation of 15) with the corresponding percentile scores for the general hearing population and for the population of the deaf. In contrast to earlier versions of the SON, no separate subtest norms are computed for the deaf.

Compared to intelligence tests that only present standard scores (which do not take measurement errors, and errors of generalisation into account), the SON-R offers several extra possibilities for a psychometrically sound interpretation of test results. These possibilities require additional work when using the norm tables, but when using the computer programme all results are automatically computed, printed and stored.

Validity

In the standardisation research with the hearing subjects, extensive data have been collected to substantiate the validity of the test. Separate research has been performed with deaf children to develop supplementary test norms and to further validate the test for this particular group. After the publication of the SON-R some small-scale studies have been performed which give information on the correlations with other intelligence tests. The main findings will be summarised below.

Sex differences
There was no difference in mean IQ-scores between boys and girls in the general population (mean scores of 100.1 and 100.0). The only significant relation (p<.01) with sex, for hearing as well as for deaf subjects, was found for Mosaics; girls scored somewhat lower than boys on this subtest.

Socio-cultural factors
For hearing as well for deaf native Dutch subjects, there is a relatively strong association between the occupational level of the parents and the IQ scores. The mean difference between children of unskilled workers and professionals (the two extremes for six categories of socio-economic status) was about 15 IQ points. The coefficient of association, eta, was significant (p<.01) in both groups. Analogies showed the strongest relation with occupational level.

In the research with hearing subjects, substantial differences in test performance on the SON-R existed between immigrant children (based on country of origin of the parents) and native Dutch children. The mean IQ score for the Moroccan and Turkish children was 84, compared with a mean score of 100.5 for the native Dutch children. The lag of the other immigrant children was small (mean IQ equals 99). Comparable differences occurred in the deaf research group, with the exception of the lag of deaf children from Surinam and the Dutch Antilles which was also considerable. For deaf and hearing subjects, ethnic differences in performance concerned all subtests, but were most pronounced for Mosaics and Analogies. Neither for the hearing, nor for the deaf immigrant children did a relation exist between the number of years of residence in the Netherlands and the test scores. This indicates that lack of knowledge of the Dutch language is not an important cause of their lower results. The differences between native and immigrant children can be explained for a great part by differences in socio-economic status of the parents, as most parents of the Moroccan and Turkish migrant children belong to the lower occupational levels. The difference between native and immigrant children decreased with about one third after controlling for occupational level (table 6). Most probably the difference would decrease even more had it been possible to control for educational level of the parents as well.

Table 6. Mean IQ scores per ethnic group according to occupational level
occup. level ethnic group
native immigrant rest Morocco Turkey
low 17% 95.2 14% 89.0 76% 82.8
mean-low 38% 97.7 40% 100.5 24% 88.1
mean-high 21% 101.4 14% 96.3 - -
high 24% 108.1 32% 103.2 - -
total 100% 100.5 100% 99.1 100% 84.1

Educational variables
Due to the strong relation between school achievement and intelligence, and the importance of intelligence assessment for prediction of school success, the relationship with school career is one of the most direct indications of the validity of an intelligence test. For the SON-R, the relationship of test performance with school career was examined by stepwise multiple regression for three indicators. These indicators are differentiation according to type of school (like special education, general education), grade repetition and report marks (table 7).

Table 7. Cumulative relationship of the school variables with the IQ scores by stepwise multiple regression
. 7-9 yrs 10-11 yrs 13-14 yrs
R2 R2 R2
school type .04 .06 .37
grade repetition (+.15).19 (+.15).21 (+.02).39
report marks (+.10).29 (+.16).37 (+.01).40
R .54 .60 .63
R (corr. attenuation) .56 .63 .65

In primary education, the relation of school type with the IQ scores was limited; the difference between pupils of special education and general education was considerable (16 IQ points), but relatively few pupils were in special schools. Grade repetition related strongly to the IQ-scores. A relatively large group of pupils in primary education had repeated one or more grades and they had a lag in IQ scores of almost 19 points. Report marks also added to the explained variance of the IQ scores; for the younger group of primary education, 10% explained variance was added and for the older group 16% was added. The correlations of the IQ score with school subjects like language, arithmetic, and history/geography were of the same magnitude. The multiple correlation of the different indicators of the school career with the IQ scores was .54 in the age group of 7-9 years, and .60 in the age group of 10-11 years.

For the children in secondary education, the multiple correlation increased to .63. For these children the relation was almost completely determined by the differentiation into school type; grade repetition and report marks added little to the explained variance.

In many primary schools, a school achievement test is administered at the end of the sixth grade. Scores on this test were available for 49 subjects. The correlation with the SON-R IQ was .66. The correlations with the different parts of the achievement test were largely similar (language: r=.67; arithmetic: r=.59; information processing: r=.58). The subtests of the SON-R for abstract reasoning and the perceptual test showed the highest correlations with the achievement test (r >.53) while the correlations of the concrete reasoning tests and the spatial tests were below .46.

Performance of deaf children
Starting with the first version of the SON, the deaf population received special attention in the research with these tests. Next to the nation-wide sample of hearing subjects, almost the complete population of deaf pupils from 6-14 years of the Institutes for the Deaf and the Schools for the Partially Hearing, with a hearing loss of at least 90 dB, were examined with the SON-R 5.5-17.

The total group of 768 deaf children had a mean IQ of 90. The difference with hearing children was reduced to 8.5 points when we controlled for the proportion of migrants, which was four times as large as in the hearing group. After controlling for occupational level, the difference between the native deaf and hearing subjects became 7.7 points. Further analysis showed that this lag in performance of the deaf children was strongly related to the presence of multi handicapped children in the deaf population (about 25%). Several causes of deafness, such as complications during pregnancy and birth, and meningitis and encephalitis, can also be the cause of mental retardation. Excluding the multi handicapped, the lag of the deaf children was 4 IQ points and related mainly to the subtests for abstract reasoning.

The correlation of multiple handicaps and teacher's evaluation of intellectual insight with the IQ-scores was .63 and this increased to .66 by also including specific evaluations of cognitive handicaps, communicative handicaps and accuracy. The IQ-scores correlated .49 with the STADO-R, a written language test for the deaf which consists of four parts: synonyms, word order, idiom, and prepositions/conjunctions (De Haan & Tellegen, 1986). The correlation increased with age (6-10 years: r=.45; 10-14 years: r=.53). The abstract reasoning tests of the SON-R showed the highest correlation with the language test.

Other intelligence tests
In this section the results of three small-scale studies into the relationship of the SON-R with other intelligence tests will be summarised. They were performed by other researchers after the publication of the SON-R 5.5-17.

A group of 35 children from an outdoor psychiatric university clinic were tested with the SON-R, the WISC-R and the Raven Progressive Matrices Test (Nieuwenhuys, 1991). The age range was from 6 to 16 years and there were no immigrant children in the sample. The WISC-R (Van der Steene et al, 1991) has recently been standardised for the Dutch population. For the Raven (Raven, Court & Raven, 1983) English norms were used; eight groups of percentile scores were transformed to standard scores. Administration of the SON-R and the WISC-R was alternated within a period of two weeks. The Raven was generally combined with one of the other tests. For the SON-R the standard IQ was used. There is a great similarity in the means of the IQ scores. Paired t-tests showed no significant differences between the means. Also the standard deviation of the WISC FSIQ was equal to standard deviation of SON-R IQ. The standard deviation of the Raven was substantially lower but the norms of that test were not comparable. There were substantial high correlations of .80 between the SON-R IQ and the WISC-R FSIQ and PIQ. The correlations of the SON-R IQ and the PIQ with the verbal scale of the WISC-R were about the same (.66 and .65) and both scores correlated .74 with the Raven. Compared to the Raven, the SON-R showed higher correlations with all the IQ scores of the WISC-R.

Fourteen children from 6 to 12 years, who had been diagnosed as having specific language impairment at a centre for speech and language disorders, were reassessed after several years with four verbal tests from the WISC-R and with the SON-R (Jansen, 1991). For these children there still existed a large discrepancy between verbal intelligence as measured by the WISC-R VIQ (m=83.1; sd=14.8) and nonverbal intelligence as measured with the SON-R (m=97.5; sd=14.0). The difference was significant at the .01 level. In this particular group the correlation of the SON-R IQ with the VIQ was moderate, r=.35, and not significant.

At a school for deaf children a comparison was made between the performance of 14 children (age-range 5 to 7 years) on the SON-R and on an adapted version of the Learning test for Ethnic Minorities (Veerman, 1993). The LEM is a nonverbal test, based on theories of learning potential assessment, in which help is given to the subject during administration (Hessels & Hamers, 1993). The means and standard deviations were very similar for the SON-R (m=101.3; sd=21.2) and the LEM (m=101.4; sd=20.6). The correlation between the standardised total scores was high (r=.86). The SON-R correlated .70 with teacher's assessment of intelligence on a three-point scale; the LEM .63.

The SON-R 2.5-7

In 1991 the revision of the SON test for young children was started (Tellegen, Wijnberg, Laros & Winkel, 1992). The main goals of this revision were:

  • to supply up to date norms,
  • to improve the psychometric qualities of the test, especially for the extremes of the age-range by enlarging the number of items,
  • to give a good connection with the SON-R 5.5-17.

In the last two years several large-scale studies have been performed to improve the item sets. This has resulted in six subtests; the number of items has been doubled and the more difficult items have a close resemblance to the more easy items of the SON-R 5.5-17. On the basis of this research we expect the administration time to be about one hour; the reliability of the total score to be .90 and the generalizability of the total score to be .80.

In the second part of 1993 the standardization will be performed on a stratified random sample of 1100 children. Next to this, separate research will be done with migrant children, children with hearing impairments and children with severe learning difficulties. The SON-R 2.5-7 will be published in 1994 with manuals in the English, German and Dutch languages.

About 500 children of the standardization sample will also be tested this year with the Dutch revision of the Reynell language development scales. This will give interesting information on the relation between language development and nonverbal intelligence.

Discussion

Considering all the abovementioned characteristics of the SON tests, we believe that these tests can be a valuable tool for diagnostic use and for research in most European and other Western countries. However, culture fairness will always be a matter of degree. The concrete pictures that are used in several subtests may be unfamiliar to children who do not live in Western industrialised countries. Also climatological differences might contribute to bias of specific items. For instance in one item, a picture of a sledge is depicted which might not be recognizable for children in Mediterranean countries. Research is needed to discern if, and to what extend, adaptations of test materials are required for cultures greatly different from the Netherlands. In this respect it is interesting to note that migrant children from Morocco and Turkey did not show the greatest lag in performance on the subtests with concrete pictures but, in contrast, did worst on Analogies and Mosaics.

The most important consideration in the evaluation of any test is whether it measures accurately what it is intended to measure. Despite the immense literature on intelligence this is not an easy matter to answer as there is no commonly accepted operational definition of intelligence, and because intelligence tests can be used for quite different purposes.

An objection to a nonverbal test like the SON-R might be that the concept of intelligence is substantially narrowed by the exclusion of verbal ability tests. However by including tests for concrete and abstract reasoning - areas that often have a verbal form in general intelligence tests - the contents of the SON-R are not limited to typical performance tests. Although the test can be administered without using language, verbal abilities are certainly included in the evaluation of intelligence with the SON-R, as is illustrated by the correlations of the test with report marks and tests for language skills. Verbal intelligence tests often require specific knowledge learned in school. When the main object of using a test is to make predictions concerning school achievement, the absence of verbal tests in the SON-R might reduce its predictive power. If, however, the goal of intelligence assessment is to distinguish between possible causes of poor school performance, a test that is not dependent on specific knowledge is more appropriate. In such cases use of the SON-R is not only indicated for special groups such as deaf and immigrant children, but also suited for children without specific problems in the areas of language and communication.

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