A problem common to all clustering techniques is the difficulty in deciding on the most appropriate number of clusters to select .sx The approach used for these data was to plot the numbers of clusters against the fusion coefficient to discover a marked change in the value of the coefficient ( Everitt , 1980) .sx This change indicates that two relatively dissimilar clusters have been merged and that the number of clusters prior to this merger is likely to be the most appropriate .sx Examination of the coefficients pointed to a four or five group cluster solution .sx This analysis was followed by a K-means iterative partitioning technique which , as a cluster technique , also produces a partitioning of the cases but differs from the hierarchical methods in that it is able to check cluster membership and reassign any suboptimally placed children to a better fitting cluster .sx Unlike hierarchical methods , the researcher must specify before the analysis the desired number of clusters .sx In this case a four-cluster and a five-cluster solution were performed .sx A split-sample replication of the five-cluster solution using the K-means iterative procedure yielded a solution which closely approximated that of the whole sample , particularly for the children with large discrepancy scores who continued to cluster together .sx Thus the validity of a five-group solution was supported on two grounds :sx similarity of solutions derived from different clustering methods and similarity of the solutions obtained for the combined sample and for the split-sample .sx An additional and critical test of the validity of any cluster solution can be provided by an examination of variables not included in the cluster analysis .sx In order to examine the external validity of the five groups a series of analyses were carried out on their performance on a range of cognitive tests .sx All analyses were carried out using SPSSX ( Statistical Package for the Social Sciences) .sx RESULTS From Table 2 it can be seen that Groups 1 and 2 ( 26 per cent of the sample ) were reading or spelling above the level predicted by both Verbal and Performance IQ .sx Groups 4 and 5 ( 63 per cent ) were achieving considerably below prediction .sx Table 3 shows the sex , age and intellectual performance of groups .sx Significant differences were found between the groups on all these variables .sx Table 4 indicates the performance of the five groups on the reading and spelling tests which were similarly found to be significantly different .sx tables&captions .sx Initial identification of the groups was followed by a series of analyses comparing performance on the battery of cognitive tests with age and IQ ( Full-Scale ) as covariates , as there were significant differences between the groups on these variables .sx On nine of the 20 cognitive measures significant differences were found between the groups ( see Table 5) .sx A chi-square analysis revealed no significant differences between the groups for foot or eye preference nor eye dominance .sx An analysis of the phonetic and visual characteristics of the first 10 spelling errors indicated significant differences ( see Table 6) .sx Parent and teacher interview .sx The results of a series of chi-square analyses indicated that the groups were significantly different on all three variables examined in this study ( see Table 7) .sx The groups differed on whether children had received remedial help and whether there were reading or spelling problems reported in the family .sx In addition the number of children who were reading prior to school entry differed between the groups .sx Emotional characteristics .sx Group scores on the anti-social and neurotic subscales of the Rutter Children's Behaviour questionnaire ( Rutter , 1967 ) were compared by analysis of covariance .sx Age and IQ were used as covariates as the groups differed significantly on these variables .sx No significant differences were found on the anti-social subscales .sx On the Neurotic subscale , cluster Group 3 had a significantly higher mean score ( ANCOVA , F=3 .sx 71 , df 4,451 ; P<0 .sx 01 ) , although none of the children in this group had a score which would be considered diagnostic in a clinical setting according to the cut-offs suggested by Rutter .sx tables&captions .sx Further examination of Group 3 .sx It has been argued that dyslexia is not a homogeneous disorder and that different groups may be discerned ( see , for example , Rourke , 1985) .sx In order to look for possible subgroups within Group 3 , the group with the poorest reading and spelling relative to IQ , further cluster analyses were carried out using the cognitive and emotional variables .sx This analysis was performed to examine whether any further meaningful subdivisions are apparent within this group , and whether these subdivisions reflect any particular pattern of abilities .sx Hierarchical cluster analysis suggested a two-group solution .sx A subsequent K-means iterative analysis , with two groups being selected , produced one group of 16 and another of 27 .sx Table 8 shows the differences between the two groups on the cognitive and emotional variables .sx As can be seen from Table 8 , the two groups differed on absolute levels of performance on 15 of the 20 cognitive measures ( 75 per cent) .sx The groups were not found to be different on age or IQ but differed significantly on all measures of reading and spelling as shown in Table 9 .sx table&caption .sx DISCUSSION One of the purposes of this study was to examine a large group of children to see whether a discrete group(s ) with large discrepancies between ability and achievement could be identified .sx Using cluster analysis it was possible both to avoid the difficulty of having to specify a particular size of discrepancy as being significant and to examine concurrently the extent and pattern of six discrepancy scores .sx The issue of heterogeneity in dyslexia was addressed at two levels .sx The first level can be termed an analysis of surface or presenting characteristics .sx This was conducted by examining all the groups identified in the analysis of the six discrepancy scores and establishing whether different patterns of disability were apparent in groups with large discrepancies .sx The second level was to examine whether those identified as a distinct group(s ) with large discrepancies had different patterns of cognitive abilities from the other groups .sx This approach examines the issue as to whether the differences evidenced in discrepancy scores reflect underlying cognitive processes .sx In the initial investigation five distinct groups appeared as a result of the cluster analysis :sx two whose reading achievement was at a level higher than that predicted by their intelligence , two whose performance was close to prediction and a group whose achievement was significantly below their ability .sx In a similar study in the USA Satz and Morris ( 1981 ) found two subgroups with large discrepancies .sx These two dyslexic groups were distinguished from one another by the extent of their discrepancy scores rather than their pattern .sx In both the Florida Longitudinal Project ( FLP ) and the Linbury study the dyslexic group(s ) which emerged showed discrepancies in all measures .sx Thus , in both studies , when cluster analysis was applied to reading and spelling in a mixed sample , no distinct dyslexic profiles appeared .sx In the Linbury study 11 per cent of children were identified as having large discrepancies while 38 per cent were found by Satz and Morris ( 1981 ) in the Florida Longitudinal Project .sx These differences are not surprising as in both studies some preselection of children had taken place , different variables were placed in the cluster analysis , the children in the two studies differed in age and both sexes were included in the Linbury study while the FLP only considered males .sx The percentage of participants identified as potentially dyslexic in these two studies contrasts with the 4-10 per cent found in studies using unselected groups of participants ( Rutter , 1978) .sx In order to examine whether the group with large discrepancies ( Group 3 ) possessed features associated with dyslexia , comparisons were made between the groups firstly on reading , spelling and IQ tests and then on the other cognitive tests in the study .sx Group 3 produced the lowest performance on all four reading and spelling measures , consistent with them being labelled a dyslexic group ( see Table 4) .sx The groups with the smallest discrepancies , 1 and 2 , had the highest scores on reading and spelling while Groups 4 and 5 had intermediate scores .sx An examination of age , Verbal and Performance IQ revealed significant differences between groups but did not indicate any particular tendency for the group with large discrepancies ( see Table 3) .sx The finding that Group 3 had the poorest performance on reading and spelling tests raises the question as to whether this group could have been identified simply by selecting those with the poorest reading performance .sx As Group 3 constituted 11 per cent of the sample a selection was made of all those children who performed at or below the 11th percentile on one measure of achievement , the Schonell Reading Test .sx Sixty per cent of these fell into cluster group 3 with the remaining 40 per cent falling into clusters 4 and 5 .sx A similar analysis was performed on the 'good' readers ( Groups 1 and 2 ) to examine whether they represented the top 26 per cent of reading .sx This indicated more than a quarter of the best readers were not in Groups 1 and 2 although none was in Group 3 .sx These analyses suggest that the cluster analysis applied in this study identifies different children from those identified by a simple examination of reading performance .sx A high incidence of reading and spelling difficulties among siblings , parents and other family members of dyslexic children has long been recognised ( Hinshelwood , 1909) .sx Yule and Rutter ( 1976 ) found that a dyslexic child was three times more likely than a non-dyslexic to have a family history of reading problems .sx The reading history of the children showed that Group 3 had the largest proportion of family members who reported difficulty with either reading or spelling .sx Groups 4 and 5 , however , which had no discrepancies between ability and achievement , had a similar reported family incidence ( see Table 7) .sx These three groups are to be contrasted with Groups 1 and 2 which had a lower reported incidence .sx These data were derived from self reports of reading and spelling difficulties in the immediate family .sx Family members were not formally assessed and thus the findings must be interpreted with caution .sx In addition to increased reports of familial incidence , Group 3 had a higher percentage who had received , or were receiving remedial help .sx Smaller percentages of Groups 4 and 5 had received , or were receiving remedial help .sx None of the children in Groups 1 and 2 had received remediation for reading and these groups also had the highest percentages of children who were reading at school entry ( Table 7) .sx These findings are consistent with the discrepancies and the overall reading and spelling performances apparent in the groups .sx There is a large body of evidence linking dyslexia with various emotional and behavioural problems ( see Thomson and Hartley , 1980) .sx Teacher ratings and observations suggest that dyslexic children are more distractible and dependent than their classmates ( McKinney et al .sx , 1982) .sx In line with these findings the results from the behaviour questionnaire showed that Group 3 had a significantly higher Neurotic subscore .sx However , in view of the findings of Rutter ( 1967 ) of a higher incidence of neurotic disorders in boys , the higher incidence found in Group 3 may reflect the sex distribution in the groups .sx The higher incidence amongst males of reading related problems is well established .sx Critchley ( 1967 ) , for example , in a review of the literature , showed that the percentage of boys in samples of children with dyslexia ranged from 66 per cent to 100 per cent .sx In a more recent review of the signs and symptoms linked with dyslexia , Wheeler and Watkins ( 1979 ) found sex differences of a similar order .sx Other large studies attempting to define dyslexic groups have limited their sample to males , presumably in an attempt to obtain a higher percentage of reading disabled participants , and therefore any direct comparison is precluded ( Satz and Morris , 1981 ; Van der Vlugt and Satz , 1985) .sx In this study even taking into account the number of males in total sample sic !sx ( 58 per cent ) , the percentage of males in Group 3 was extremely high ( 92 per cent) .sx The analyses of group differences on reading , spelling and IQ are not independent of the group differentiation as these variables were included in the cluster analysis .sx