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The relationship between laterality and numerical and spatial ability
Neuropsychologra, Vol. 27. No. Printed in Great Bntain.
7. pp.
1019~1022,
1989. i(l) 1989
Maxwell
0028-3932/X9 %3.OO+O.OC Pergamon Macmdlan plc
NOTE THE RELATIONSHIP
BETWEEN LATERALITY SPATIAL ABILITY
CHRISTOPHER
Department
of Psychology,
C.
AND NUMERICAL
AND
FRENCH and ELIZABETH A. ATTREE
University of London Goldsmiths’ London SE14 6NW, U.K.
(Received 5 September 1988; accepted 4 March
College,
New Cross,
1989)
Abstract-Hypotheses derived from right shift theory concerning the relationship between laterality and mathematical ability were investigated. This was done by dividing a group of 129 subjects into subgroups with presumably different distributions of the IS + +, rs + - and rs - - genotypes on the basis of their manual skills and then assessing their numerical and spatial abilities. No relationship was found between laterality and ability when the group as a whole were considered, but some marginal effects were found for numerical ability when data for a subgroup of 96 young female subjects were analysed separately. The results did not, however, conform to the predictions of right shift theory.
INTRODUCTION ANNETT [3] describes her right shift model of laterality in detail and considers the implications of the model in depth. Space limitations preclude detailed description of the theory here, but one prediction of the theory is that rsf + carriers will be at a relative disadvantage in any area which requires maximum efficiency on both sides of the brain including the application of spatial and mathematical concepts (see [3], p. 405). In support of the theory, ANNETT and KIL~HAW [4] found evidence that a reduction in dextral bias for both hand preference and skill was associated with special ability in mathematics by comparing mathematics students and teachers with academic and general controls. As ANNETT [3] herself comments, however, one is struck by the relative paucity of statistically significant effects despite the fact that the trends tend to be in the predicted direction. Furthermore, due to the hypothesized distribution differences between males and females in terms of expression of the rs + gene, it is ironically the case that it is more difficult to demonstrate increased incidences of left- and mixed-handedness in groups of female mathematicians than in groups of male mathematicians compared to appropriate controls (see [3] for detailed reasoning). However, as predicted, differences between the speed of left and right hands on a peg-moving task were reduced more for female mathematicians compared to controls than males. Overall, these results were seen as being consistent with the notion that groups of high mathematical ability are unlikely to contain rs+ + carriers. (Recently, ANNETT et al. [S, 61 have claimed that extreme dextrality is associated with disadvantages for both “right hemisphere” and “left hemisphere” functions.) An alternative and complementary approach to that used by ANNETT and KILSHAW [4] of assessing lateral biases in groups of known high ability in order to test whether the distributions are as predicted was used in the current study. This approach involved assessing a group of subjects in terms of hand preference and skill and in terms of numerical and spatial ability. It would be expected that a group from the general population would consist of a mixture of all possible genotypes in the following proportions: rs + + (0.3242), rs + - (0.4904), and rs - - (0.1854). Although it is not possible to be sure of the genotype of any individual, by assessing the difference between left and right hand skill one would expect that the greater the bias towards the right, the higher the probability that the subject was rs + +, vice versa. A group showing an extreme bias to the right would contain a higher proportion of rs + + individuals and might therefore, according to right shift theory, be expected to show a relative impairment in mathematical ability. This would apply to both sexes, but in this case the effects should be more apparent in female subjects. ANNETT [3] has suggested that university populations may not be representative of the general population in that they may include relatively more rs + - genotypes. This study therefore drew a sample from a population of further 1019
1020
NOTE
education students taking courses in psychology at various pre-university levels. Students on such courses span a wide range of ability levels. Some are taking courses with a view to university entrance, but many are simply taking the courses out of interest alone. Previous studies have not made clear which aspect of mathematical ability is affected by rs + + The present study therefore assessed subjects in terms of both numerical and spatial abilities.
METHOD Subjects One hundred and twenty-nine volunteer subjects (107 females) taking introductory level courses in psychology were tested for this study. Ages ranged from 16 to 55 yr. Handedness was assessed using ANNETT’S[l] questionnaire which asks subjects to indicate which hand they would use for each of 12 everyday actions. Procedure Hand skill was assessed using a peg-board test which involved timing subjects in moving 10 dowelling pegs from a row of 10 holes, each i in. deep and 1 in. apart, to an identical parallel row 8 in. away. Five trials were made with each hand with hands being alternated between trials. Subjects were randomly assigned to begin with either the right or the left hand. The time was measured to the nearest & set using a stopwatch. All subjects then performed the standardization edition of the numerical subtest of the NFER General Ability Tests followed by the spatial subtest. Tests were administered according to the standard instructions allowing 20 min for each test. The spatial test consisted of 80 items requiring a Yes/No response and thus a score of 40 would be expected by chance for a subject attempting all items. In fact, most subjects did not attempt all items within the time available and thus could have scored considerably less than 40. Two subjects, however, scored significantly lower than chance expectation for the number of questions attempted (3OjSO and 31/79) and it was concluded (following a suggestion from Marian Annett) that they must have misunderstood the instructions and responded to items by crossing out “Yes” on the answer sheet when they should have crossed out “No” and vice-versa. These subjects were therefore recorded as having scored 50 and 48 respectively.
RESULTS The mean difference between hand times (left minus right) on the peg-board task was calculated for each subject. Subjects were then ranked on the basis of this L-R difference. Subjects showing larger positive scores would be expected to have a higher probability of carrying the rs+ + gene and thus the whole group could be divided into subgroups of arbitrary size for the purposes of analysis. When the whole group was divided up in this way, none of the many groupings tried revealed any relationship between laterality and spatial or numerical ability. It is possible, however, that effects were being masked by noise in the data due to the fact that groups contained differing numbers of male and female subjects of varying ages. Comparisons between male and female subjects gave some support to this suggestion indicating that males scored higher on the numerical test (males: 20.18; females: 15.89; t (127)=3.29, P
NOTE TABLE 1. Means
1021
(and SDS) for peg-moving times (in set), L-R differences, and numerical each approximately equal-sized subgroup of young female subjects
and spatial
scores for
N
R hand
L hand
L-R
1
12
2
12
3
12
4
13
5
12
6
12
7
12
8
11
9.69 (0.95) 9.11 (0.93) 8.49 (0.71) 8.63 (0.60) 8.64 (0.47) 8.22 (0.41) 8.52 (0.81) 8.69 (0.98)
8.66 (0.76) 9.17 (0.94) 8.96 (0.74) 9.29 (0.61) 9.45 (0.47) 9.19 (0.43) 9.76 (0.82) 10.87 (1.47)
-1.03 (0.68) 0.06 (0.22) 0.48 (0.05) 0.65 (0.06) 0.81 (0.03) 0.97 (0.07) 1.25 (0.10) 2.19 (0.81)
15.75 (3.08) 13.42 (4.91) 18.00 (4.92) 14.31 (5.84) 18.75 (4.60) 16.00 (3.52) 15.17 (5.24) 18.09 (4.83)
41.58 (15.68) 35.00 (21.67) 45.33 (19.56) 44.15 (18.76) 50.25 (12.96) 44.25 (15.99) 44.17 (15.95) 48.36 (19.97)
8.75 (0.85)
9.41 (1.01)
0.66 (0.93)
16.15 (4.88)
44.09 (17.62)
Group
Overall
Numerical
Spatial
greater than 2.00. Table 2 presents the results of such a division. The extreme dextral group of only four subjects scored slightly below the mean on the numerical test and considerably above the mean on the spatial test. No differences were significant however (for numerical test, F(3,92)=0.37; for spatial test, F (3,92)=0.63). So far analyses have been based upon the classification of subjects according to hand skill rather than preference, in line with the notion that self-expressed hand preference may well be influenced by cultural pressures. However, data were collected with respect to hand preferences and thus it was possible to allocate subjects to different handedness subgroups according to the association analysis classification used by ANNETT [Z] (see [2] for details). This classification allows one to classify subjects on the basis of their questionnaire responses into eight subgroups ranging from pure right-handedness to pure left-handedness (not to be confused with the previous groupings based on L-R differences). Most previous studies of laterality and cognitive ability have been based upon looking for differences between groups ofdifferent self-reported handedness and so it was ofsome interest to consider our data in this manner. Table 3 presents the mean numerical and spatial ability scores for each handedness group. In examining the data there is a slight trend for lower scores to be found in handedness groups 5,7 and 8. Groups 2 to 4 and 5 to 8 were combined (in order to increase cell sizes) and a one-way analysis of variance was performed on these groupings. Again, no significant differences were found (for numerical scores, F (2,93)=0.64, ns; for spatial scores, F (2,93) = 0.87, ns).
DISCUSSION The results of this study offer no suport to the predictions of the right shift theory relating laterality to differences in mathematical ability. Despite several analyses, only marginal significant effects were found for numerical ability and no effects for spatial ability. The effects for numerical ability would appear to contradict right shift theory insofar as, amongst other effects, the most dextral groups were found to have significantly higher scores than the least lateralized group, but too much weight should not be attached to this effect unless other studies found a similar pattern. As stated, several different groupings were tested and the others showed no effects. The possibility of spuriously significant effects cannot be ruled out but the pattern of results is hard to reconcile with the predictions of right shift theory. Grouping subjects according to self-expressed hand preference also failed to reveal any significant differences. It should be pointed out that this study may be open to criticism on two counts. Firstly, the sample employed was rather small. ANNETT [3] points out that strong tests of the theory must rely on large samples as the presence of the rs + + genotype cannot be inferred with certainty in any individual even though there is an increased probability of rs + + at the right of the distribution of L-R scores. Secondly, even though an attempt was made to avoid using university students, our sample may still not have been representative of the general population. Although the overall mean scores suggest that the current sample was not of particularly high ability, the fact that all were self-
1022
NOTE
TABLE 2. Means (and SDS) for peg-moving times (in set), L-R differences, and numerical and spatial scores for each subgroup of young female subjects grouped according to the groupings used by ANNETT and KILSHAW [S]
Group
N
R hand
L hand
L-R
Numerical
Spatial
L-R time
18
o.o(M.99
49
1.00-1.99
25
9.48 (0.99) 8.62 (0.66) 8.46 (0.69) 8.94 (1.45)
8.75 (0.79) 9.25 (0.66) 9.79 (0.78) 11.93 (1.97)
-0.73 (0.70) 0.63 (0.21) 1.33 (0.29) 2.99 (0.87)
15.17 (3.78) 16.57 (5.25) 16.08 (4.88) 15.75 (5.56)
40.67 (20.05) 44.33 (17.11) 44.56 (17.60) 53.75 (13.74)
>2.00
4
TABLE 3. Mean numerical
Handedness Group 1 2 3 4 5 6 7 8
(pure right) (mixed right) (mixed right) (mixed right) (mixed right) (mixed left) (mixed left) (pure left)
and spatial
ability scores for each self-expressed subjects
handedness
group
of young
female
Spatial
Numerical N
Mean
SD
Mean
SD
69 12 5 2 3 0 1 4
16.10 15.50 19.60 19.00 15.33
4.99 5.33 2.19 4.24 6.51
43.83 48.50 45.00 49.00 37.00 -
17.59 15.57 21.37 11.31 29.55
16.00 13.75
2.99
29.00 36.00
20.90
selected for introductory level psychology courses is a cause for concern. It might be the case that such a group would by its nature contain fewer extreme dextrals than the general population. Acknowledgements-The authors wish to thank Marian Annett for her advice and encouragement, NFER-Nelson for allowing us to use pre-publication copies of their General Ability Tests and Nigel Wellock for the construction of equipment. Thanks are also due to the lecturers at East Ham, Woolwich and Southwark Colleges for their cooperation in providing access to students.
REFERENCES 1. 2. 3. 4. 5.
ANNETT, M. A classification of hand preference by association analysis. Br. J. Psycho/. 61, 303-321, 1970. ANNETT, M. The growth of manual preference and speed. Br. J. Psychol. 61, 545-558, 1970. ANNETT, M. Left, Righf, Hand and Brain: The Right Shift Theory. Lawrence Erlbaum Associates, London, 1985. ANNEZTT,M. and KILSHAW, D. Mathematical ability and lateral asymmetry. Cortex 18, 547.-568, 1982. ANNETT, M. and KILSHAW, D. Lateral preference and skill in dyslexics: implications of the Right Shift Theory. J. Child Psychoi. Psychiat. 25, 357-377, 1984. 6. ANNETT, M. and MANNING, M. The disadvantages of dextrality for intelligence. Br. J. Psychol., in press.
7. pp.
1019~1022,
1989. i(l) 1989
Maxwell
0028-3932/X9 %3.OO+O.OC Pergamon Macmdlan plc
NOTE THE RELATIONSHIP
BETWEEN LATERALITY SPATIAL ABILITY
CHRISTOPHER
Department
of Psychology,
C.
AND NUMERICAL
AND
FRENCH and ELIZABETH A. ATTREE
University of London Goldsmiths’ London SE14 6NW, U.K.
(Received 5 September 1988; accepted 4 March
College,
New Cross,
1989)
Abstract-Hypotheses derived from right shift theory concerning the relationship between laterality and mathematical ability were investigated. This was done by dividing a group of 129 subjects into subgroups with presumably different distributions of the IS + +, rs + - and rs - - genotypes on the basis of their manual skills and then assessing their numerical and spatial abilities. No relationship was found between laterality and ability when the group as a whole were considered, but some marginal effects were found for numerical ability when data for a subgroup of 96 young female subjects were analysed separately. The results did not, however, conform to the predictions of right shift theory.
INTRODUCTION ANNETT [3] describes her right shift model of laterality in detail and considers the implications of the model in depth. Space limitations preclude detailed description of the theory here, but one prediction of the theory is that rsf + carriers will be at a relative disadvantage in any area which requires maximum efficiency on both sides of the brain including the application of spatial and mathematical concepts (see [3], p. 405). In support of the theory, ANNETT and KIL~HAW [4] found evidence that a reduction in dextral bias for both hand preference and skill was associated with special ability in mathematics by comparing mathematics students and teachers with academic and general controls. As ANNETT [3] herself comments, however, one is struck by the relative paucity of statistically significant effects despite the fact that the trends tend to be in the predicted direction. Furthermore, due to the hypothesized distribution differences between males and females in terms of expression of the rs + gene, it is ironically the case that it is more difficult to demonstrate increased incidences of left- and mixed-handedness in groups of female mathematicians than in groups of male mathematicians compared to appropriate controls (see [3] for detailed reasoning). However, as predicted, differences between the speed of left and right hands on a peg-moving task were reduced more for female mathematicians compared to controls than males. Overall, these results were seen as being consistent with the notion that groups of high mathematical ability are unlikely to contain rs+ + carriers. (Recently, ANNETT et al. [S, 61 have claimed that extreme dextrality is associated with disadvantages for both “right hemisphere” and “left hemisphere” functions.) An alternative and complementary approach to that used by ANNETT and KILSHAW [4] of assessing lateral biases in groups of known high ability in order to test whether the distributions are as predicted was used in the current study. This approach involved assessing a group of subjects in terms of hand preference and skill and in terms of numerical and spatial ability. It would be expected that a group from the general population would consist of a mixture of all possible genotypes in the following proportions: rs + + (0.3242), rs + - (0.4904), and rs - - (0.1854). Although it is not possible to be sure of the genotype of any individual, by assessing the difference between left and right hand skill one would expect that the greater the bias towards the right, the higher the probability that the subject was rs + +, vice versa. A group showing an extreme bias to the right would contain a higher proportion of rs + + individuals and might therefore, according to right shift theory, be expected to show a relative impairment in mathematical ability. This would apply to both sexes, but in this case the effects should be more apparent in female subjects. ANNETT [3] has suggested that university populations may not be representative of the general population in that they may include relatively more rs + - genotypes. This study therefore drew a sample from a population of further 1019
1020
NOTE
education students taking courses in psychology at various pre-university levels. Students on such courses span a wide range of ability levels. Some are taking courses with a view to university entrance, but many are simply taking the courses out of interest alone. Previous studies have not made clear which aspect of mathematical ability is affected by rs + + The present study therefore assessed subjects in terms of both numerical and spatial abilities.
METHOD Subjects One hundred and twenty-nine volunteer subjects (107 females) taking introductory level courses in psychology were tested for this study. Ages ranged from 16 to 55 yr. Handedness was assessed using ANNETT’S[l] questionnaire which asks subjects to indicate which hand they would use for each of 12 everyday actions. Procedure Hand skill was assessed using a peg-board test which involved timing subjects in moving 10 dowelling pegs from a row of 10 holes, each i in. deep and 1 in. apart, to an identical parallel row 8 in. away. Five trials were made with each hand with hands being alternated between trials. Subjects were randomly assigned to begin with either the right or the left hand. The time was measured to the nearest & set using a stopwatch. All subjects then performed the standardization edition of the numerical subtest of the NFER General Ability Tests followed by the spatial subtest. Tests were administered according to the standard instructions allowing 20 min for each test. The spatial test consisted of 80 items requiring a Yes/No response and thus a score of 40 would be expected by chance for a subject attempting all items. In fact, most subjects did not attempt all items within the time available and thus could have scored considerably less than 40. Two subjects, however, scored significantly lower than chance expectation for the number of questions attempted (3OjSO and 31/79) and it was concluded (following a suggestion from Marian Annett) that they must have misunderstood the instructions and responded to items by crossing out “Yes” on the answer sheet when they should have crossed out “No” and vice-versa. These subjects were therefore recorded as having scored 50 and 48 respectively.
RESULTS The mean difference between hand times (left minus right) on the peg-board task was calculated for each subject. Subjects were then ranked on the basis of this L-R difference. Subjects showing larger positive scores would be expected to have a higher probability of carrying the rs+ + gene and thus the whole group could be divided into subgroups of arbitrary size for the purposes of analysis. When the whole group was divided up in this way, none of the many groupings tried revealed any relationship between laterality and spatial or numerical ability. It is possible, however, that effects were being masked by noise in the data due to the fact that groups contained differing numbers of male and female subjects of varying ages. Comparisons between male and female subjects gave some support to this suggestion indicating that males scored higher on the numerical test (males: 20.18; females: 15.89; t (127)=3.29, P
NOTE TABLE 1. Means
1021
(and SDS) for peg-moving times (in set), L-R differences, and numerical each approximately equal-sized subgroup of young female subjects
and spatial
scores for
N
R hand
L hand
L-R
1
12
2
12
3
12
4
13
5
12
6
12
7
12
8
11
9.69 (0.95) 9.11 (0.93) 8.49 (0.71) 8.63 (0.60) 8.64 (0.47) 8.22 (0.41) 8.52 (0.81) 8.69 (0.98)
8.66 (0.76) 9.17 (0.94) 8.96 (0.74) 9.29 (0.61) 9.45 (0.47) 9.19 (0.43) 9.76 (0.82) 10.87 (1.47)
-1.03 (0.68) 0.06 (0.22) 0.48 (0.05) 0.65 (0.06) 0.81 (0.03) 0.97 (0.07) 1.25 (0.10) 2.19 (0.81)
15.75 (3.08) 13.42 (4.91) 18.00 (4.92) 14.31 (5.84) 18.75 (4.60) 16.00 (3.52) 15.17 (5.24) 18.09 (4.83)
41.58 (15.68) 35.00 (21.67) 45.33 (19.56) 44.15 (18.76) 50.25 (12.96) 44.25 (15.99) 44.17 (15.95) 48.36 (19.97)
8.75 (0.85)
9.41 (1.01)
0.66 (0.93)
16.15 (4.88)
44.09 (17.62)
Group
Overall
Numerical
Spatial
greater than 2.00. Table 2 presents the results of such a division. The extreme dextral group of only four subjects scored slightly below the mean on the numerical test and considerably above the mean on the spatial test. No differences were significant however (for numerical test, F(3,92)=0.37; for spatial test, F (3,92)=0.63). So far analyses have been based upon the classification of subjects according to hand skill rather than preference, in line with the notion that self-expressed hand preference may well be influenced by cultural pressures. However, data were collected with respect to hand preferences and thus it was possible to allocate subjects to different handedness subgroups according to the association analysis classification used by ANNETT [Z] (see [2] for details). This classification allows one to classify subjects on the basis of their questionnaire responses into eight subgroups ranging from pure right-handedness to pure left-handedness (not to be confused with the previous groupings based on L-R differences). Most previous studies of laterality and cognitive ability have been based upon looking for differences between groups ofdifferent self-reported handedness and so it was ofsome interest to consider our data in this manner. Table 3 presents the mean numerical and spatial ability scores for each handedness group. In examining the data there is a slight trend for lower scores to be found in handedness groups 5,7 and 8. Groups 2 to 4 and 5 to 8 were combined (in order to increase cell sizes) and a one-way analysis of variance was performed on these groupings. Again, no significant differences were found (for numerical scores, F (2,93)=0.64, ns; for spatial scores, F (2,93) = 0.87, ns).
DISCUSSION The results of this study offer no suport to the predictions of the right shift theory relating laterality to differences in mathematical ability. Despite several analyses, only marginal significant effects were found for numerical ability and no effects for spatial ability. The effects for numerical ability would appear to contradict right shift theory insofar as, amongst other effects, the most dextral groups were found to have significantly higher scores than the least lateralized group, but too much weight should not be attached to this effect unless other studies found a similar pattern. As stated, several different groupings were tested and the others showed no effects. The possibility of spuriously significant effects cannot be ruled out but the pattern of results is hard to reconcile with the predictions of right shift theory. Grouping subjects according to self-expressed hand preference also failed to reveal any significant differences. It should be pointed out that this study may be open to criticism on two counts. Firstly, the sample employed was rather small. ANNETT [3] points out that strong tests of the theory must rely on large samples as the presence of the rs + + genotype cannot be inferred with certainty in any individual even though there is an increased probability of rs + + at the right of the distribution of L-R scores. Secondly, even though an attempt was made to avoid using university students, our sample may still not have been representative of the general population. Although the overall mean scores suggest that the current sample was not of particularly high ability, the fact that all were self-
1022
NOTE
TABLE 2. Means (and SDS) for peg-moving times (in set), L-R differences, and numerical and spatial scores for each subgroup of young female subjects grouped according to the groupings used by ANNETT and KILSHAW [S]
Group
N
R hand
L hand
L-R
Numerical
Spatial
L-R time
18
o.o(M.99
49
1.00-1.99
25
9.48 (0.99) 8.62 (0.66) 8.46 (0.69) 8.94 (1.45)
8.75 (0.79) 9.25 (0.66) 9.79 (0.78) 11.93 (1.97)
-0.73 (0.70) 0.63 (0.21) 1.33 (0.29) 2.99 (0.87)
15.17 (3.78) 16.57 (5.25) 16.08 (4.88) 15.75 (5.56)
40.67 (20.05) 44.33 (17.11) 44.56 (17.60) 53.75 (13.74)
>2.00
4
TABLE 3. Mean numerical
Handedness Group 1 2 3 4 5 6 7 8
(pure right) (mixed right) (mixed right) (mixed right) (mixed right) (mixed left) (mixed left) (pure left)
and spatial
ability scores for each self-expressed subjects
handedness
group
of young
female
Spatial
Numerical N
Mean
SD
Mean
SD
69 12 5 2 3 0 1 4
16.10 15.50 19.60 19.00 15.33
4.99 5.33 2.19 4.24 6.51
43.83 48.50 45.00 49.00 37.00 -
17.59 15.57 21.37 11.31 29.55
16.00 13.75
2.99
29.00 36.00
20.90
selected for introductory level psychology courses is a cause for concern. It might be the case that such a group would by its nature contain fewer extreme dextrals than the general population. Acknowledgements-The authors wish to thank Marian Annett for her advice and encouragement, NFER-Nelson for allowing us to use pre-publication copies of their General Ability Tests and Nigel Wellock for the construction of equipment. Thanks are also due to the lecturers at East Ham, Woolwich and Southwark Colleges for their cooperation in providing access to students.
REFERENCES 1. 2. 3. 4. 5.
ANNETT, M. A classification of hand preference by association analysis. Br. J. Psycho/. 61, 303-321, 1970. ANNETT, M. The growth of manual preference and speed. Br. J. Psychol. 61, 545-558, 1970. ANNETT, M. Left, Righf, Hand and Brain: The Right Shift Theory. Lawrence Erlbaum Associates, London, 1985. ANNEZTT,M. and KILSHAW, D. Mathematical ability and lateral asymmetry. Cortex 18, 547.-568, 1982. ANNETT, M. and KILSHAW, D. Lateral preference and skill in dyslexics: implications of the Right Shift Theory. J. Child Psychoi. Psychiat. 25, 357-377, 1984. 6. ANNETT, M. and MANNING, M. The disadvantages of dextrality for intelligence. Br. J. Psychol., in press.