Ann. Hm. Genet., Lond. (1960), 24, 23 P&ted i m Great B&h

23

The intellectual resemblance between sibs

BY JAMES MAXWELL AND A. E. G. PILLINER

This paper is an interim report on the intelligence testing of younger sibs of a representative group of Scottish 11-year-old children.

In the 1947 Scottish Mental Survey, a representative sample of 1215 children waa selected for a follow-up of their subsequent careers in school and beyond. This sample, known aa the ‘Six- Day Sample’, was selected from the total year group of Scottish children born in 1936, on the basis of date of birth, and consists of children born on the h t day of each even month in 1936. Comparison of the data obtained in the survey for these children and for the whole age-group shows that the 1215 children selected constitute an excellent representation of the whole year group-

Each of the 1215 children waa tested individually on form L of the Terman-Merrill Revision of the Binet test. Various testers co-operated in the testing; the results are discussed elsewhere.* In addition to the recording of data concerning the future progress of these children, the Mental Survey Committee, with the co-operation of educational psychologists and other testers in Scotland, arranged that the younger sibs of the childien should be tested, aa near to their eleventh birthday as possible, by the Terman-Merrill form L. The organization of the testing and the recording of the scores have been undertaken, with the aid of a grant from the Nuffield Foundation, by the Mental Survey Committee of the Scottish Council for Research in Edu- cation, to whom the writers express their indebtedness for permission to use the material discussed in this paper.

The data discussed in this paper are those obtained before 1 April 1956, approximately 9 years after the original testing of the sample of 1215 children. The testing of their younger sibs waa not then complete ; not all younger members of their families had reached their eleventh birth- day. Nor had it proved possible to obtain data for all the original 1215 children tested. The effective size of the sample is, for the purposes of this paper, reduced from 1215 to 1127, a, loss of 88 children. For fifty-nine children information is not available, mainly due to refusal of parents to co-operate, emigration from Scotland, death and failure to maintain contact. Also, four pairs of twins were excluded from this discussion to obtain simplicity of recording sibs. Finally, a further twenty-one children were excluded as the family situation was obscure ; most of these were either illegitimate or adopted. For all of the remaining 1127 the family structure is known, though it-has not proved always possible to maintain the regular testing of their younger sibs.

The Terman-Merrill I . Q . ’ ~ have in all cases been converted into standard scores, with a mean of 50 and a standard deviation of 10. The conversion was done from the I.Q.’S of the 1215 children tested in 1947, whose mean I.Q. wa8 102.52 and whose standard deviation waa 20.036 (Trend of Scottish Intelligence, p. 58). The standard scores are used throughout, and obviate any need for correction for the skew distribution obtained in the Terman-Merrill 1.8.’~. A rough and ready conversion is that a difference of one point of standard score is equal to two points of

* The Trend of Scottiah Intelligence 1949; The Eleven-year-olda &ow Up, 1968.

24 JAMES MAXWELL AND A. E. G. PILLINER I.Q. Throughout, the scores of the children in the original sample, known as the subjects, are designated x, and those of their younger sibs are designated y.

Table 1 presents the results of the intelligence testing of the subjects and their younger sibs. Two observations may clarify the interpretation of the data presented. Of the 1127 subjects, 654 have younger sibs tested. By expectation, half of the subjects in families of size two would

SF I 2

3 4 5 6 7 8 9 I 0 +

Total

Table 1. Mean scores and variances, by family size, for all subjects. subjects with younger sibs tested, and all younger sibs tested

(I) All subjects

n 31 c: 113 56.44 88.33

219 52.63 93-12 184 50'21 72-39 1 1 0 48.06 72-13 91 46-18 49'49 61 48-08 82-91 40 46.53 65-10 17 45-18 49-67 32 WOO 87.13

260 55'03 77'95

(2 ) Subjects with sibs tested

h

- n X d

1x5 54.80 90-22 132 5 2 . ~ 0 90.15 126 50-33 71-76 83 47-19 70'48 74 46.68 49'21 47 48.13 83-80 36 47-03 65-57 16 44-94 55'27 25 41.28 59-79

(3) All younger sibs tested (4) Mean sibs tested --

n j i d n Y uw

115 53-43 99.06 115 53.43 99-06 158 52-23 84.49 (132) 52.11 81-82 183 49-59 82.88 (126) 49.80 58.36 148 46.98 117.36 ( 83) 46-99 100'52 150 47.23 78.70 ( 74) 48-29 94-88 87 46-02 62.60 ( 47) 46.43 52.40 84 47-24 77-56 ( 36) 47-85 41'73 36 45.75 75-11 ( 16) 46.37 70.07 75 42-67 1'07.52 ( 25) 42'85 60.58

1036 48.5792 96.767 (654) 49.6769 85.614

Significance of differences of means

dl o;,

r, = 0.5

- - Meen .' - x1 51.3824 0.0806 k0.2839 xl-x - = 1*5170+_0'4612 x, 50.8185 0.0866 fo.2943 g-j i = 1.0977f0.4736 x 49-8654 0.1321 k0.3635 x-ji = 1*2862+0*3382

j j 49.6769 0.1309 fo.3618 Z-5 = 0.1885 k0.3626

-

-

48'5792 0.0934 k 0.3056 Z2-g = 2'2393 kO'3OO2

-Y = 2.8032 f 0.2953 Note: ( I ) x1 = Score for all subjects.

x, = Score for all subjects, except SF I. x = score for subjects with tested sibs. y = score for all sibs. j i = meen score for sibs in each family. y = mean score for 'average' sibs. qF = size of family.

=

(2) r,, = +0.5 haa been taken aa the best estimate throughout. (3) The 't' test has been applied directly to the figures for Z1-Z and G-a, though both variables

are drawn from the same population, not mutually exclusively.

be the latter born, and therefore have no younger sibs. Similarly, one-third of those of families of three, one-fourth of those of families of four, and so on, would be last born and have no younger sibs to be tested. According to this expectation, after deducting the 113 children without sibs, the estimated number of children with younger sibs would be 709.* This exceeds by 55 the number actually recorded; the deficiency is probably due to random divergence from expectation, and to a number of subjects whose younger sibs have not yet reached their eleventh birthday. There are, for instance, thikty such cmes in families of two.

* Derived from the complete range of family sizes; Table 1 is truncated.

The intellectual resemblance between sibs 25

The heading of col. (4) ‘Mean sibs tested’ may be rather cryptic. Two measures of the average score of younger sibs of given subjects are possible. The scores of all the younger sibs may be summed, for constant family size, as in col. (3). Alternatively, for any given subject, the mean score of his younger sibs may be calculated, so that for each subject is recorded the score of one ‘average’ sib. This was done in col. (4). The variances were obtained in the same way.

SOME IMPLICATIONS FOR SAMPLING

(1) Though it is known that the losses from the original sample of 1215 children aTe pot random for intelligence, the remaining 1127 children will be taken for the purposes of discussbn as being a reasonable representation of a total population of children. The error involved in this assumption is slight. If from this population are drawn dl children having sibs, the average intelligence of the children with sibs is lower than that of the population from which they are selected. This is a well-known phenomenon, and can be satisfactorily accountedfor in terms of differential fertility, i.e. the negative correlation between intelligence and size of sibship. If the selection is of subjects with sibs, the reduction in mean intelligence score is the result of the exclusion of children of family size one, who tend to be of above average intelligence. Ex- pressing the data in Table 1 in terms of I.Q. the effect of excluding families of one child from the total sample is to lower the mean I.Q. by approximately one point.

If, however, as in our data, the selection is confined to subjects with younger sibs, the effect is intensified. The maximum chance of any subject in a family of two having a younger sib is 1/2; the maximum chance of a subject in a family of ten is 9/10. The sample of subjects with younger sibs is clearly biased to the larger families, and hence to the less intelligent children. The effect is clearly shown in Table 2, col. (4). From Table 1 it appears that the expected mean I.Q. of subjects with younger sibs would be about 3 points lower than that of the total population of subjects, and about 2 points lower than that of the population of subjects with sibs. This is the maximum effect, but in so far as the basis of selection is biased towards younger sibs as against all sibs, the effect will be operative.

It may be noted in passing that the effect of selection by sibs may have some bearing on the intellectual inferiority of twins so regularly observed. The proper basis of comparison is not with a complete population, but with a population of children with sibs. This is clearly not the whole explanation of the lower average intelligence of twins, but it may be a part of it.

(2) A further consequence of the method of selection may be observed in Table 1. When the average intelligence test score of the sibs is compared with that of their subjects, a difference of about 1.3 points of test score (almost 2 points of I.Q.) is noted. This is almost certainly due to the effect of differential fertility acting in conjunction with a positive correlation between size of family and number of younger sibs tested.* The extent of the latter effect is shown in Table 2,

* The correspondence between family size and group-intelligence test score, expressed rn a product- moment correlation coefficient, is for the Scottish Survey population of 70,200 children, r = - 0-28 (Trend of Scottish ImnteZZigence, p. 115). The corresponding figure for the Six-Day Sample, who are virtually the same rn ‘All Subjects’ in this paper, is r = -0.28 (0). The difference is negligible. For the Terman-Memill test scores, the correlation for the Six-Day Sample is r = -0.32, which is not significantly Merent from the value of r = - 0-34 for ‘Subjects with tested sibs ’ in Table 3. These coefficients suggest : (a) that the differential fertility for intelligence test score may be greater for Terman-Memill than for Group Test Scores, though the difference is not statistically significant; (b ) that the pattern of differential fertility for the subjects of this paper is virtually the same as that of the whole Scottish Survey population from whom they were drawn.

26 JAMES WELL AND A. E. G. PILLINER col. (6). As we have seen, the sib sample is biased towards the larger families, with the con- sequent lowering of the average 1.8. of the sibs. This bias can be eliminated by taking one sib per subject, the notional 'average' sib. The mean score of these 'sibs' (Table 1, col. (4)) is not sigrdicantly different from that of their subjects (Table 1, col. (2)).

Table 2. Percentage of subjects with tested younger sibs, by family size

(2) (1) No. of

(4) (5) No. of subjecta (3) all with NO. of (2) 88 % (3) 88

of (2) SF subjects sibs tested sibs tested of (I)

I 113 2 260 3 219 4 1 84 5 I I 0 6 91 7 61 8 40 9 I7

I 0 + 32 Total 1127

- 1 I5 132 I 26 83 74 47 36 16 25

654

44'25 60.27 68-47 75'45 81-32 77'05 90.00 94-12 78-13 64-50

100'0

119.7 145.2 178.3 202.7 185.1 233'3 225.0 300.0

158.4

(3) It is possible from the data in Tables 1 and 2 to make certain rough generalizations about the effect of selecting by sib from a total population. These may be formulated as follows:

(a) If, from any population measured for a character exhibiting negative Merential fertility, there are drawn all subjects vith sibs, the average of these subjects will tend to be lower than that of the population, to an extent depending on the degree of differential fertility. For intelligence, the appropriate standard of reference for such subjects appears to be about 99 I.Q.

(b) If, from the same population, there are drawn all subjects with younger sibs (or if the probability of a subject being drawn is positively correlated with the size of his sibship), the average of such subjects will be still lower than that of the population. For intelligence, the appropriate standard of reference for such subjects appears to be about 97 1.8.

(c) If the younger sibs of the subjects in (b) are drawn from the population, and if the number of sibs measured (or the probability of a sib being measured) is positively correlated with the size of sibship, the average of the sibs will be lower than that of both the population and the subjects, depending on the correlation between the number of sibs memured and size of sibship. For intelligence, the appropriate standard of reference for such sibs would appear to be about

The values given for intelligence in the above statements are, of course, approximate, and are based on the data of Table 1. The results, however, do imply that a mean 1.8. of 95 for such sibs is compatible with their being selected, on the basis of sibship, from a population with an average I.Q. of 100.

95 1.8.

REQRESSION OF SCORE ON FAMILY SIZE

The data are presented in Table 3. Inspection of Table 1 suggests there is a tendency for younger sibs in smaller families to be less intelligent than the subjects, and for younger sibs in the lazger families to be more intelligent than the subjects. The regression of subjects' test score

The intellectual resemblance between sibs 27

on size of sibship is b = -1*47+0.16 and that of sibs' test score is b = - 1.20+0-13. The difference between these two regression coefficients is not statistically significant ; and though the correlation/regression statistic is not wholly applicable to this type of data, it is improbable that the skewness of the sibship distribution seriously invalidates the significance tests. The differences in Table 1, between the means of subjects and sibs for constant size of sibship, also fall short of statistical sigmficance.

Table 3. Regression of score on family size (8)

n. 8 2 8 c8' Z8 c (m) r, bz,

( I ) Subjects with tested sibs (z on 8 )

654 56,409'2 3 9044'53 3 2,346 -4,473'33 -0.341 - 1.4693 k0.158

(2) All sibs (y on 8)

n EY* Zea c8 ( Y 4 r,* bv. I ,036 100,153'5 5 9494' I 9 4.395 -6,619-37 -0.282 - 1.2048 k0 .127

(3) Mean sibs (3 on 8)

n cp ESP c8 c ( V 4 T i , bis 654 55,905'9 39044'53 3 2,346 -3,623'8 -0.278 - 1 ~ 1 9 0 + 0 ~ 1 6 1

Note: ( I ) NO differences of regression coefficients (b) are significant at 5 yo. (2) The regressions do not depart significantly from linearity.

The divergence (in opposite directions) between average scores of subjects and their younger sibs in very large and very small families appears on statistical evidence to fall within the limits of chance. The total numbers involved are such that we are unable to say whether the observed phenomenon is a random departure from identity of the two regressions, or whether there is a systematic divergence such as we have mentioned above, but which is too small to reach the level of statistical significance within the limits of our data. If the latter hypothesis should be confirmed by more extensive inquiries, certain interesting consequences would follow. It would imply that the assumption, that any one child selected from a family is as likely to be repre- sentative of the family as any other child, is not wholly tenable. Though over the whole range of family sizes there appears no systematic relation between parity and test score, yet at the extremes of the range there would appear to be a small systematic relationship. Secondly, if the hypothesis should be confirmed, there arises the question of what may be the explanation. On the face of it, the data suggest some sort of regression effect, such that parity is associated with regression to the mean of the population. The genetic implications of this are not clear. The phenomenon is, however, not firmly established by the data investigated here, so extensive discussion is not warranted. It may well be that it is a random feature of the particular set of observations under examination, but it is put on record as a point worthy of attention in future similar inquiries.

INCOMPLETE FAMILIES

The negative relationship between family size and intelligence test score has now been firmly established as a result of various investigations, the 1947 Scottish Mental Survey being one of the major ones. It has been pointed out on more than one occasion that the families of the Scottish Mental Survey children were not completed, and it has been suggested that this may have obscured to some extent the exact relationship between family size and test score in that

JAMES MAXWELL AND A. E. G. PILLINER population. Nine years after the Scottish Survey, the families appear to be virtually complete, the latest recorded birth of a younger sib being November 1953. It is possible at the time of closing the record (April 1956) that further births may occur, but the numbers are likely to be so small as to be of negligible effect on the family size-test score relationship. As the dates of birth of all the younger sibs of the 1127 children in the present sample are known, it is possible to calculate easily what would have been recorded as the size of family for these children in June 1947, the date of the Scottish Survey; from that, it is possible to compare the degree of differential fertility as recorded for the virtually complete families in 1956 with that for the incomplete families as they would have been recorded in 1947. In making the comparisons in Table 4, deaths between 1947 and 1956 have been ignored, only additions to the family being counted. It is clear from Table 4 that differences between the 1956 and 1947 means for constant size of family are very small, apart from some random fluctuations in the larger families where the numbers of children are small. The regressions of test score on family size for the two records are not significantly different, and the difference is small. It seems safe to conclude that the effect of incomplete families is a very minor one, and that estimates of differential fertility obtained by testing children while their sibships were incomplete would not differ significantly from the estimates which would have been obtained had the sibships reached completion.

Table 4. Cornparison of mean test score by family size 1956 and 1947

SF I

2

3 4 5 6 7 8 9 I 0 +

Total

1 I3 (I34* 260 219 184 I I 0

91 61 40 I7 32

I 127

56-44 54'77) 55'03 52-63 50'21 48.06 46-18 48-08 46.53 45.18 44-00 51.382

56.44 54'82) 54'62 52-46 50.01 48.28 45'59 46-41 45-16 46-38 46.80 51.382

0

+ 0.41 +0*17 + 0'20 + 0.59 + 1.67 + 1'37 - 2.80

- 0'22

- 1-20

* Family size I including illegitimates, adopted, eta.

CORRELATION BETWEEN TEST SCORES OF SIBS

The correspondence between members of a family in respect of any measurable character has been presented in various ways. To render possible comparison between this and similar studies, the correspondences in test score between sibs are presented here in three forms.

(a) Product-moment correlations between the score of the subject and the mean score of his or her younger sibs (Table 5 ) .

( b ) Product-moment correlations between the score of the subject and the scores of all younger sibs. This involves entry of each subject's score n times, where n is the number of younger sibs tested (Table 6).

(c) Intra-clam correlation within the sibship. This measure expresses the relationship between the mean variance of score within families and between families (Table 7).

SF

2

3 4 5 6 7 8 9

I 0 + Total

The intellectual resemblance between sibs

Table 5. Correlation between subject (2) and mean swre of sibs (ij). Uncorrected sums of squares and s u m of products

(1) (2 ) (3) (4) ( 5 ) (6) n EX CXB zca cgz cw

1 I 5 132 I 26 83 74 47 36 16 25

6,302 6,891 6,342 3.917 39454 2,262 1,693 719

I ,032

355.635

328,184 190.633 164,810 I 12,720 81,913 33,139 44,036

371 ?55 1 6,144.0 6,879-0 6,274.8

3,573'1 2,182.0 1,722'5 741'9

1,071-2

3.900'2

3399489'0 369.208.5 3 19.779'6 191,524.1 179,453'9

839877.5 3 5447'4 47935 3'0

103.71 1'1

3419742'0 366,000-0 320,000-2

1879794.1 169,718.4 106,2152 81,565.3 3 3 9940' 1 44,702'0

654 32,612 1,682,621 32,488.7 1,669.844.1 1,651,677.3

Unadjusted analysis

Source D.F. 5.9. (2) S . S . (V) S.P. (W) T G

29

(7) T G

+ 0'47 +0*61 + 0'52 + 0'54 + 0'59 +0'39 + 0'35 + 0.65 + 0'33

b,,

Botween family sizes 8 7,5584 59102.87 5,990'69 0.9646 0'7925 (bB) Within family sizes 645 48,850'20 50,802.96 25,623.18 0.5143 0.5245 (b,)

Total 653 56,409'16 55,905'83 31,613.87 0.5629 0.5604 ( b T )

Adjusted analysis

Source D.F. S.S. M.S. F

Residual from regression of m e w 7 355'08 50.726 < I

Residual from 'average' regression 644 37.362'95 58.017 Remainder (between bB and bw) I 470.17 470.170 8.104 (D.F. I ; 644)

Residual from 'total ' regreeeion 652 38.1 88-20

sig. beyond 1%

Reference : Weatherburn ( I 947).

Table 6. Correlation between subjects (2) and younger sibs (y)

Y A

I 'I

X

80-84 7579 7-74 65-69 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 15-19

Total

80- 75- 70- 84

0

79

I

I

2

74

I I I I

I

5

65- 69

2 I1

5 4

6 I

2

31

60- 64 I

5 6 17

16 5 4

21

75

55- 59

3 4

26 40 36 26 14 5 4

10

2

170

50- 45- 40- 54 49 44

I 1 I 1

13 10 2

33 I5 I3 69 49 28 53 47 4' 42 48 29 14 25 22

2 5 14 I . 2

I

229 201 152

35- 39

3 3

I8

24

4

I 0

20

I 0

I

93

30- 34

2

3 5

I5

5 3

1 0

43

25- 20- 15-

29

I 2

5 4 6 2 I I

22

24

I I 2 I I I I

8

19

I I

2

0-

'4

I

I

I

3

n

1

3 16 30 78 134 216 208 181 108

43 15 2 1

1036 T, = 0.508 & 0.022; b,, = 0.498; bwz = 0.518.

30 In considering the above correlations it must be kept in mind that it is younger sibs only who

are tested, so that the selection of one member of the family aa subject is arbitrary, that there is a negative correlation between test score and family size, and between family size and number of sibs tested.

JAMES ~KAXWELL AND A. E. G. PILLINER

SF

2

3 4 5 6 7 8 9

I 0 +

Table 7. Intra-class correlation for each farrlily size

Total VM./D.F. Between/D.F. Within1D.F. F KO r,t.

582011 15 60201 I 58 94131183 81 171148 45491150 3929187 41 24/84

864136 d 6 106175

2.741 3.817 2.283 3'313 4'871 2-6 I 9 2.682 7-25 I '700

2

2.173 2'45 1 2.780 3'023 2.846 3'324 3.218 3'975

0.47 0.56 0'34 0.46 0.56 0.36 0'34 0.66 0.14

Specimen analysis for family size three

Variance D.F. 8.8. Y.8. F - - Total 289 25074

Between families 131 I9054 145'54 3.817 Within f d i e s 158 6020 38.101

where 71 = number of families; Kd = number of subjecta+sibs tested in ith family;

F-l = 0.564. F + K o - I

rlnt. =

Refepnces: Snedecor (1946)~ Kempthorne (1952).

The first presentation, product-moment correlation between subject and ' average ' sib, gives an overall value of T = + 0.563 k 0.027. This value includes correlation- between family size and test score. The average correlation coefficient at constant family size, after removing the effect of differences between family sizes, is r = + 0.51. It may also be observed that none of the correlation coefficients set out in col. (7) of Table 5 differ significantly (at the 5 yo level) from T = + 0.5. There is, therefore, no evidence of differential correlation by family size. At the foot of Table 5 is presented an analysis of variance and covariance which brings out the difFerence between the two regression coefficients, the first that of mean sib score on mean subject score by family size ( 0 ~ 7 9 3 ) ~ i.e. across family sizes; the second that of sib score on subject score at constant family size (0.524), i.e. within family sizes. The analysis shows these regression co- e5cients to differ significantly beyond the 5 yo level. This difference, which shows the two effects operating, should be taken into account in interpreting the overall correlation coefficient (T = 0.563) and the overall regression coefficient (O-SSO), both of which are inflated by the inclusion of the high regression of the family size means. A clear distinction should be made between these regressions of sibs on subjects and those of Table 3 which are of subjects and of sibs, respectively, on family size.

The intellectual resemblance between sibs 31

The second presentation, product-moment correlation between subject and each of the younger sibs, involves the entering of the subject’s score as many times as he or she has younger sibs. This tends to bias the subject entries towards the low scorers, possibly reducing slightly the value of the correlation coefficient. This was found to be r = 0-508+0.022, a result not greatly different from that obtained in the first presentation. The data are given in Table 6.

Table 7 gives the intra-class correlations for all tested members of the families, no distinction between subject and sib being required. These computations give values for rhc. for each size of family, which when pooled by using ‘2’ give a mean Tint. within family size of r = 0.45; this does not differ significantly from rint, = 0.5 ( p = 0-2 approx.). The pooling by ‘2’ within family sizes excludes the component due to correlation between family size and test score. The cor- relations are based, within each family size, on the scores of the children actually tested, not on the scores of all children within each family size (except for families of size two). Hence the average effective family sizes (k,) are less than the nominal family sizes and have been estimated by the method presented by Kempthorne and Snedecor (q.v.). An alternative method of obtaining Tint. is that of Smith (1957) and Fieller & Smith (1951) which would have made possible the estimation of the standard error of each Tint., but the labour of applying the iterative processes necessary for this method would have been prohibitive in view of the number of analyses of variance involved and unnecessary in view of the fact that this is not a final report on the investigation.

The best approximation to an overall correlation coefficient for test scores among sibs is r = + 0.5. This value of r = + 0.5 agrees closely with values obtained in similar investigations.

The interpretation of such results is clearly a matter for speculation only. It may be pointed out, however, that a correlation of r = +0.5 is what would be derived from a very simple genetic model of a panmictic population. It is known that the parents of the families studied here are to some degree assortatively mated, by educational and social status certainly and probably by intelligence if this had been assessed. This assortative mating would have led to the prediction of a value higher than r = + 0.5. The fact that the observed value coincides with the prediction from a simple panmictic model is almost certainly fortuitous. The genetic pattern is much more complex and must include genetic processes, possibly counteracting each other, of whose nature and effects virtually nothing is at present known.

It is also established that there is a positive relationship between test score and social condi- tions. In this connexion there is again little known of the differential effects of various aspects or components of what goes under the broad term of social conditions. It may, however, be stated that in respect of education, one of the social factors associated with test score, the educational conditions for 11-year-old children in Scotland are more uniform than in most countries. The effect of the method of selecting the children tested in this inquiry should not be overlooked ; the sample is almost certainly more homogeneous for social class than the popu- lation from which it was drawn, as a result of the bias towards larger family sizes. But, as with the genetic model, the relation between the test scores and social factors is more complex than the present state of knowledge can analyse.

32 JAMES MAXWELL AND A. E. G. PILLINER

SUMMARY

The younger -._ sibs of a random sample of 1 1-year-old Scottish children were tested individually as they reached the age of 11 years. The average intelligence of the younger sibs is found to be lower than that of the random sample, and explanations of this difference are discussed. It is shown, however, that if one ‘average’ sib is taken for each subject, then the mean score of these ‘sibs’ is not significantly different from that of their subjects.

Some implications for the selection of samples of sibs are examined, together with the effect of incomplete families on the estimation of the relationship between intelligence test score and size of sibship. Different methods of ascertaining the correlation for 1.8. among sibs are dis- cussed, and the results presented. The correlation coefficient for I.Q. between sibs is found to be of the order of r = +0-5.

REFERENCES

FIELLER, E. C. & SMITH, C. A. B. (1951). Note on the analysis of variance and intrack correlation. Ann. Eugenics, Lond., 16, 97.

KEMPTHORNE, 0. (1952). The Design and Analysis of Experiments. Wiley. MACPHERSON, J. S. (1958). Eleven-Year-OklA Grow Up. Scottish Council for Research in Education, XLII.

SMITH, C. A. B. (1957). On the estimation of intraclass correlation. Ann. Hum. Genet., Lond., 21, 363. SNEDECOR, G. W. (1946). Statistical Methods (4th ed.). Iowa State College Press. Social Implicationa of the 1947 Scottish Mental Survey (1953). The Scottish Council for Research in Education,

Trend of Scottish Intelligence (1949). The Scottish Council for Research in Education, XXX. University of

University of London Press.

xxxv. University of London Press.

London Press. WEATHERBURN, C. E. (1947). A Firat Course in Mathematical Statistics. Cambridge University Press.