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APPENDIX V
Statistical Detail of the Survey
This appendix, which is contributed by Mr GF Peaker CBE HMI, gives a brief account of the sampling design of the survey, and a few examples of the more detailed tables from which the short tables in the main text have been condensed.
1. THE SAMPLING DESIGN
1.1 The Modern School Sample
The main object of sampling design is to get reliable information at low cost. Previous experience of some of the variables suggested that with a stratified sample of about 150 modern schools the standard errors would turn out to be small enough for the purpose in hand. At the present time a sample of this size includes about 18,000 pupils in the fourth year, and since the most onerous task undertaken by the selected schools was to provide detailed information about fourth year pupils it was decided to reduce the 18,000 to 6,000 by sub-sampling within the selected schools.
The sampling fraction was 1/24. Before the sample was drawn the schools were stratified by size, sex and region. For size the schools were divided into large, middling and small, the middling group covering the range from 400 to 600 pupils. With this definition there are about the same number of pupils in each stratum, while the schools are divided in the ratio 3:5:7. There are fewer single sex than coeducational modern schools, the proportion being 1:1:3 for boys', girls' and mixed. To produce the regional stratification the draw was made systematically with random starts, beginning from the northern end of the Scottish border and working through to Land's End. To provide a quick means of estimating standard errors in complicated cases the draw was made twice, producing two independent and interpenetrating samples of 75 modern schools, each as follows:
| Boy's | Girl's | Co-educational | Total |
| Large | 3 | 3 | 9 | 15 |
| Middling | 5 | 5 | 15 | 25 |
| Small | 7 | 7 | 21 | 35 |
| Total | 15 | 15 | 45 | 75 |
No attempt was made to stratify by neighbourhood, chiefly because it seemed better to ask the schools to classify their own neighbourhoods rather than to
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impose on them an external and possibly outdated or otherwise erroneous description. Consequently neighbourhood was included in the questionnaire and not in the prior stratification.
1.2 Schools in the Slums
Chapter 3 of the report is about a special group of schools that did not form part of the sample, but was selected by a supplementary procedure for this reason. It was clear from prior knowledge that the probability sample would include about 30 schools in areas of the kind described as 'problem neighbourhoods' in paragraph 559. But if the neighbourhoods of all the 3,606 modern schools in the country at the time of the survey could be ranked in ascending order, beginning with the deepest slums, it is an arithmetical fact that half the possible samples of 150 schools would not include any of the most extreme 16 neighbourhoods. All samples being equally likely the risk of omitting all the most extreme tenth of the neighbourhoods is only one in 10,000,000, which is not the sort of risk that needs attention. On the other hand the risk of not including any of the most extreme 3% of these neighbourhoods is one in a hundred. This is a risk that deserves respect, and therefore some supplementary procedure seemed advisable, to make sure of including a few of these 109 neighbourhoods in the survey, even in the somewhat unlikely event of their being omitted from the probability sample.
For this purpose Her Majesty's Inspectors working in the LCC [London County Council] area and the five largest and two other county boroughs were each asked to nominate three schools (six in the case of the LCC) as being those for which the neighbourhoods were the most difficult. From these lists a final selection of 20 schools was made. Since these areas together include about a sixth part of the population of the whole country, and since the proportion of difficult neighbourhoods in them must at least be greater, and perhaps considerably greater, than that in the rest of the country, it is reasonable to suppose that the neighbourhoods of these 20 schools are among the most difficult in the whole country. The evidence subsequently collected in the survey confirmed that their circumstances were far more difficult than those of most schools, and the method of selecting them gives ground for thinking that some of them at least are very close to the foot of the scale.
The inverse problem, of estimating how many schools in the country are represented by this special group, is attended by more uncertainty, but upper and lower limits can be reached by the following arguments. If 3% of the modern schools in the whole country had neighbourhoods as bad as those in the special group there would be 108 such neighbourhoods altogether, of which rather more than 20 would fall in the sixth of the country from which the schools of the special group were chosen. If 10% of neighbourhoods in the whole country were as bad there would be 360 such neighbourhoods altogether, of which rather more than 60 would fall within the sixth of the country from which the special group was chosen. In the former case the judgement shown in selecting the 20 neighbourhoods for the special group would have been remarkably accurate; in the latter it would have been rather poor. Consequently 3% and 10% may be regarded as the upper and lower limits, and splitting the difference between them gives 7% as a rather loose
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estimate of the proportion of schools in neighbourhoods as bad as those of the schools in the special group. This estimate is compatible with the estimate from the probability sample that 20% of the neighbourhoods fall into the 'problem' class, since this class should include, but be considerably larger than, the 'slum' class as here defined.
1.3 Comprehensive Schools
The comprehensive schools form a much smaller class than the modern schools, so that a larger sampling fraction is needed for them. On the other hand they are much more homogeneous. These opposing considerations taken together suggested that a sample of 12 schools - two boys', two girls', and eight coeducational - would be enough to give estimates with reasonably small standard errors, and such a sample was in fact taken.
1.4 Sub-sampling of Pupils Within Selected Schools
The schools were asked to give detailed information about one in three of their fourth year pupils, and to select these pupils from their registers systematically with a random start. For this purpose each school was given one of the first three digits. A very accurate check against bias in the sub-sampling was available in the shape of the scores in the Reading Test. If the rule of selection is strictly followed the sub-samples will be single stage samples of the pupils in the selected schools, with pupils as the primary sampling units. Consequently the standard errors for means and class proportions can easily be calculated, by the rules for simple random sampling. Such a calculation ignores the gains from systematic selection compared with purely random selection, but this merely means that the estimates of error are slightly too large.
For the modern schools the agreement was excellent. The differences between the sample and the sub-sample estimates were well within their standard errors. But in the case of the comprehensive schools something went wrong. The sub-samples gave mean reading scores for girls and for boys that were excessive by four and five times their standard errors respectively. Comparing the numbers in the score groups 0 to 11, 12 to 17, 18 to 23, 24 to 29, and 30 to 35, for boys and girls together, gave a chi-squared of 37, on 4 degrees of freedom, which is preposterous. Owing to the pressure of other work it was a long time before the comprehensive school sub-samples reached the head of the queue for coding, so that by the time this heavy bias was discovered many of the boys and girls had left school, and nothing could be done to correct it. To expedite the coding, the sub-sampling fraction for comprehensive schools had been reduced from one in three to one in six - that is to say, only half the returns were coded - but a post mortem showed that the bias had occurred before this point.
Since the comprehensive school sub-samples contained too few Robinsons and too many Browns all the estimates based on them are subject to a doubt, and this applies particularly to the Robinsons, for whom the absolute, as well as the relative, numbers are very small. (See paragraph 621).
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2. THE READING TEST
2.1 The Choice of Test
The test chosen was the one that had been used for the National Reading Surveys described in 'Standards of Reading 1948/1956'. (1) Paragraph 5 of this pamphlet describes the test and paragraphs 72-74 explain and justify the use to which it was put. This choice had the advantage of giving a useful by-product. The 1961 results formed another link in the chain of surveys extending from 1948, and provided evidence that the progress observed in 1952 and 1956 was still continuing.
It will be noted that in the surveys of 1948, 1952 and 1956 the test was used as a measure of progress. In 1961 it has again been used as a measure of progress. But it has also been used as a measure of ability for the classification of individual pupils. At first sight this seems to involve a contradiction. How can the same test be used both as a measure of improvement in the achievement of the schools, and as a measure of ability in the pupil? If the test is a measure of ability, how can the schools claim credit for an improvement in the test scores? If, on the other hand, it is a measure of achievement, how can it be used as a measure of ability? There is in fact nothing either illogical or unusual in such a dual use. The same questions might be asked of the records of athletic performances. Do these measure the native ability of the athletes concerned, or do they measure the effects of training? They do both. No amount of training would have enabled William Bunter to defeat Roger Bannister on the track. None the less a trained Bunter could have knocked one or two minutes off the time of an untrained Bunter for the mile. A trained Bunter would still have been lapped by an untrained Bannister, but this does not show that training is useless. Athletic excellence depends mainly on natural endowment, but can be improved by training. Intellectual excellence depends mainly on native wit, but can be improved by education. Where native capacity is equal, or nearly so, training or education dominates. Where training or education are not very different native capacity dominates. This holds not only for individuals, but also for groups. It is likely that the distribution of native ability among the crews of two of Her Majesty's ships is much the same; the fact that one ship has better seamanship or gunnery than the other is the effect of training. The crews of Beatty's ships could read; most of Nelson's men could not. This again is not a difference of native ability but a difference of education. The performance itself is a function both of native ability and of the effects of education. Which predominates depends upon the kind of comparison that is being made. If the comparison is between individuals whose education has been much the same, ability is dominant; if it is between groups each covering much the same in range of ability, then ability tends to cancel out and the effects of education predominate.
Englishmen in general do not know Chinese because they have had neither occasion nor opportunity to do so. For the same reason Chinese do not know English. To conclude that the ignorance of English common among Chinese was a mark of lack of wit would be a monstrous absurdity into which no one
(1) Standards of Reading 1948/1956 (Ministry of Education Pamphlet No. 32).
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is likely to fall. But in less extreme cases very similar conclusions have been reached and maintained. The general principle, which is of great importance in judging the future possibilities of education, is therefore worth restating, though it has for long lacked the charm of novelty. Macaulay, for instance, wrote in 1854, in his report on the appointment of Indian civil servants by open competition:
'The marks ought, we conceive, to be distributed among the subjects of examination, in such a manner that no part of the Kingdom, and no class of schools, shall exclusively furnish servants to the East India Company. It would be grossly unjust, for example, to the great academical institutions of England, not to allow skill in Greek and Latin versification to have a considerable share in determining the issue of the competition. Skill in Greek and Latin versification has indeed no direct tendency to form a judge, a financier, or a diplomatist. But the youth who does best what all the ablest and most ambitious youths about him are trying to do well, will generally prove a superior man; nor can we doubt that an accomplishment by which Fox and Canning, Grenville and Wellesley, Mansfield and Tenterden first distinguished themselves above their fellows, indicates powers of mind, which, properly trained and directed, may do great service to the State. On the other hand, we must remember that in the North of this island the art of metrical composition in the ancient languages is very little cultivated, and that men so eminent as Dugald Stewart, Homer, Jeffrey and Mackintosh would probably have been quite unable to write a good copy of Latin alcaics, or to translate 10 lines of Shakespeare into Greek iambics. We wish to see such a system of examination established as shall not exclude from the service of the East India Company either a Mackintosh or a Tenterden, either a Canning or a Homer.'
So much for the general principle. Here we are concerned to apply it to comparisons in which the reading test plays a part, and we have to decide in each case whether the comparison is one in which it is reasonable to suppose that native ability averages out, or nearly so, in which case estimates of general progress or retrogression are appropriate, or whether it is one in which occasion and opportunity average out, or nearly so, in which case judgements of ability can reasonably be made.
The first comparison with which we are concerned is that between the whole modern school population in 1956 and the corresponding population in 1961. In 1961 the average score, over the whole sample, was very considerably in advance of the average score in the 1956 sample. It would be grossly unreasonable to suppose that, in so short a period, there could have been any marked change in the total native ability of the whole of the youth of England. The proportion of that youth that attends other kinds of school is very much the same in 1961 as in 1956, from which it follows that the total ability of modern school pupils must still be much the same. The advance must therefore be an effect of education in the widest sense, of which education in school is at least a major part. It is reasonable, therefore, to regard the advance as in part an achievement of the schools, for which they are entitled to credit.
Another comparison is between the schools in the 1961 sample and those in the special group of schools in the slums. It was to be expected that the
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adverse environment of the latter would have a depressing effect on the test scores, and that these would therefore be lower on the average than those in the sample, unless either the natural ability of the pupils or better staffing in the schools of the special group compensated for the effects of environment. There is no reason to suppose that the natural abilities of the pupils in these schools are, on the whole, either much superior or much inferior to those of pupils in modern schools at large, and the fact that on the average their scores were very substantially lower may therefore be regarded as an effect of environment, somewhat mitigated by the more favourable staffing ratios enjoyed by these schools. On the average there were two pupils fewer per teacher in the special group schools than in the sample schools. It cannot be doubted that this is an advantage, but it is not enough to close the gap. It can only reduce it.
In comparisons between large groups it is mainly differences of education and environment that emerge. On the other hand in comparisons of individuals within groups where environment and education are much the same it is mainly differences of ability and native wit.
2.2 Bias in the Test
The test has a well marked bias of about a point in favour of boys. This has been steadily evident in the three previous surveys, and it appears again in 1961. Most tests have such a bias, sometimes strong and sometimes weak, sometimes in favour of girls and sometimes in favour of boys. The reason for regarding it as a bias, rather than as a mark of superiority in the boys (or the girls) is simply that the sign varies from test to test.
To locate the bias in this case a rather lengthy piece of analysis was done with the cooperation of members of one of the Ministry's short courses. The scripts from twelve large mixed schools in the sample were used for this purpose. From the scripts from each school four sub-samples - two for boys and two for girls - were drawn systematically, giving 48 sub-samples and 960 scripts for analysis. Between sub-samples within schools and sexes there were no significant variations. Pooling the sub-samples for boys and for girls within each school and subtracting gave, for each of the 35 questions in the test, twelve independent estimates of the bias, one being derived from each of the twelve schools. From these twelve estimates a mean estimate, and its standard error, was calculated for each question. The 35 standard errors thus obtained did not differ significantly from the corresponding binomial estimates. In other words there was no evidence that the bias had a school component.
Altogether the 480 boys produced 10,637 right answers, and the 480 girls 10,110, the average scores being 22.16 and 21.06, and the bias 1.10. On 25 of the questions the boys had a higher score, with a total excess of 592; on 10 questions the girls did better, with a total excess of 65. Question 28 by itself accounted for more than a fifth of the total bias, with 273 successes for boys (57%), and 149 for girls (31%). There were three other questions where the boys' successes exceeded the girls' by more than 10%, and five more where the excess was over 5%. These nine questions together account for 452 out of the net 527 by which the boys' score exceeded the girls'.
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Although the data from these twelve schools locate the bias they do not provide the most accurate estimate of it. In the complete sample there were 90 mixed schools, of which 88 replied, and their data supply an estimate of 0.90, with a standard error of 0.12. The 59 single sex schools that replied yield a much less accurate estimate of 0.83 with a standard error of 0.41. If these are pooled they give 0.87, with a standard error of 0.18 for all schools. But, since the estimate for single sex schools is blunted by the difference between schools within each kind, it is better to take the accurate mixed school estimate by itself. This shows that the bias is very steady. In fact the scatter in the relevant table is no more than would occur if the scripts, instead of being divided into boys' and girls', were divided alphabetically without regard to sex, though in this case the mean would be approximately zero instead of 0.9. This means that for the sex difference there is no component of variation between schools. The difference between the sexes for boys' and girls' schools vanishes when it is adjusted by the difference found in mixed schools.
It would have been possible to take account of the bias in defining Brown, Jones and Robinson and their sisters in the main text, and to have adjusted all the tables in which this nomenclature is employed accordingly. But it would have been extremely laborious to do so, and on the whole it seemed enough to draw attention to the bias and leave the tables as they stood.
2.3 The Reliability of the Reading Test
The tables prepared to locate the bias in the test served also to estimate the reliability. By dividing the twelve schools into two groups of six, and comparing the scores on the questions with odd and with even numbers four independent estimates of reliability were obtained, namely 0.92 and 0.91 for boys and 0.90 and 0.88 for girls. Pooling these gives 0.90 with a standard error of 0.009. The latter does not differ significantly from the 0.006 obtained by the simple random sampling formula, so that once again there is no evidence of difference between schools.
A reliability co-efficient of 0.90 is high for a ten minute test containing only 35 questions. It corresponds to 0.95 for a test of double the length.
3. GENERAL NOTES ON TABLES
1.1 TO 3.3
These notes are supplementary to those attached to the tables themselves.
Table 1.1 shows the mean scores for modern schools in the reading test. It is noteworthy that there is a range of nine points, from 25 to 16. There is, as would be expected, an even larger range in the quartiles. For example, the lower quartiles range from 24 to 11.
Table 1.2 gives a number of pupils in score ranges each covering six points. These sample frequencies are graduated in table 1.3 to give the scores corresponding to every tenth percentile rank. It is from these data, and the corresponding data in later tables, that diagrams 7, 8, 9 and 11 have been drawn.
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It will be seen that the nine point range between school means shown in table 1.1 corresponds to about 50 percentile ranks, and the eleven point range in the lower quartiles to more than 60.
Table 1.4 shows the improvement from 1956 to 1961, and its standard error. The improvement can be stated as 2.4 points, or as 17 months, or as 17 percentile ranks in the middle of the scale.
In table 2.1 the school mean scores are arrayed by zone and by neighbourhood. The middle zone extends from 80 to 160 miles from London. The outer zone covers the six northern counties and Cornwall completely, with most of Cheshire and Devon, and a fringe from other counties. Ipswich, Kettering, Chipping Norton and Southampton are just inside the inner zone.
The summary at the foot of table 2.1 gives the mean scores for neighbourhoods within zones, and the weighted and the unweighted means of these means. The weighted means of means for the three zones take account of the varying proportions of kinds of neighbourhood within zones; the unweighted means of means eliminate this. There is a similar relation for the weighted and unweighted means of means for neighbourhoods. The scores for the outer zone are somewhat higher than those for the middle zone, but decidedly lower than those for the inner zone. Since the variance per school is 2.96 these means all have a standard error of about 0.25, so that the differences are not negligible. They are however smaller than the differences between neighbourhoods shown at the foot of the summary. The fact that there is a preponderance of small schools in problem neighbourhoods is mainly responsible for the lower scores of small schools shown in table 1.1.
Table 2.2 compares the mean scores for all modern schools, schools in problem areas, and the special group of schools in the slums. It will be seen that, although two of the special group have lower scores than any schools in the other groups, yet there are five schools in the special group with scores at or above the general average. This is a notable achievement.
In Table 2.3 the corresponding deciles for pupils are given. Diagrams 8A and 8B have been drawn from these data.
Tables 3.1 and 3.2 give the mean scores and deciles for all fourth year pupils, fourth year examination candidates, and fifth year examination candidates. Diagrams 9A and 9B have been drawn from these data.
Table 3.3 gives the deciles for all pupils, for fourth year examination candidates and for fifth year examination candidates in comprehensive schools, with the deciles for grammar schools in 1956 added for comparison. One of the twelve comprehensive schools in the sample failed to supply this information; among the eleven schools who did reply the range of school means was from 26 to 22, and the variance per school was 0.90. The mean score for the group was 24.4, with a standard error of 0.29.
Table 1.1 Mean Scores for Modern Schools in the Reading Test
There were 150 schools in the modern school samples, grouped by size and sex as shown below. Middling schools had between 400 and 600 pupils on roll.
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The definition of the middling size group (400-600) was chosen so that the numbers in the populations were roughly equal. Within size groups the means for schools and for pupils approximate closely, between size groups equal weights are appropriate, and between sex groups weights of 1, 1, 3 for boys, girls and mixed. This leads to the estimate 21.30 ± 0.14 for all pupils, which agrees very closely with the estimate 21.34 obtained directly from pupils' score groups in the next table. It is rather larger than the unweighted mean for all schools at the foot of the right hand column above, because size is neglected in reckoning the latter, and large schools score rather higher than small. This difference is significant, at the 5% level, but ceases to be so when the scores are adjusted for environment.
The difference between the scores of girls and boys is a feature of the test, and can be traced to half a dozen of the 35 questions (see 2.2).
Table 1.2 Modern Schools
Grouped Scores for Pupils in the Reading Test.
The differences between boys in boys' schools and in mixed schools are not significant, nor are those for girls. Pooling gives:
Table 1.2
This table gives 6.21 and 5.89 as the standard deviations of the scores for boys and girls respectively, and pooling gives 36.6 as the variance per pupil. The harmonic mean of the number of pupils per school is close to 100, so that
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if S and P are the components per school and per pupil (within schools) S + P = 36.6 and S + P/100 = 2.96, from the previous table. This gives S = 2-6 and P = 34.0. For the later estimates based on sub-samples of pupils S + P/100 must be replaced by S + 3P/100 and 2.96 by 3.84.
Table 1.3
The data in the preceding table give the following distribution when graduated. The 1956 results, adjusted to the same age, are inserted for comparison.
| Rank | Boys | Girls |
| % | 1961 | 1956 | 1961 | 1956 |
| 90 | 29.1 | 26.6 | 28.0 | 25.8 |
| 80 | 27.4 | 26.9 | 26.0 | 23.5 |
| 70 | 25.8 | 23.3 | 24.4 | 21.6 |
| 60 | 24.1 | 21.8 | 23.1 | 20.3 |
| 50 | 22.8 | 20.2 | 21.7 | 18.9 |
| 40 | 21.4 | 18.8 | 20.2 | 17.3 |
| 30 | 19.6 | 17.1 | 18.3 | 15.6 |
| 20 | 16.9 | 14.4 | 16.0 | 13.5 |
| 10 | 12.8 | 10.3 | 12.9 | 10.7 |
| Mean score | 21.8 | 19.5 | 20.9 | 18.5 |
Table 1.4
The table below shows the improvement in reading standards in modern schools since 1956. The 1961 sample on the average was four months younger than the 1956, and on the average scored 1.8 more points in the test The age allowance is seven months to the point, so that the improvement can be expressed either in points or months, as follows:
| Improvement
from 1956 to 1961 |
| 1956 | 1961 | Points | Months |
| Mean Score | 19.5 | 21.3 | 1.8 | 13 |
| Standard error | 0.42 | 0.14 | 0.44 | 3 |
| Age | 15y 0m | 14y 8m | 0.6 | 4 |
| Total Improvement | | | 2.4 | 17 |
It may be noted that the standard error in the estimate of the improvement arises almost entirely from the standard error for 1956, which is three times that for 1961. This was because the case studies that played an important part in 1956 made it necessary to have three-stage sampling, with the selection of 23 LEA areas as the first stage. This extra stage enlarged the standard error, since the variation between LEAs is not inconsiderable.
The major source of uncertainty, however, is not the sampling of pupils, but the sampling of tests. It is well known that different tests give somewhat different results, but this knowledge is vague, whereas knowledge about the sampling of pupils is precise, for the reasons given in the text. Nonetheless, taking both hazards together, it seems reasonably safe to say that the improvement is not less than one year and not more than two.
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[click on the image for a larger version]
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Table 2.2
Mean scores per school for (1) All modern schools and (2) the schools in problem areas, in the sample, and (3) the special group of schools in the slums.
| Sample | Special Group
Schools in
the Slums |
School
Mean Score | All Modern
Schools | Schools in
problem areas
|
| 25 | 2 | |
|
| 24 | 7 | |
|
| 23 | 22 | 3 | 1
|
| 22 | 38 | 7 | 1
|
| 21 | 28 | 3 | 3
|
| 20 | 27 | 6 | 1
|
| 19 | 14 | 4 | 5
|
| 18 | 3 | 2 | 4
|
| 17 | 5 | 4 | 2
|
| 16 | 1 | 1 |
|
| 15 | | | 1
|
| 14 | | |
|
| 13 | | | 1
|
| Total | 147 | 30 | 19 |
Mean Score
per school | 21.15 | 20.07 | 18.79
|
Standard
deviation per
school | 1.72 | 2.05 | 2.37
|
The deciles corresponding to the preceding table are:
Table 2.3
Table 3.1
Mean scores in the reading test of candidates for external examination in modern and comprehensive schools.
| Modern
Schools | Comprehensive
Schools |
| Boys | Girls | Boys | Girls |
| All 4th Year Pupils | 21.8 | 20.9 | 24.2 | 23.9 |
| 4th Year Examination Candidates | 25.7 | 24.0 | 28.3 | 28.0 |
| 5th Year Examination Candidates | 27.6 | 27.2 | 28.4 | 27.8 |
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The deciles for candidates in modern schools are:
Table 3.2
The deciles for external examination candidates in comprehensive schools in 1961, and those for grammar school pupils in 1956, are:
Table 3.3
[click on the image for a larger version]
4. THE RELATION BETWEEN THE READING SCORE AND HEIGHT, WEIGHT AND AGE
The average height of the boys and girls was 64.5 and 62.8 inches respectively [1.64m and 1.59m]. The average weights were 116.9 and 114.7 Ibs [52.6 and 51.6kg]. The standard errors are a tenth of an inch [2.5mm] and two thirds of a Ib [300g].
The London County Council Survey (Report on the heights and weights of school pupils in the county of London in 1959) gives 64.6 and 62.9 inches [1.64m and 1.59m] and 119 and 116 Ibs [53.55 and 52.2kg] for boys and girls of the same age, namely the year group centred on 14 years 8 months. The London figures have been obtained by interpolation in the table on page 30 of the LCC report. The number of schools in the London sample is not given. It seems likely to have been smaller than the number in our national sample, but on the other hand it was possible to make more use of stratification in London, so that the standard errors are likely to be much the same. The agreement between the London and the national estimates is remarkably close. The difference of 2 Ibs [0.9kg] in the average weight for boys is about twice its standard error, but the other three differences are well within the range of sampling fluctuation. The national sample showed no differences clear of sampling fluctuation between
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zones or neighbourhoods; to find such differences it was necessary to go to the special group of schools in the slums. This perhaps reflects the social and economic changes of the last quarter of a century, which have, in London itself, been narrowing the gap between the physique of children in different districts. The nine educational divisions of the county of London now show a range of only 1.5% in stature for boys and 1.8% for girls. For weight the ranges are 1.6% for boys and 2.6% for girls. These ranges are less than they used to be, and it may well be that the same tendency for the backward districts to catch up holds throughout the country as a whole.
Even the differences shown by the special group are quite slight. In this group the average height was 63.2 and 62.0 inches [1.60m and 1.57m] for boys and girls respectively, the weights being 112.5 and 115.6 [50.63 and 62.02kg]. Since this group was purposively selected the standard errors are, strictly speaking, unknown. If the selection is treated as random they turn out to be 0.27 inches [7mm]and 1.8 Ibs [0.81kg]. The boys in the special group fall short of the national average by 1.3 inches [33mm] and 4.4 Ibs [1.98kg], and the girls by 0.8 inches [20mm]. These are all clear of sampling fluctuation, taking the standard errors as above. The average weight of the girls in the special group is 1.1 Ibs [0.49kg] greater than the general average, the standard error of this excess being 1.9 Ibs [0.86kg].
For the comprehensive schools no reliable estimates of height and weight could be made, owing to the bias in the sub-sampling in these schools that has been mentioned in 2.2 above. That they would be slightly greater than in the modern schools may be inferred from the correlation with the reading scores given below.
The statistics calculated from the modern school sample to explore the relations between height, weight, age and reading score are given in Table 4.
This table gives the statistics calculated from the modern school sample for the relations between height, weight, age and reading score. They are as follows:
Table 4
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5. CLOSING THE GAP
Paragraph 558 refers to 'a tendency for the lower occupational groups to show a somewhat greater improvement than the higher ones'. Part of the evidence for this emerges from a comparison of Table 12 in Early Leaving with Table 12 in the Supplement to Part 2 of Statistics of Education 1961. The data in Early Leaving relate to the age group that entered grant aided grammar schools in 1946, and those in the Supplement to leavers from grant aided grammar schools in 1961. Those members of the former cohort who left school with four O level passes or fewer would for the most part leave in 1951, so that, both for this category and its complement, the proportions are on much the same footing, at a ten year interval. Taking the complementary proportions - those who achieved at least five O level passes, including those with various combinations of A level passes, we have:
It will be seen that on the whole there has been an improvement of about 17% over the ten years, but that within this total improvement there has been a levelling up, which is most marked towards the foot of the table.
Parental occupation was not recorded for the boys and girls in the modern school sample of the 1961 Survey, but since most of the parents fall into the two groups at the foot of the table above it is reasonable to conclude that the improvement shown in the successive reading surveys is another aspect of this process of closing the gap.
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6. VOLUNTARY ACTIVITIES
The data collected for each boy and girl in the sub-samples include information about five voluntary activities. The five activities and the numbers and percentages of boys and girls in the modern schools engaging in them, were as follows:
(i.e. the 3257 boys shared 5146 activities, an average of 1.58; and the 2945 girls shared 3692 activities, an average of 1.25).
If membership of a school club made membership of an outside club neither more nor less likely the expected number of boys belonging to both would be 26.7% of 48.9% of 3,257, that is to say, 424. The actual figure is 557 - an excess of 133 - which means that members of school clubs are more likely than non-members to belong to outside clubs, and vice versa.
When the same principle is applied to the 32 combinations of the five activities it produces tables with 32 rows and 26 degrees of freedom, for which chi-squared is 885 for boys and 828 for girls. These tables condense to:
Table 6
There are far more boys and girls with no activities, or with the maximum possible, than would be the case if the propensity to join one activity was independent of the propensities to join others. The evidence is conclusive in favour of a common factor, or general propensity. This propensity is positively correlated with height and weight, and also with the reading score. If R, P, T, C, K, E stand for reading, school post, school team, school club, other club and part-time employment respectively the extraction of two factors and a rotation give the patterns:
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which account for 32% of the variance in each case. The angles between the successive vectors, in the order in which they occur above, are 11, 4, 14, 30 and 29 degrees (boys), and 6, 10, 9, 28 and 27 degrees (girls), with angles of 88 and 80 degrees between the extremes P and E.
The lengths of the vectors are squared in the third column, and the angles and lengths together give patterns that accord with expectation. P is, so to speak, the extreme 'school' factor, and E the extreme factor for outside activity. In both patterns these form the wings, with K closer to E, and R, T and C closer to P, though the order of these three differs from boys to girls. The relative shortness of the vectors for R and E indicates that they have less in common with the other four than the latter have among themselves.
For the boys a third factor with a heavy negative loading on T and light positive loading on R and E accounts for another 12% of the variance, but the third factor for girls is less clear cut.
7. NOTE ON HOLDING POWER (Chapter 24)
Since every teacher was either an original member or a newcomer, and either stayed to the end of the period or left, there are four exclusive and exhaustive classes, u, v, x, y, giving (1) u/(u + v) and (2) x/(x + y) for any school as the proportions of (1) the original and (2) the newcomers staying to the end of the period. The second of these is the school's 'holding power' for newcomers as defined in chapter 24.
For a category represented in the sample by n schools the holding power is therefore estimated by the ratio
The standard error thus obtained can be compared with the binomial estimate. If it is significantly greater there is evidence that the schools in the category differ in holding power; if not, not. Similarly for original members. There was more frequent evidence of differences between schools in the same category for newcomers than for original members. Some of the latter no doubt had moved to more congenial schools before the period began. Others, perhaps, had come to appreciate the wisdom of Mrs Gamp's advice to young Bailey. (1)
(1) 'He was born into a wale', said Mrs. Gamp with philosophical coolness, 'and he lived in a wale; and he must take the consequences of sech a sitiwation.'
(Dickens: Martin Chuzzlewit chapter 49.)
[page 296]
Index
The references are to paragraphs except where otherwise indicated.
Ability 4-7, 10, 15-17, 35, 36, 46, 102, Ch. 21, Ch. 22, App. V
Absence from School (see Attendance, School)
Adolescence 309-312, 326
Adult Life, Preparation for 3, 98-119, 315, 322, 323, 388, 405
Advertising 87, 315, 396, 472
Agnostics 158, 163, 164
Agreed Syllabus 166, 172, 173
Albemarle Report 411
All-age Schools 551
Ancillary Staff 307, 359, 387
Apprenticeships 12, 102, 103, 109, 567
Architects and Building Branch (Ministry of Education) 268
Arithmetic (see Mathematics)
Art and the Studio Crafts 94-96, 254, 312, 352, 361, 374, 376-378, 632, 639, 640
Rooms and Equipment, 58, 95, 268, 662
Teacher Training, 287, 289
Assignments 353, 470, 522
Attendance, School 36, 58, 70, 183, 202, 309, Ch. 22
Audo-Visual Aids (see also Films, Radio, Tape recorders, Teaching Machines, Television) 41
Automation 11, 12
Backward Classes 281, 343
Behaviour in School (see also Discipline) 34, 47, 56, Ch. 8, 309, Ch. 22
Personal (see also Moral Judgements, Sex) 87, 117, 315, 324
Beloe Report 241, 245, 257
Boarding School (see also Journeys, School and Residential Provision) 201
Books (See also Library) 41, 93, 370, 371, 428, 469-71
Boredom 47, 120, 213
Brass Bands 127, 413, 419
British Employer's Confederation 239
'Brown, Jones and Robinson' Ch. 22, 630, 635, App. V
Budgeting 119, 321, 449
Building, Courses in 109, 322, 361, 383, 528, 663
Buildings and Equipment
Existing Schools 25, 37, 45, 58, 184, 197, 265, 409, 418, 539, 655, Ch. 25
New 38, 41, 146, Ch. 11, 372, 408, 409, 452-454, 506, 655
Overcrowded 32, 38, Ch. 25
Catering 100, 109, 113, 361, 375, 389
Certificate of Secondary Education Ch. 10, 355, 356, 486
Child care 119, 286, 392, 399
Choice, Pupil's choice of Subject 99, 100, 105, 325-327, 357, 361, 374, 407, 431, 432, 518, 643, 644
Civics (see under Geography, History, Social Studies)
Clothing Trades 109, 113, 375, 389
Clubs
Adult, 138, 231, 402, 411
School, 34, 41, 61, Ch. 6, 366, 384, Ch. 22
Youth, 34, 144-148, 200, 206, Ch. 22
Co-educational and Single Sex Schools 179, 186, 206, 627, 643, 644, 663, 664, 665, 671, 674, 675
Colour Bar (see also Minorities, Cultural, Immigrants, New) 163
Commerce 41, 109, 113, 114, 123, 633-635
Communication, Problems of 49, 50, 86, 291, 329, 330, 467, 498, 490
Community Service (see also Social Service) 128, 196, 200, 221, 384, 670
Comprehensive Schools 4, 19, 30, 494, 551, 619-624
'Concurrent Training' of Teachers 299, 300, App. IV
Conscience Clause 169, 517
Consumer Research 87, 211, 388, 396, 435
Cookery (see also Housecraft) 94, 318, 375, 531
Corporal Punishment 186, 187, 201
Cost of Education
in relation to Buildings 74, 146, 271
in relation to Research 306
in relation to Teachers 69, 145, 288, 296, 297, 302, 307
Total Cost 9, 26
Council Estates and New Towns 31, 134, 559, Ch. 22, 652, 664, 667, 668, 673, 680, 684
County Schools 158, 166, 641
Coursework in External Examinations 246
Courses, Organisation of Forms on a course basis (see also Vocation) 100-116, 525-527, 643
Crowther Report (15 to 18) 19, 22, 31, 32, 245, 277, 555
Current Affairs (see under Geography, History, Social studies)
Curriculum, Contents of Ch. 4, Ch. 14, Ch. 23
Fields of 349, 358, 538, 625-636
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Day Training Colleges 296
Decimal System 449
Delinquency 73, 120, 178
Dinners, Free 70, Ch. 22
Discipline
in School 34, 43, 47, Ch. 8, 305, 309, Ch. 22
at home 56, Ch. 8
Display Space 372
Doctor, School 268 (XVI), 359
Drama 116, 268 (VI), 330, 406, 478-480
'Early Leaving' Report 558
Eliot, George (quoted) 168
Emotions 77, 377
Employment, Part-time Paid 34, 36, 221 Ch. 22
Engineering 94, 100, 107, 109, 110, 361, 385, 663
English Ch. 19A
as Form Subject 283, 284, 546
General 254, 341, 342, 352, 367, 396, 399, 634, 641
Spoken 49, 50,86,87, 247, 322, 324, 329, 330, 346
Teachers 487, 542, 543, 544
Written 88, 345, 346, 365, 428, 507
Environment (see Neighbourhoods)
Evening Institute (see also Further Education) 230, 231
Examinations
Fifth Year 40, 154, Ch. 10, 355, 356, 486, 636, Ch. 22
Fourth Year 249, Ch. 22
Intemal 344, 345
Non-exammation candidates 251-253, Ch. 22
Non-examined subjects 254, 417
Safeguards 255
Teachers and 280, 544
Examinations Bulletin No. 1 (SSEC) 246, 257
Extended Courses, 'Signing on for' 525, 527
Extra-Curricular Activities (see also Community service, Journeys, School Residential Experience, Social Service Visits, School Work Experience) 41, 42, 61, 92, 121, 125-135, 290, Ch. 22
Family Size 35, Ch. 22
Fathers' Occupations 32, 219, 557, 558, Ch. 22
'Fifteen to Eighteen' (see Crowther Report)
Films 87, 125, 129, 215, 361, 465, 473-476, 501, 502, 506
Flats, Housecraft 268 (sections XV, XVI), 391-394
Food Supply, World 79, 438
Foreign Languages 41, 125, 353, Ch. 19a, 532, 633-635
Teachers 493
Form Teachers 194, 282-284, 288, 533, 546
France, Method of raising school leaving age 21, 22
French (see Foreign Languages)
Further Education 23, 24, 209, 228-231, 235, 257, 386, 432, 434, 451, 536, 567
Games (see also Physical Education and Playing Fields) 162, 265, 404, Ch. 22
GCE 242, 245, 251, 253, 544, 557, 568, 569, 574, 636
Geography (see also Social Studies) 41, 350, 429, 447, Ch. 19c, 545, 632, 641, 682
Teachers 514
Ghandi, Mahatma 503, 515
Girls' Domestic Duties 34, 182
Graded Posts 288
Grammar Schools 4, 18, 124, 160, 222, 287, 339, 526, 531, 551, 558, 619
Gymnasium 45, 58, 265, 408, 668, 669
Hadow Report (1926) 93
Handicraft (see also Vocation) 58, 93-96, 211, 268 (iii, iv, v, ix), 319, 361, 374, 375, 379-336, 432, 433, 639, 663
Teachers 285-287
Heads, Courses for 534
Health Education 359, 438, App. II
Hire Purchase 211, 358
History (see also Geography, Social Studies) 125, 163, 213, 350, 438, 447, Ch. 19c 545, 641, 682
teachers 514, 543
Homework 34, 36, 61, 92, 122-124, 337, 338, 507, 557, Ch. 22
Housecraft (See also Cookery, Needlework) 268 (XVI), 374, 388-401, 447, 639, App. II
Teachers 285-287
Housemasters 194, 282
Housing 54, 124, 559
Humanities, the 349, 358, 359, 401, Ch. 19, Ch. 23A, 641
Imagination 77, 116, 321, 377
Immigrants, New 55, 71, 79
Incentives 190-192, 345-348, 362-366
India 501-503
Industrial Training, White Paper (1962) 12
In-service Training 286, 287, 302, 514, 534
Italian (see Foreign languages)
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Jewish schools 166
Journeys, School 42, 72, 149-156, 162, 290, 410, 491, 505
Laboratories 45, 58, 265, 268 (III & IV), 395, 432, 672, 673
Labour, Ministry of 226
Leavers' Forms 99, 525, 643
Leaving Certificates 240, 258-260, 348
Library (see also Books) 45, 93, 265, 370, 371, 502, 677, 681
Public 123, 124, 469, 502
Lincoln, Abraham 499, 509
Literacy 76, 88, 331-334, 340, 346, 349, 368, Ch. 19, 556
Macaulay, Lord 15 503
Machines 78, 111, 385
Maladjusted, Classes for 201
Manual Work, Workers 12, 32, 111, 324, 557, 558, Ch. 22
Marriage and Home-making 56, 113, 116, 119, 164, 322, 398-400, App. II
Mathematics (see also Numeracy) 76, 88, 211, 310, 314, 341, 342, 429, Ch. 18B, 634, 638, 674-676
as Form Subject 283, 546
Teachers 286
Mathematics and Science as a Curriculum Field 314, 349, 358, Ch. 23A
Memory 77, 343, 344, 429
Metalwork 94, 382, 663, 665
Mining areas 31, 559, Ch. 22, 652, 664, 668, 680, 682, 684
Minorities, Cultural 71
Moral Judgements and Standards 76, 157, 159-164, 321, 327, 396, 438, 439, 509, 515
Music 41, 45, 125, 127, 254, 265, 268 (viii), 366, 374, 412-420, 632, 639, 640, 671
Music Teachers 285, 416
National Advisory Council on the Training and Supply of Teachers 25, 274, 301, App. IV
National Foundation for Educational Research 520
National Union of Teachers (Survey of School Buildings) 685
Needlework 94, 95, 374, 388-401, 665
Neighbourhoods 31, Ch. 3, 134, 152, 505, 559, 561, 562, 563, Ch. 22, 652, 664, 667, 668, 673, 676, 680, 682, 684
Newspapers 327, 465, 472
New Towns (see Council Estates)
Numeracy (see also Mathematics) Ch. 15, 349, 368, 531
Nurse, School 268 (XVI), 359
Nursing 109, 361
Options (see also Choice) 357, 531-532, 644
Oral Examinations 247
Overcrowding of Schools (see Buildings)
Parent-Teacher Associations 128, 204
Parents, Influence of 50, 56, 124, 152, 179-183, 204, 219, 329, 330, 359, 411
Periods, Length of 356, 630, 645
Photography 361
Physical Education 125, 349, 353, 359, 374, 402-411, 639, 666-670
Teachers 285-287, 289, 407
Physique 35, 70, 119, 404, Ch. 22
Plastics 361
Playing Fields 32, 58, 408, 660, 666, 667, 669
'Practical Subjects' 61, 93-97, 318-320, 349, Ch. 17, 548, Ch. 23A and C, Ch. 25A
Prefects 119, 195, Ch. 22
Primary Educaton, Schools 299, 308, 311, 312, 325, 332, 333, 335, 443, 444, 450, 464, 471, 482, 495, 520
'Problem Areas' 31, 64, 178, 182, 559, 562, Ch. 22, 652, 664, 667, 668, 673, 680, 682, 684
Projects 123, 327, 366, 485
Punctuation 481, 482
Punishment 185-187, 201
Race (see Immigrants, New)
Radio 419, 473, 506
Reading Test 8, 57, 65, 332-334, 553, 556, 564, 615, App. V
Real, Realistic 93, 97, 321, 324
Records, Record-Players 419, 473, 477
Regions 560, Ch. 22, 654, 665, 668, 673, 676, 682
Religion, Religious Instruction 82, Ch. 7, 254, 349, 515-17, 544, 545, 641
Teachers 168-170, 283, 284, 517, 544, 548
Remedial Class, Work 281, 343, 458
Residential Experience, Provision (see also Boarding) 42, 72, 73, 149-156, 209, 410
Retail Trade 13, 100, 109, 361
Robbins Committee 300, App. IV
Rotary Club 223, 236
Rural Areas 31, 329, 559, Ch. 22, 652, 664, 667, 673, 680, 684
Rural Studies 94, 218, 227, 361, 375, 387, 432, 447, 663-635, 664
Safety 380, 385
School Day, Length of 92, 120, 136-142, 181, 210, 645
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School Leaving Age, Case for Raising 3, 18-24
Numbers staying after 19, 40, 61
and External Examinations 249, 525
and Teacher Training 279
Science 78, 163, 211, 314, 353, 359, 395, 401, 415, Ch. 18A, 636, 637, 672, 673, App. II
Teachers 286, 287
Scotland 150, 240
Secondary School Examinations Council 246
Senior (Elementary) Schools 37, 524
'Sets' 531
Sex, Sex Education, Relation between Sexes (see also Behaviour, Personal, Moral Judgments and Standards) 56, 164, 179, 205-207, 296, 359, 398-400, 439, App. II
Size of Schools 71, 193, 519, 521, 535, 536, 537, 644, 663, 665
Skill, Increasing Demand for 10-14
Skills, Basic (see Literacy, Numeracy)
Slums 30, Ch. 3, 561, App. V
Smoking 183, 359
Social Service (see also Community Service) 162, 196, 200, 212, 221, 227, 380, 399
Social Studies (see also Geography, History) 211, 213, 641
Social Workers 70, 204, 232, 293, 294
Spanish (see Foreign languages)
Special Schools 4, 18, 201
Spelling 481, 482
Streaming 508, 520-524, 526, 643
Student Christian Movement in Schools 173
Surveys
Early Leaving 558, App. V
National Service 31, 555-557, 564
NUT 685
1961 29, 30, Ch. 21A, App. V
Sweden 222
Swimming 58, 408, 670
Switzerland 490
Tape recorders 41, 247, 346, 419, 473, 506
Teachers (see also entries under individual subjects)
as Careers Advisers 233-239, 295
Climate of Opinion among 158
Form Teachers 283, 284, 541, 546
Graduates 301-303, 541, 543
Heads of Departments 254, 280, 288, 448, 487, 544
Married Women 141, 179, 296, 297, 540, 547, 658
Mature Entrants 237, 296
Probationary Period 298
Residential Accommodation for 69
Specialists 285, 541
Supply of 25, Ch. 12
Supply in difficult areas 68, 69, 203, 276, 277, App. III
Training 287-304
Turnover 33, 59-60, 189, 193, 241, 541, 563, Ch. 24
Teachers' Assessments (as part of external examinations) 248
Teaching Groups, size of 171, 367, 368, 547
Teaching Load (Pupils per teacher per week) 171, 545
Teaching machines 455
Technical Drawing 94, 375, 452, 632, 639, 674-676
Television 214-216, 268 (VII), 465, 474, 506
Theatres 480
Time Allocations for Subjects 171, 356, 506, 532, 538, Ch. 23
Training Colleges 287, 290-294, 541, 543
Transfers between Secondary Schools 201, 536
Age of, from Primary to Secondary 198
Truancy (see Attendance, School)
Tutorial Groups 194, 282, 533
Uniform 188, 199, 309, Ch. 22
United States of America 12, 21, 222
Visits, School 42, 129, 130
Vocational, Vocationally biased courses, Vocational Incentive 3, 100-116, 322-324, 357, 378, 382, 383, 389, 432, 450, 518, 527-530
Vocational Guidance (see also Teachers, Careers, Youth Employment Service) 211, 218, 222, 233
Voluntary Schools 56, 158, 166
Welfare State 212
Wolfenden Report on Sport 411
Women, changed position of 80
Woodwork (see also Handicraft) 58, 94, 639, 663, 665
'Work Experience' 222-227, 295
Worship, Corporate 174
Youth Employment Service 223, 232-238, 257, 293-295
Youth Service 144-148, 290, 293
Zones (see Regions)
