As you are aware, the Central Advisory Council are shortly to report to you on the education between the ages of 13 and 16 of children of average and below-average ability. At the last meeting of the Council we discussed in particular the form of training most suitable for the teachers of such children. We were aware that this matter, which is of such importance to us, must also concern the Committee now sitting under Lord Robbins, and as we were so emphatic and united in our views, I as Chairman felt it to be a matter of urgency that I should inform you of them in the hope that if you think fit you will pass them on to Lord Robbins and his Committee.
We were unanimous in our opinion that an intending teacher whose personal and professional training are carried on together over a span of at least three years is much more likely to become a successful teacher of less able children than one who completes a degree course in a special subject and follows it with a year of training.
Briefly, we believe experience to show that 'concurrent training' and 'consecutive training' tend to produce different kinds of teachers. The former, because it entails a prolonged study of child development over a three-year period coupled with a study of a range of subjects, is more likely to produce teachers who succeed with the less able child. The latter tends to produce teachers who, having studied an academic subject in depth, are anxious to impart it to children sufficiently able to master it and derive satisfaction from it.
We do not deny that there is a considerable overlap between these categories, but, whereas the teacher trained to deal with the less able child will have little difficulty with the more able in his early years, the teacher who is trained in the expectation of presenting his subject to the more academically minded children is likely to be ill-equipped, discontented, and consequently less competent in teaching his subject (or, as is so often the case, some other subject) to slower children.
We are, of course, aware that within the resources at present being applied to teacher training the country's need for primary school teachers has led to a limitation for the time being of the number of secondary school teachers trained by the three-year colleges. We are deeply concerned lest what we hope will be a temporary expedient should be assumed to have educational merit on which long-term proposals for training might be based.
In informing you of these matters I am, of course, well aware that the National Advisory Council on the Training and Supply of Teachers is the proper body to advise on teacher supply. Since, however, the kind of training most likely to produce the best teachers for a large proportion of secondary
school pupils is an issue of fundamental importance to our present concerns as a Council, I hope you will find it possible to submit our views, on which we are unanimous, to Lord Robbins and his Committee at this stage in their deliberations.
There is perhaps just one final point which I ought to make. We are concerned less with existing institutions than with types of training. It may well be that new patterns of training will emerge in the newer universities or in existing colleges. What we do believe, however, is that the longer study of teaching problems coupled with the study of a wider range of subjects generally speaking produces better teachers of the less able children than a more specialised course followed by a markedly shorter period of training.
The Rt Hon Sir Edward Boyle, Bt, MP,
Minister of Education,
Ministry of Education,
Curzon Street House,
W1.
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.
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.
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).
The differences between boys in boys' schools and in mixed schools are not significant, nor are those for girls. Pooling gives:
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.
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 |
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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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:
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:
The deciles for external examination candidates in comprehensive schools in 1961, and those for grammar school pupils in 1956, are:
Table 3.3
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:
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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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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:
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.
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.)
