Plowden (1967)

Notes on the text

Volume 2

Preliminary pages Foreword and Contents
Appendix 1 Teachers' questionnaire
Appendix 2 Health of school children

The 1964 National Survey:

Appendix 3 1964 National Survey
Appendix 4 Regression analyses
Appendix 5 Data from the schools
Appendix 6 Infant starters
Appendix 7 Standards of reading of 11 year olds
Annexes to the National Survey

Appendix 8 Social services and primary education
Appendix 9 The Manchester Survey
Appendix 10 National Child Development Study
Appendix 11 School organisation and effects of streaming
Appendix 12 Gypsies and education
Appendix 13 Management of primary schools
Appendix 14 Variation in LEA provision

Volume 1

Report (full text)

Articles

about Plowden

The Plowden Report (1967)
Children and their Primary Schools

A Report of the Central Advisory Council for Education (England)

London: Her Majesty's Stationery Office 1967
© Crown copyright material is reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland.

Volume 2 Appendix 4
The regression analyses of the National Survey
[pages 179 - 221]

by GF Peaker

1. The broad outline

1. In marshalling the evidence to test conjectures about the reasons why some children make more progress in school than others a prime difficulty is to know what evidence is relevant, and to what extent. There would be no purpose in an inquiry if we knew this at the outset. The difficulty lies mainly in the right application of the phrase 'other things being equal'. For example, consider the question of the effect of the size of the teacher's class. It is very hard to believe that, if other things are equal, merely adding several more children to the class will improve the average achievement. Yet most surveys, including our own, show mild positive simple correlations between the average size of class in a school and the average test score for that school. Thus for our survey the highest such simple correlation is -25 for lower junior boys. In other words schools with larger classes tend, on the whole, to do rather better than schools with smaller classes. But this can hardly be the whole story. The result has only to be stated to arouse the conjecture that there must be various favourable circumstances, associated with large classes, to explain a result that would otherwise be incredible. But what can these circumstances be?

2. It is natural to think that the way to explore this question is to replace the simple two-way table, in which schools are grouped according to their average size of class and their average score, by a number of tables, in each of which there is only a small range for the other relevant circumstances. Thus we could classify the schools according to their average parental income, into three grades, and replace the single table by three tables, one for high, one for middling, and one for low average income. In the same way we could make another three-fold classification for the next variable that we think may be relevant. We now have nine tables. Bringing in a third variable will produce 27 tables. Continuing on these lines we should reach 59,049 tables for 10 variables, and more than two hundred billion for 30 variables. If we had more than three grades for each variable the number of tables needed would of course be much larger.

3. But, it may be said, the number of variables that can have any perceptible influence must be far smaller than 30. Long before we reach this point we must reach the point beyond which the influence of further variables is small and altogether uncertain on any evidence we can find. This is quite true. The trouble is that in order to apply it we should have to know in advance which variables were relevant and which were not, and the whole purpose of the inquiry is to find this out. It might be thought that it would be safe to take the variables in the descending order of their simple correlation, but, as is shown later, this is not the case. It is not the case because the relevance of a variable depends not only upon its simple correlation with the criterion, but also on its correlation with its fellows, and with their correlations among themselves. This makes it impossible to guess the order of importance. All the variables in the picture have to be considered before any of them can be declared irrelevant.

4. These considerations make it clear that a direct attack on the problem is bound to break down, from sheer numerical complication, before it has made any appreciable progress. For a practicable method it is necessary to invoke some rather complicated algebra which, together with electronic computation, enables a solution to be found. The algebra has a long history, going back to the Gaussian method of solving linear equations by successive elimination. In recent years electronic computation has made it possible to apply this to equations with a hundred unknowns or more. This in turn makes it practicable to apply the method of stepwise multiple regression even to cases like ours where there are initially more than a hundred variables in the correlation matrix. It is hardly practicable to describe the process without resort to mathematical language. For the moment it will be enough to say that the computer selects the variables that turn out to be relevant, on the evidence of the sample, and rejects the others. The proviso 'on the evidence of the sample' is material. Other samples drawn in the same way would provide somewhat different evidence, and lead to a somewhat different selection of variables. It is therefore important to consider the extent to which the results may be affected by sampling variation. The main point here is that the estimates of the total effects of broad classes of variables are more reliable than the estimates for individual variables. This suggests grouping the variables into three classes representing (1) parental attitudes, (2) home circumstances, (3) schooling. The estimate for the first class shows the effect on the child's progress of hopeful and encouraging interest on the part of the parents. The second class shows the effect of the parents' material circumstances, and of their own education. The third class shows the effect of the variation of various school circumstances. Before the inquiry it was plain, as a matter of common sense and common observation, that parental encouragement and support could take the child some way. What the inquiry has shown is that 'some way' can reasonably be interpreted as 'a long way', and that the variation in parental encouragement and support has much greater effect than either the variation in home circumstances or the variation in schools. The reason why the school variables play so small a part is not, of course, that schooling is unimportant. It is that the variation between schools is much less than the variation between parental attitudes. If the least cooperative parents rose to the level of the most cooperative the effect would be much larger than if the worst schools rose to the level of the best or the least prosperous parents to the level of the most prosperous, because the effect of the range in cooperation is much greater than the effect of the range in parental prosperity or that of the range in schooling.

5. This part of the inquiry shows how much could be gained if less cooperative parents became more cooperative. It throws no light on the extent to which this could be brought about by persuasion. On this point we have two kinds of evidence. In the first place we can use regression again to test the firmness of the link between the parents attitudes and their circumstances. It is reasonable to regard the attitudes as being partly determined by the other circumstances, and if we take the attitudes as criteria and the other circumstances as predictors we can get some light on the interpretation of 'partly'. We find that up to a quarter of the variation in attitudes can be put down to the variation in circumstances. This leaves three quarters or more to be accounted for in other ways. It is reasonable to suppose that among these other ways persuasion, from a great variety of sources, must play a large part, and it is therefore reasonable to hope that attempts to change attitudes by persuasion might have some success. On the other hand such direct evidence as we have on this point is not very encouraging. It falls under three heads. In the first place several of our variables (e.g. Is there a parent/teacher association? How many meetings with parents are held?) were intended to measure aspects of persuasion already in use. But these variables often failed to reach significance in the regression analyses. Secondly, a special group of schools where the relations between parents and teachers were thought to be particularly good was selected by HM Inspectorate. But although the evidence subsequently collected from these schools vindicated the judgements that led to their selection there was little difference between the average achievement of the children in this group and those in the representative sample. Thus the special group merely confirmed the result from the sample (which was, of course, not yet known when the special group inquiry was planned). In the third place rather more encouraging results were obtained from the experimental attempt to influence parental attitudes that was carried out in one school with the cooperation of the Institute of Community Studies. In this case a small but recognisable improvement in the children's achievement was obtained. The first two results are less encouraging than might have been hoped, though perhaps not surprising when we remember the vast sums spent by the advertising industry in attempts to change attitudes about relatively trivial matters. On the other hand the modest success of the experiment is encouraging, and suggests that we should remember the principle, though not the particular instance, of Mr Pickwick's views on brandy and water as a prophylactic - that where it failed it was because the sufferer had fallen into the vulgar error of not taking enough of it. On the evidence we may be confident that there is ample scope for persuasion, while recognising that to find the right kind and amount of persuasion will be a matter of difficult and delicate experiment, needing ingenuity and above all tact.

6. The conclusions reached may be set out as follows:

(a) The variation in parental attitudes can account for more of the variation in children's school achievement than either the variation in home circumstances or the variation in schools.

(b) Among the school variables of which we took notice the most important appeared to be the quality of the teaching. Although we found, as other inquiries have done, an association between better work and larger classes we also found that there were invariably other favourable circumstances, associated with the larger classes, to account for their apparent superiority.

(c) Although the variation in parental material circumstances and parental education can account for some of the variation in parental attitudes it cannot account for very much, and leaves open the possibility that attitudes may be changed by persuasion.

(d) There is no doubt that attitudes have changed and are changing. Perhaps the strongest evidence of the change in attitudes is the large and continuing rise in the proportion of children who stay at school beyond the statutory leaving age.

(e) Despite the evidence that attitudes are not closely conditioned by material circumstances, and that they have changed with time, our positive evidence on the question of how far they are open to persuasion was rather disappointing. A number of our variables attempted to measure the efforts and persuasion applied by the schools, but these variables were not very conspicuous in their contributions to the children's achievements.

(f) Consequently we may be confident that there is ample scope for persuasion while recognising that to find the right kind and amount of persuasion will be a difficult and delicate experiment, needing much ingenuity and tact.

2. The analyses in detail

Analyses between and within schools

7. The allocation of the sample of schools and pupils is set out in some detail at the end of the previous appendix. Here it will be enough to recall a few salient facts. To make the sampling frame schools were stratified by size. Within each size group they were drawn with probability proportionate to size. From each selected school within each size group a constant number of children was drawn. This number was 12, 8, or 4 per age group, according to the size group to which the school belonged. Boys and girls were drawn in equal numbers from mixed schools. Since the junior mixed and infants schools contained children in all six age and sex groups there were about a hundred schools and about five hundred pupils in each group.

8. Two kinds of analysis - between and within schools - were carried out. For the analyses between schools the variables were either attributes of the school, such as the average size of class in that school, or the sample means of pupil variables for that school, such as the mean parental income of the selected boys, or girls, in that school. For the analyses within schools the variables were the deviations from the mean of each school. These are of course zero for the school attributes, which do not therefore figure in the analyses within schools.

9. Since there are about a hundred schools and five hundred pupils in the sample for each of the six age and sex groups it will be seen that the standard errors of the simple correlation coefficients lie in the range from .10 to .07, according to the size of the correlation, for the analyses between schools, and in the range of .05 to .03 for the analyses between pupils within schools. This sampling variation determines the number of variables subsequently picked up by the stepwise regression process, and the size of the standard errors of the regression coefficients for these variables, which centred round .08 and .035 respectively for the two kinds of analysis. The general effect of sampling variation is to make the estimates for broad classes of variables more reliable than those for individual variables, particularly when the number of variables is large. This has a bearing on the selection of a short list from the long list of variables, as described in the next sub section.

The long and the short lists of variables

10. The original, long list of variables is set out in the two attached tables. Table 1 contains the variables that were derived from the interviews with parents conducted by the Social Survey. In drawing up the long list the general principle was to try to think of variables that might be relevant, and to include them if it seemed likely that reliable information could be obtained. Some variables that failed to satisfy the second condition were excluded after a pilot inquiry. After the field work had been done the Social Survey carried out a factor analysis in order to group some of the original questions into more satisfactory composite variables. This is described in the previous appendix. The first 14 variables in the Social Survey list are such composites.

11. The Social Survey list provides two of the three broad classes into which the variables can be divided. In the first place we have variables that measure parental attitudes. These are marked A in the list. Secondly we have the variables that represent the pupils' home circumstances, such as the parental income, the number of dependent children, the father's occupation, and the physical amenities of the home. These are marked B in the list. The parents' education is included in the second class, since it represents events that have already occurred. On the other hand the literacy of the home, which is perhaps less firmly anchored to the past, has been included in the first category.

12. Table 2, containing the school variables, comprises the third broad category. This information was supplied partly by the schools and partly by the Inspectorate, who provided, for example, the teaching assessment for each member of the staff concerned. In this list the letter P attached to a variable means that for this variable information was obtained for each pupil in the sample. Thus P is attached to the teaching assessment because the latter refers to the pupil's teacher. For the analyses between schools these variables provided a score for each school made by averaging them for the pupils in the sample for that school. For the analyses between pupils within schools the scores were the deviations from each school average. Some variables, originally included for the other purposes, have been deleted from the regression analyses either because they overlapped heavily with others or because they were quasi criterion variables. These are marked D.

13. The school list contains the criterion variables. For the analyses between schools the criterion was the score in a test of reading comprehension appropriate to the pupils' age. (The infants also had a picture intelligence test.) For the analyses between pupils within schools it was the pupils' rank order converted to a normal deviate. The rank order was, of course, based on the teacher's judgement, and since this analysis was within schools the usual difficulty of comparing the judgements of teachers in different schools did not arise.

14. The first set of analyses was run on the long list of variables. After deletions there were 104 variables for the analyses between schools, and 73 for those between pupils within schools. With a rather lenient significance stop (as described in the final section) about a dozen variables emerged from each analysis as making significant contributions to the criterion variation. These contributions were summed over the three broad classes of variable., and the results are set out in Table 3. The complete tables for the long list have not been printed, but they served their purpose in two ways. In the first place they enabled the long list summary table to be made. Secondly they were a useful guide to the composition of the short list. The long list summary is probably a better guide than the short list summary to the total amount of variation accounted for by each of the three classes of variable. This follows from considerations set out in the final section. The detailed tables for the long list were useful as a guide to the composition of the short list because variables appeared in them with different frequencies. Although these tables are not replications, since each refers to a different sex, age group, or test it seems reasonable to say that a variable that never, or hardly ever, appears in them is unlikely to have much relevance. This enabled a large number of variables to be rejected, of which perhaps the most notable were average size of class and number on the school roll. There were no variables that appeared in every table, so the short list was made up of Aspiration, Literacy, and Interest, which appeared most frequently, and 14 others chosen either because they appeared often, or because, owing to their special interest, it was urged that they should be given another chance of appearing. It could in fact be foreseen, with fairly high probability, that these variables were unlikely to take advantage of their second chance, and in the upshot they did not. This accounts for some of the blanks in the detailed tables for the short list.

15. A variable that was not included in the short list, because it never emerged from the long, was average size of class. Owing to the special interest attaching to this variable its correlations were subsequently included in the matrices for the short list, and the normal equations solved iteratively by hand. The resulting regression coefficients uniformly failed to reach significance, despite the fact that the simple correlation was, in one case (lower junior boys), as high as .25.

The results and their interpretation

16. Reserving further discussion of the stepwise regression process and the effect of sampling variation until the final section let us now turn to the results and their interpretation. The summary of the results derived from the long list is set out in Table 3. The short list is covered by Tables 4.1-4.6 (between schools) and Tables 5.1-5.6 (between pupils within schools) and their attached summaries.

17. All these tables bear a strong family likeness. Two main points emerge. In the first place more of the variation in the children's school achievement is specifically accounted for by the variation in parental attitudes than by either the variation in the material circumstances of parents or by the variation in schools. Secondly, the relative importance of the parental attitudes increases as the children grow older.

18. The new results extend, but are not incompatible with, those derived from the surveys reported in Early Leaving, Fifteen to Eighteen and Half our Future. Those surveys dealt with parental variations of the second kind. The new survey brings in the first kind (parental attitudes) as well. The effect of bringing in the attitude variables is two-fold. In the first place much more of the variation in the children's achievement is accounted for. Secondly, part of the variation that would be attributable to home circumstances, if attitudes were ignored, is transferred to the account of attitudes when these are brought in. This is analogous to the relations between the statures of fathers, mothers, and children. Tall fathers tend to have tall sons partly because they tend to marry tall wives. The simple correlations are .5 between parents and children and .3 between spouses. If fathers alone are considered they account for 25 per cent of the variations in sons. But when mothers are brought into the picture the total accounted for rises from 25 per cent to 38 per cent, but the father's contribution is reduced from 25 per cent to 19 per cent, because in the earlier assessment he was, so to speak, borrowing from the mother. In this way bringing in the parental attitudes increases the total amount of variation accounted for while reducing somewhat the amount attributed to the other kind of variable before the attitudes were brought in. This point is discussed further in the final section.

19. It will be seen from Table 3 that the long list of variables accounts for about two thirds of the total variation between schools and for about half of the total variation within schools. The remaining third (or half) is attributable to the circumstances that we have not taken into account, such as individual differences between children that are not related to their parents' attitudes or circumstances, or to those aspects of schooling that we have not taken into account, and also to our errors of measurement. To some extent the individual differences are averaged out when the pupil variables are summed over each school for the analyses between schools. This is the main reason why our variables account for two thirds of the variation between schools, and only half the variation between pupils within schools. But in both cases the amount of variation accounted for is remarkably high, and in particular the high contribution from the attitude side indicates the care and skill with which the difficult task of interviewing parents was carried out by the workers of the Social Survey.

20. Qualitatively the results are in no way surprising. Common sense and common observation lead us to expect that a child's school achievement will be determined, to some extent, by the attitudes of his parents, and that these attitudes in turn will partly depend upon their material circumstances. It was indeed this common sense expectation that guided the planning of the inquiry. What could not be foreseen, until the inquiry was complete, was the quantitative aspect. We could foresee that parental attitudes, parental circumstances, and schooling would each make a contribution. What we could not foresee, and what the inquiry has shown, is the relative size of these contributions. The fact that attitudes play so large a part is hopeful, since it is at least possible that attitudes may be open to persuasion. Two kinds of evidence on this point have already been mentioned, in paragraph 5. Let us now consider the first kind of evidence in more detail.

21. In the first part of our inquiry we have used multiple regression with the children's achievement in school as the criterion, and parental attitudes, parental circumstances, and school variables as the predictors. But we can also use it with parental attitudes as the criteria and parental circumstances as the predictors. In this way we can test the firmness of the link between attitudes and material circumstances. Without falling into the error of assuming that correlations are sufficient, as well as necessary, evidence of causal relations we can, at any rate, make an assumption, or set up a model, and work out its consequences. For example, we can assume that causal lines run from parental circumstances to parental attitudes, and thence to the children's achievement, in the way shown in the diagram below (Figure 1), which is based on the variables used in the short list. On the left of the diagram we have the five variables of the second kind in the short list namely (8) Physical amenities of the home, (12) No. of dependent children, (13) Father's occupational group, (14) Father's education, (15) Mother's education. In the middle column we have the three variables of the first kind, namely, (9) Aspiration for the child, (10) Literacy of the home, (11) Parental interest in school work and progress. On the right we have the final criterion, the child's school achievement. The arrows are the causal lines, and the number on each arrow is the percentage of the variance, of the variable to which it runs, that it carries. These are determined from the regression equations. Since these contributions always fall short of 100 per cent we also need the arrows coming in out of the blue to carry the residuals. For the final criterion there is also a contribution from the schooling variables.

Figure 1 A path diagram

22. Figure 1 relates to the analysis between schools for the top junior boys. The connections shown in it between parental circumstances and parental attitudes, and the corresponding facts for the top junior girls, can also be exhibited in tabular form as follows. (The variables denoted by numbers in the following tables can be identified by Fig. 1):

For the analyses between pupils within schools the corresponding tables are:

23. Among the five variables placed on the left in Figure 1 there are two which stand in a special position. These are (14) Father's education and (15) Mother's education. As we have defined them these are entirely records of past events, and this may be held to give them a better right than the other three to be put first in a causal sequence. If we take them by themselves we obtain:

It is interesting to note that (11), Parental interest, depends less upon parental education than either (9) or (10). It is easy to see a possible reason for this. It is also interesting to note in the summary that, as usual, fathers are rather more important for daughters and mothers for sons.

24. The main point to be noted in Figure 1, and in the corresponding diagrams for other age and sex groups that could be drawn from the tables above, is the size of the residual terms. It is the arrows coming in out of the blue that carry the weight. The variables representing parental circumstances and past history account for only about a quarter of the variation in attitudes, leaving about three quarters to be accounted for by other variables that we have not brought into the picture. Common sense, common observation, and introspection suggest that among these variables communication and persuasion, from a great variety of sources, must play a considerable part. Or, to put the matter another way, if we were able to see through the eyes of omniscience, and use a measure of parental education that included the whole impact of other minds, far more of the variation in attitudes could be accounted for. And although, like the younger Mr Weller *on a famous occasion, we have to confess that our vision is more limited we may none the less conclude that it is not unreasonable to hope that parental attitudes can be changed by persuasion in such a way that on the whole parents and teachers become more cooperative. On the one hand the fact that parental circumstances do not account for very much of parental attitudes leaves plenty of room for believing that persuasion may be effective. On the other hand the fact that they account for some of the variation gives grounds for expecting that as circumstances improve so will attitudes. These grounds are strengthened by the fact that our evidence shows direct links between parental circumstances and children's school achievements, in addition to the indirect links through parental attitudes.

*See final section

Summary

25. Two questions may be asked at the end of any inquiry. They are:

(a) Are the conclusions compatible with earlier evidence?

(b) If so, have we learnt anything that we did not know at the outset?

26. The conclusions suggested are that:

(1) The specific contributions made by the variation in parental attitudes are greater than those made by the variation in home circumstances, while the latter in turn are greater than those made by the variations between schools and teachers that we have taken into account.

(2) Only about a quarter of the variation in parental attitudes is conditioned by the variation in circumstances. The remainder must be conditioned to a large extent by communication and persuasion, so that it is reasonable to hope that an attempt to improve the cooperation of parents and teachers by persuasion might attain some success.

(3) Although parental attitudes are largely independent of home circumstances they are conditioned by them to some extent. For this reason, and also because parental circumstances operate directly, as well as through parental attitudes, on children's progress it is reasonable to hope that the latter will improve as circumstances improve.

3. Some technicalities

'Yes, I have a pair of eyes', said Sam, 'and that's just it. If they wos a pair o' patent double million magnifyin' microscopes of hextra power, p'raps I might be able to see through a flight o' stairs and a deal door; but bein' only eyes, you see my wision's limited'.

28. Like most of the younger Mr Weller's remarks this has a wide application. Its bearing upon educational inquiries, of whatever kind, is to remind us of the extent of our ignorance. None of us can know much about the workings of other's minds, though we may reasonably hope to learn a little more. That is to say, we can reasonably hope to obtain new evidence that makes some conjectures rather more probable, and others rather less so. New evidence can only do this if it is both well founded and appropriately analysed. The foundations of our evidence have been discussed above. The least familiar aspect of the analysis is the use of stepwise regression, to which we now turn.

Stepwise regression

29. In this process successive regression equations, like

y=b_i x_i ------------------------------ (1)

y=b'_i x_i + b'_j x_j -------------------- (2)

y=b'_i' x_i + b'_j' x_j + b'_k' x_k ------- (3)

etc. etc.

30. The first variable to be selected is, of course, the one with the largest simple correlation with the criterion. But the subsequent order of selection is not necessarily the same as the descending order of the simple correlation, as may be seen by looking down the right hand column, which shows (7) selected before (10), although the latter has a larger simple correlation. Furthermore, the last two variables to reach significance, (5) and (2), have much smaller simple correlations than several variables which are not selected at all. For example (13), which is Father's occupational group, has a simple correlation of .20, and there are simple correlations of .20 and .16 for (14) and (15), which are Father's education and Mother's education respectively. A variable with a fairly high simple correlation may fail to enter the regression equation because it is too highly correlated with variables that the equation already contains. This is illustrated below for (13).

31. It will be seen that as the process goes on the coefficients tend to settle down. Thus the changes produced by the first three steps are much greater than those produced by the last three. Variable (11), which is the pioneer, takes some hard knocks to begin with, but is pretty steady after the fifth step, while (10), which only comes in at the fifth step, is steady from the start. This illustrates a general feature of the process.

32. The contributions to the assigned variation can be obtained by multiplying the regression coefficient by the simple correlation, and are as follows (in percentages):

33. Since each row in this table is derived from the corresponding row in the previous table by multiplying by the same quantity the new table shows the same tendency to settle down as the old one. The total of the assignable variation increases as each new variable comes in, but the increase, at first rapid, is very slight for the last three steps. This is partly because the later variables to be selected have smaller simple correlations, and partly also because they have smaller regression coefficients. The final row in the table shows what the assignable variation would be if the predictors were uncorrelated among themselves. If this were so each regression coefficient would simply be the corresponding simple correlation with the criterion. Since 42.9 is only 60 per cent of 71.0 there is a 40 per cent loss of efficiency owing to the intercorrelation of the seven predictors among themselves.

34. This intercorrelation is shown in the following table, which also contains the correlations with the criterion Y, and three supplementary columns that are explained below:

Correlation matrix

35. The first supplementary column, headed A, contains the regression coefficients for the seven variables, taken from the first table above but rearranged in the new order. The sum of the products of each entry in this column and the corresponding entry in any of the predictor columns is the simple correlation at the head of that column, as may be verified. This is the clue to the iterative method of obtaining the regression coefficients, which is an alternative to the process of inverting the intercorrelation matrix. It also enables us to see how it is that variable (13), with a substantial correlation of .20 with the criterion, does not enter into the regression. The column headed B contains the simple correlations of (13) with the criterion and the other seven variables, the entry [1.000] at the foot being its correlation with itself, like the diagonal entries in the matrix. Each entry in A is multiplied by the entry in B to give the entry in C. The seven entries in C sum to .187, which is .013 short of .200, the simple correlation between (13) and the criterion. If we now enter .013 at the foot of the A column, and multiply it by 1.000 in the B column, we get .013 at the foot of the C column, which now sums to .200, the simple correlation of (13) with the criterion. Consequently .013 would be the first shot at the regression coefficient for (13) if we were using the iterative solution for the stepwise procedure. It is not the final value because inserting it produces small additions to the sums of products for all the other variables, so that slight adjustments in the other regression coefficients are needed to get rid of these, and this in turn will alter the .013 somewhat. The reader who is interested can carry out the process for himself by going back a step in the regression, starting with the first six variables, and obtaining by the iterative process the coefficients when (2) is brought in. The iterative method shows both why every coefficient needs adjustment when a new variable is brought in, and also why the adjustments are small in the later stages.

36. Here however the immediate point is that (13) does not enter the regression equation because the seven regression coefficients already found give it a total entry in the C column which differs from its simple correlation with the criterion by an insignificant amount. It can be seen from the column that all the preceding seven variables, except for (2) and (5), contribute roughly equally to this result. By the same token it can be seen from columns (2) and (5) that the reason why these variables enter into the regression equation, despite their low simple correlations, is the presence of negative intercorrelations in their columns. A variable tends (not) to enter the equation if it has a high (low) simple correlation with the criterion, or if it has a low (high) correlation with the resultant of the previous predictors. As these cases illustrate the two requirements may be in conflict.

37. The iterative solution shows why a variable with a small simple correlation may none the less be important. The computer programme proceeds on different lines. It begins with the complete correlation matrix and transforms it step by step until the regression coefficients and the inverse matrix are obtained for the significant variables. At each step it examines all the variables to find which makes the largest reduction in the outstanding variation at that stage, and puts that variable in the regression if the reduction is significant. At the mth step the test of significance is that F should exceed F_o, where

R_m is the multiple correlation when m variables are in the regression, and n is the number of schools, or pupils as the case may be, in the sample for this sex and age group. Thus, for the fourth step in the table on page 190, with 498 top junior boys in the sample,

= 28.0, or 28.2088 from the computer, which retains more figures.

For the seventh and final step

=9, the more accurate value being 8.4780 from the computer.

F_o is at choice, in the range from three to six: the higher the value the more severe the test of significance. In this case all choices in the range produce the same result, since the lowest F is nine, which exceeds six. But in general a low choice for F_o may admit one or two steps that would be excluded by a high choice. For the present work the low choice, three, was fed into the computer throughout. The grounds for this are that one does not know at the outset how the results will come out, and that steps that have been taken can always be excluded by a revised choice of F_o, whereas steps that have not been taken at first cannot subsequently be added without running the whole programme again.

38. It should be noted that while the reduction made by the mth variable in the outstanding variation is, of course, the same as the addition made to the assigned variation it is not the same as the 'contribution'. Thus at the fourth step in the preceding table the reduction (or addition) is 38.3 - 34.8 = 3.5 per cent, while the contribution is 6.1 per cent. The contributions from the earlier steps are changed somewhat at each new step, and the new contribution is made up partly of the addition and partly of the amount transferred from variables chosen earlier. At the second step the addition made by (9) is 29.6 - 17.2 = 12.4 per cent, but the contribution is 14.5 per cent. The difference of 2.1 per cent had, so to speak, been 'borrowed' by (11) at the first stage. Comparing the extreme entries in the top row shows that the total 'borrowings' of (11) from the other six variables were 17.2 - 10.5 = 6.7 per cent.

39. With a sample of this size the process for this sex and age group stops at the seventh step, but if the sample were much larger it would go on for one or two more steps, and evidence of further slight borrowings would appear - 'slight' because the process is clearly settling down by the seventh step. But if we had a much larger sample it would be better to divide it into interpenetrating random sub-samples and so obtain replications of the tables. Four replicated sets of tables from four samples of 100 schools each would give a better idea of the stability of the estimates than one set from 400 schools. This is because the stepwise procedure has the defects of its virtues. Its merit is that it excludes variables that fail to make significant addition to the assigned variation, on the evidence of a particular sample. Its demerit is that the evidence of a particular sample may lead to the inclusion of variables that ought, on their population values, to be excluded, and vice versa. The lowest regression coefficients admitted to our between schools and within schools tables are .11 and .06 respectively, on the long list, and .13 and .07, on the short list. The standard errors of the coefficients in the 'between schools' tables are all close to .08. In the 'within schools' tables they are all close to .035, there being about five times as many boys (or girls) as schools in the sample for each sex and age group.

40. We know that about a sixth of the estimates will be too large by one standard error or more, and another sixth too small. Similarly we know that about one estimate in 40 will be too large by two standard errors, or more, and about one in 40 too small. We know nothing about the actual errors beyond the fact that they are distributed in this way. But this is enough to make us confident that some of the variables with small coefficients that are in the table ought not to be, and that others that are not included ought to be. 'Ought to be' means here 'would have been included more often than not' if we had had a great many samples instead of only one.

41. The effects are more serious for the 'between schools' tables than for the 'within schools' tables, because the standard errors are twice as large for the former, and more serious for the long list than the short list, because the tables from the long list contain more variables with small coefficients. many of which would be replaced by others if we could afford to replicate.

42. The advantage of a long list is that it gives a very large number of variables a chance of appearing in the evidence. Of this large number there are probably some that are real, but small, contributors. But which of these real but small contributors actually appear in the tables depends very much on the chance of sampling, as has been shown. A short list has the initial, and serious, disadvantage that the variables excluded from it cannot appear in the evidence however much they deserve to do so. On the other hand the evidence about the variables that are included is less at the mercy of chance effects, and no variable that appeared important in the results from the long list has been excluded from the short.

43. What this amounts to is that only the summary tables from the long list are worth interpretation. For the short list interpretation may reasonably be applied to the individual variables that appear, as well as to the summaries. The summary tables for the long list have been made by dividing the variables into the three broad classes, and summing the contributions from each class of variable over each sex and age group. This has also been done for the tables from the short list, but in addition the summaries include the contributions of individual variables. Complete tables, giving the simple correlations and the regression coefficients as well as the contributions, have also been given for the short list.

Bias

44. It should be noted that the estimate of the assignable variation is subject to bias as well as to sampling variation. If we had a large number of samples instead of only one each sample would give a somewhat different value of R² and the average of these values would be somewhat greater than the true value. If the true value is R² the expected value is

where n is the number of sampling units (schools or pupils) in the sample and p the number of variables that emerge as significant. Thus, with 100 schools and 10 variables emerging, and a true R² of 50 per cent, the expected estimate would be 54.5 per cent. With 500 boys and girls it would be 50.9 per cent. For the analyses within schools the effect is altogether trifling, but it is less so for the analyses between schools. The reason for the bias is that the addition of any variable, even a purely random one, is bound to make some addition to the multiple correlation, in the absence of a fantastically improbable numerical coincidence, and that since R is essentially positive these small contributions add up. The significance stop in the stepwise regression process prevents much damage being done, but where the number of emerging variables is an appreciable fraction of the number of sampling units the effect is not completely negligible though it is less than that of sampling variation. In the case of the analyses between schools it is like having a gun aimed five degrees off the target with two thirds of the shots falling within seven degrees of the aiming point. Within schools this becomes one degree and three degrees.

Cause and effect

45. The form of the argument is as follows. The previous evidence makes it initially probable that variations in parental attitudes, parental circumstances, and school circumstances all have some effect on the progress of children in school. The regression analysis with school achievement as the criterion increases this probability, and also gives us estimates of the relative parts played by the three classes of variable. This first part of the evidence strongly suggests that if parental attitudes could be changed by persuasion there would be a marked rise in the general level of school achievement. The second part of the evidence comes from the regression analyses with parental attitudes as the criteria. This shows that while the variation in circumstances can account for some of the variation in attitudes it cannot account for very much. This part of the evidence leaves the door open, so to speak, for persuasion, and taken in conjunction with the first part suggests that more educational effort could profitably be directed to changing parental attitudes by persuasion. However, when we look for positive evidence on this the results are rather disappointing. On the one hand the 'persuasion' variables turned out to have negligible regression coefficients for the most part, and on the other the average performance of the special group of schools with good parent-teacher relations was no better than the general average. The most hopeful feature is that there was an improvement in achievement in the one school where a deliberate experiment in persuasion was made. This result needs replication in other schools before great weight can be attached to it, but so far as it goes it is encouraging.

46. Elderly observers like the writer can have little doubt that the general level of parental attitudes, and with it the general level of school achievement, has risen a great deal during the last half century, so that the question is really whether this progress can be accelerated by persuasion. The general conclusion seems to be that a successful attempt to accelerate the improvement in attitudes by persuasion would be extremely rewarding, but that the attempt is likely to be a difficult and delicate task, demanding both ingenuity and tact in a high degree.

Table 1 Variables from the parental interviews for the multiple regression analysis (Long List)

Variables marked A have been classified as Attitudes.
Variables marked B have been classified as Home Circumstances.
Variables marked F are composites reached through the factor analysis.

A1 F.1. Responsibility and initiative taken by parents over child's education
Transform items as follows and then sum the new codes for each parent.

(i) Whether talked to class teachers
  Code 1. Yes.
  Code 2. No. D.K.

(ii) Number of talks with head or class teacher
  Code 1. Four or more talks.
  Code 2. Three talks.
  Code 3. Two talks.
  Code 4. One talk or D.K.
  Code 5. No talks.

(iii) Whether seen head or class teacher about educational matters
  Code 1. Yes.
  Code 2. No. D.K.

(iv) Whether had talk about teaching methods used
  Code 1. Had talk.
  Code 2. No talk.

(v) Whether talked to head when child started school
  Code 1. Yes.
  Code 2. No. D.K.

(vi) Whether husband has been to child's school and talked to head
  Code 1. Husband has been to school and talked to head
  Code 2. Husband has been to school but not talked to head
  Code 3. Husband has not been to school.

(vii) Whether asked for work for child or how to help child at home
  Code 1. Asked for homework.
  Code 2. Homework already given.
  Code 3. Has not asked for homework.

(viii) Number of possible types of school function attended.

(i) It's very easy to see the teachers whenever you want to
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

(ii) The teachers seem very pleased when parents go along to see them
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

(iii) Whether happy with arrangements for seeing head or class teacher
  Code 1. Yes.
  Code 2. D.K.
  Code 3. No.

(iv) I feel that teachers would like to keep parents out of the school
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(v) The teachers definitely seem interested in what you think about your child's education
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

(vi) I would feel that I was interfering if I went to the school uninvited
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(vii) If you go up to the school they only tell you what you know already
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(viii) The teachers seem really interested in all the children
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

(i) Whether husband helps with control of children
  Code 1. Husband takes big or equal part.
  Code 2. Husband takes small part.
  Code 3. No husband/wife.

(ii) Whether husband takes interest in how child is progressing at school
  Code 1. Husband takes interest.
  Code 2. No interest, or no husband.

(iii) Whether husband does things with child at weekends
  Code 1. Yes, most weekends.
  Code 2. Yes, occasional weekends.
  Code 3. No, or no husband.

(iv) Whether husband plays with child in evenings
  Code 1. Yes, most evenings.
  Code 2. Yes, occasional evenings.
  Code 3. No, or no husband.

(v) Whether husband took interest in school child went to
  Code 1. Husband took interest.
  Code 2. No interest or no husband.

(vi) Husband's hours away from home at work
  Code 1. Less than 10 hours.
  Code 2. Ten but less than 12 hours.
  Code 3. Twelve hours or over.

(vii) Whether husband has been to child's school and talked to head
  Code 1. Husband has been to school and talked to head.
  Code 2. Husband has been to school and not talked to head
  Code 3. Husband has not been to school.

(i) Having the cane is very bad for most children
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

(ii) I would agree to the school using the cane occasionally
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(iii) Most children need to be smacked quite often
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(i) Whether fixed bath or shower
  Code 1. Yes, own.
  Code 2. Yes, shared.
  Code 3. No.

(ii) Whether hot water from a tap
  Code 1. Yes, own.
  Code 2. Yes, shared.
  Code 3. No.

(iii) Whether child usually plays in street or not
  Code 1. Does not play mainly in street.
  Code 2. Plays mainly in street.

(iv) Whether dwelling has garden or yard child can use
  Code 1. Yes.
  Code 2. No garden or yard.

(i) Parents should leave all teaching and helping with school subjects to the teachers
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(ii) Whether help with school work given to child at home
  Code 1. Yes, by husband and/or wife.
  Code 2. Yes, but not by husband or wife.
  Code 3. No.

(iii) I have too much to do to spend time on helping with school work
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(iv) Whether mother plays with child in the evenings
  Code 1. Yes, most evenings.
  Code 2. Yes, occasionally.
  Code 3. No.

(v) Teaching children to behave should be mainly the school's job
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(i) Whether particular type of secondary school wanted for child
  Code 1. Yes, particular type wanted.
  Code 2. No, doesn't mind. D.K.

(ii) Whether grammar school wanted for child
  Code 1. Yes, grammar wanted.
  Code 2. No, doesn't mind.

(iii) Preferred age of leaving school for child
  Code 1. 18 or over.
  Code 2. 16 or 17.
  Code 3. Can't say, depends on child.

(i) Whether father has taken any recreational/leisure courses
  Code 1. Yes.
  Code 2. No. D.K.

(ii) Whether mother has taken any recreational/leisure courses
  Code 1. Yes.
  Code 2. No. D.K.

(i) Whether made inquiries about school before child started
  Code 1. Made inquiries.
  Code 2. No inquiries made, or not needed.

(ii) Whether knew what school was like before child started
  Code 1. Knew about school.
  Code 2. Did not know about school.

(iii) Whether parent talked to head when child started school
  Code 1. Yes.
  Code 2. No.

(i) Whether parent has complained to head or class teacher
  Code 1. Not complained.
  Code 2. Complained.

(ii) Whether parent has seen head or class teacher on own initiative
  Code 1. No. D.K.
  Code 2. Yes.

(iii) Whether teachers treat all children fairly
  Code 1. Children treated fairly.
  Code 2. D.K.
  Code 3. Children not treated fairly.

(iv) The teachers have favourites among the parents
  Code 1. Disagrees.
  Code 2. D.K.

(i) Whether husband or wife belongs to library
  Code 1. One or both belongs.
  Code 2. Neither belongs but one belonged within 10 years.
  Code 3. Neither belonged within last 10 years.

(ii) Whether wife reads
  Code 1. Yes, non-fiction.
  Code 2. Yes, newspapers, magazines, or fiction.
  Code 3. No reading, or no wife.

(iii) Number of books in home
  Code 1. More than five books.
  Code 2. One to five books.
  Code 3. No books.

(iv) Whether husband reads
  Code 1. Yes, non-fiction.
  Code 2. Yes, newspapers, magazines, or fiction.
  Code 3. No reading, or no husband.

(v) Whether child has library books at home
  Code 1. Yes.
  Code 2. No. D.K.

(vi) Whether child reads at home apart from homework
  Code 1. Yes, four times a week or oftener, books.
  Code 2. Yes, two or three times a week, books.
  Code 3. Yes, less than twice a week, books.
  Code 4. Comics or magazines only.
  Code 5. No reading.

(i) Whether child talks to parent about school work
  Code 1. Yes, often.
  Code 2. No, or rarely.

(ii) Whether child brings books home from school to read
  Code 1. Yes.
  Code 2. No. D.K.

(iii) Whether child reads at home
  Code 1. Yes, four times a week or oftener, books.
  Code 2. Yes, two or three times a week.
  Code 3. Yes, less than twice a week, books.
  Code 4. Comics or magazines only.
  Code 5. No reading.

(iv) Whether mother plays with child in evenings
  Code 1. Yes, most evenings.
  Code 2. Yes, occasionally.
  Code 3. No, no answer.

(v) Whether parent happy about teaching methods used
  Code 1. Happy.
  Code 2. Worried.

(vi) I would like to be told more about how my child is getting on
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(vii) I think that the teachers should ask me more about my child
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(i) Starting age preferred
  Code 1. 6 or older.
  Code 2. 5½ but less than 6.
  Code 3. 5 but less than 5½.
  Code 4. 4½ but less than 5.
  Code 5. 4 but less than 4½.
  Code 6. Less than 4.

(ii) Whether better for child to have started morning and afternoons or not
  Code 1. Only mornings or afternoons best.
  Code 2. D.K. Can't say.
  Code 3. Mornings and afternoons best.

(i) The schools should be stricter with the children
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

(ii) Whether teachers should be firmer or less firm with the children
  Code 1. Should be less firm.
  Code 2. Quite happy or D.K.
  Code 3. Should be firmer.

(iii) The teacher should try to get the children on faster in their work
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

A15 I feel that teachers have enough to do already without having to talk to parents
  Code 1. Disagrees.
  Code 2. D.K.
  Code 3. Agrees.

A16 Whether streaming preferred or not
  Code 1. Better for quicker and slower children to be in one class together
  Code 2. D.K. No opinion, depends on child.
  Code 3. Better for quicker and slower children to be in separate classes

A17 Whether child should be given some school work to do at home
  Code 1. Should be given homework.
  Code 2. D.K.
  Code 3. Should not have homework.

A18 Whether parents bought copies of school books
  Code 1. Yes.
  Code 2. No. D.K.

A19 There is too much concentration on working for the eleven plus exam
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

A20 Whether parent finds child easy or difficult to control
  Code 1. Easy to control.
  Code 2. Some ways easy, some difficult.
  Code 3. Difficult to control.

A21 I think schools which give children a lot of freedom are good
  Code 1. Agrees.
  Code 2. D.K.
  Code 3. Disagrees.

A22 Whether grammar school particularly disliked for child
  Code 1. No. D.K.
  Code 2. Yes, grammar school disliked.

A23 Whether type of secondary school should be decided by exam or teacher
  Code 1. Mainly by teacher.
  Code 2. Both equally, no opinion.
  Code 3. Mainly by exam.

B24 Number of types of amenity in area
  Code 1. Seven types of amenity.
  Code 2. Six types of amenity.
  Code 3. Five types of amenity.
  Code 4. Four types of amenity.
  Code 5. Three types of amenity.
  Code 6. Two types of amenity.
  Code 7. One type of amenity.
  Code 8. No amenities.

B25 Number of types of amenity in area used
  Code 1. Seven types of amenity used.
  Code 2. Six types of amenity used.
  Code 3. Five types of amenity used.
  Code 4. Four types of amenity used.
  Code 5. Three types of amenity used.
  Code 6. Two types of amenity used.
  Code 7. One type of amenity used.

A26 Whether husband strict or lenient with the children
  Code 1. Husband strict.
  Code 2. Husband moderate, in some ways strict/lenient.
  Code 3. Fairly lenient, no husband.
  Code 4. Very lenient.

A27 Whether family goes on outings together
  Code 1. Yes, Christmas or more recently.
  Code 2. Yes, but before Christmas.
  Code 3. No.

B28 Whether family has a car
  Code 1. Yes.
  Code 2. No.

B29 Whether lives in whole house
  Code 1. Yes, in whole house.
  Code 2. In flat, rooms, caravan.

B30 Whether owns dwelling
  Code 1. Own or buying dwelling.
  Code 2. Dwelling rented or rent free.

B31 Whether father on shift work
  Code 1. Father not on shift work.
  Code 2. Father on shift work or away from home.

A32 Whether parent ever asked for permission for child to go to a different school
  Code 1. No. D.K.
  Code 2. Yes.

A33 Whether child went to a nursery school or nursery class
  Code 1. Yes.
  Code 2. No. D.K.

A34 Age child started to go to school in morning and afternoon
  Code 1. Under 3½.
  Code 2. 3½ but less than 4.
  Code 3. 4 but less than 4½.
  Code 4. 4½ but less than 5.
  Code 5. 5 but less than 5½.
  Code 6. 5½ but less than 6.
  Code 7. 6 or older.

B35 Whether child has changed schools
  Code 1. Not changed schools.
  Code 2. Changed schools once.
  Code 3. Changed schools twice.
  Code 4. Changed schools thrice.
  Code 5. Changed schools four or more times.

B36 Total number of persons in household

B37 Total number of children in household
    (i.e. Selected child and brothers and sisters)

B38 Whether natural or substitute parents in family
  Code 1. Natural father and natural mother in household.
  Code 2. Natural father and/or natural mother missing from household.

B39 Whether mother only in family, no father
  Code 1. Natural or substitute father present in household.
  Code 2. No father in household, mother only.

B40 Whether selected child is eldest or only child
  Code 1. Selected child is eldest or only child.
  Code 2. Selected child is not eldest or only child.

B41 Total number of dependent children, i.e. those still undergoing or not yet started full-time education

B42 Bedroom deficiency index
  Code 1. Three or more bedrooms above standard.
  Code 2. Two bedrooms above standard.
  Code 3. One bedroom above standard.
  Code 4. Equal to standard.
  Code 5. One bedroom less than standard.
  Code 6. Two bedrooms less than standard.
  Code 7. Three or more bedrooms below standard.

B43 Occupation of father
  Code 1. Professional S.C. I.
  Code 2. Managerial, minor professional S.C. II.
  Code 3. Skilled and clerical S.C. III.
  Code 4. Semi-skilled S.C. IV.
  Code 5. Unskilled, labourers S.C. V.

B44 Mother's hours of work
  Code 1. Mother not working.
  Code 2. Mother working under five hours per day.
  Code 3. Mother working over five hours per day, no mother.

B45 Income of father or head of household
  Code 1. Over £30.
  Code 2. Over £25 to £30.
  Code 3. Over £20 to £25.
  Code 4. Over £15 to £20.
  Code 5. Over £12 10s. to £15.
  Code 6. Over £10 to £12 10s.
  Code 7. £10 and under.

B46 Income of family
  Code 1. Over £30.
  Code 2. Over £25 to £30.
  Code 3. Over £20 to £25.
  Code 4. Over £15 to £20.
  Code 5. Over £12 10s. to £15.
  Code 6. Over £10 to £12 10s.
  Code 7. £10 and under.

B47 Whether parents born in UK. or not
  Code 1. Both parents born in UK.
  Code 2. One parent only born in UK.
  Code 3. Neither parent born in UK.

B48 Age at which father completed full-time education
  Code 1. 18 and over.
  Code 2. 17 but under 18.
  Code 3. 16 but under 17.
  Code 4. 15 but under 16.
  Code 5. 14 and under.

B49 Age at which mother completed full-time education
  Code 1. 18 and over.
  Code 2. 17 but under 18.
  Code 3. 16 but under 17.
  Code 4. 15 but under 16.
  Code 5. 14 and under.

B50 Whether any member of child's family has been to a selective secondary school
  Code 1. At least one member has been to selective secondary school.
  Code 2. Not known whether member has been to selective secondary school.
  Code 3. No member of family has been to selective secondary school.

B51 Whether father has had any further education since leaving school
  Code 1. Yes, had some further education.
  Code 2. No further education. D.K.

B52 Whether mother has had any further education since leaving school
  Code 1. Yes, had some further education.
  Code 2. No further education. D.K.

B53 Whether any qualifications obtained by father
  Code 1. Qualifications above 'O' level.
  Code 2. Qualifications 'O' level or below.
  Code 3. No qualifications.

B54 Whether any qualifications obtained by mother
  Code 1. Qualifications above 'O' level.
  Code 2. Qualifications 'O' level or below.
  Code 3. No qualifications.

Table 2 School variables

Variables marked P are those for which information was obtained for each pupil in the sample.
Variables marked D were deleted from the regression analyses (see para 12).

1. Age range of school (JM & I junior or infants).

2. Status of school (county, voluntary controlled, voluntary aided).

3. Zoning (strict, broad or not).

4. (D) Percentage of parents over whole school in professional or managerial occupations (head's assessments).

5. (D) As above, for semi and unskilled occupations.

6. Parent/Teacher Association in school.

7. Parents' meetings arranged on educational matters.

8. Social functions arranged for parents.

9. Parental help for school (money, kind, or labour).

10. Number of social functions for parents, arranged when fathers are probably working.

11. Number of social functions, arranged when fathers are available.

12. Total number of parents' meetings arranged when fathers probably working.

13. Total number of parents' meetings arranged when fathers available.

14. Number of families seeking interview(s) on their initiative in a year.

15. Number of children on school roll.

16. Average size of class.

17. Classes streamed in the school.

18. (D) Percentage of pupils going on to 100 per cent comprehensive schools (JM & I and junior schools only) over previous three years.

19. (D) Percentage of pupils going on to secondary modern schools without extended courses (as above).

20. Number of school and class library books per 100 pupils.

21. Average annual expenditure per pupil on school and class library books (over 3½ years).

22. Children allowed to take library books home.

23. Men stayers, on staff 1 Sep 1961 until June 1964 (as percentage of total full-time staff members who have taught in school during period).

24. Women stayers, on staff Sep 1961 until June 1964 (percentage expressed as above).

25. Transient men staff, appointed to school and left between Sep 1961 and June 1964 (percentage expressed as above).

26. Transient women staff, appointed to school and left between Sep 1961 and June 1964 (percentage expressed as above).

27. (P) Teacher's sex.

28. (P) Age of teacher.

29. (P) Marital status of teacher.

30. (P) Teacher's responsibility (status in school).

31. (P) Years of teaching experience since break in service (if any).

32. (P) Total years of teaching experience.

33. (P) Average length of service in each school.

34. (P) Number of days spent since 1 June 1961 on short courses of inservice training (each course less than 30 days).

35. (P) Number of long courses of in-service training attended since 1 June 1961 (each course lasting 30 days or more).

36. (P) Teaching mark (assessed by HMI; given to teachers of sample children only).

37. (P) Size of class including sample child.

38. (P) Sample child in streamed class.

39. (P) Sample child's sex (later combined into regression group number).

40. (P) Sample child's age (in months).

41. (P) Sample child's height (in centimetres).

42. (P) Number of half-days sample child absent 1 Sep 1963 - 31 March 1964 (i.e. two terms).

43. (P) Reasons for sample child's absence satisfactory to teacher.

44, 45, 46. (P)

Sample child's first test score (criterion variable).

Top juniors Watts-Vernon closed test.

Bottom juniors NFER Sentence Reading Test I (AF Watts).

Top infants NFER NS45 Reading Test (EJ Standish).

Sample child's second test score (criterion variable).

Top juniors no second test.

Bottom juniors NS45 Reading.

Top infants NFER Picture Test I (JE Stuart).

49. (D, P) Marked improvement or deterioration in achievement of sample child over previous three years (top juniors only).

50. (D, P) Linguistic ability markedly different from sample child's normal achievement.

51. (D, P) Mathematical ability markedly different.

52. (D, P) Artistic ability markedly different.

53. (D, P) Skill in physical movement markedly different.

54. (D, P) Sample child's attitude to school (assessed on 3-point scale).

55. (D, P) Sample child's cooperation with other children.

The next four variables were assessed by HMI on a 5-point scale, with national distribution over the five intervals retained as 5 per cent, 20 per cent, 50 per cent, 20 per cent and 5 per cent.

56. All-round quality of school.

57. Head's leadership (taking into account particular needs of school).

58. Average teaching competence of staff.

59. School's adoption of modern educational trends (permissive discipline; provision for individual rates of progress; opportunities for creative work; readiness to reconsider content of curriculum; awareness of unity of knowledge).

The next six variables were assessed by HMI on a three-interval scale.

60. Quality of books provided.

61. Backwash of selection procedures on curriculum.

62. LEA public relations, as shown by dealings with parents.

63. Continuity home to school.

64. Continuity from infant to junior school.

65. Continuity within JM & I school.

66. Sex of head teacher.

Table 3 Percentages of the Criterion variation accounted for by the three classes of variable in the long list. See paragraphs 13 and 14.

Table 4.1 Top junior boys: between schools

Table 4.2 Top junior girls: between schools

Table 4.3 Lower junior boys: between schools

Table 4.4 Lower junior girls: between schools

Table 4.5 Infant boys: between schools

Table 4.6 Infant girls: between schools

Summary of Tables 4.1 - 4.6 (between schools)

Table 5.1 Top junior boys: within schools

Table 5.2 Top junior girls: within schools

Table 5.3 Lower junior boys: within schools

Table 5.4 Lower junior girls: within schools

Table 5.5 Infant boys: within schools

Table 5.6 Infant girls: within schools

Summary of Tables 5.1 - 5.6 (pupils within schools)