 |  |
| |
Bullock (1975) (page numbers in brackets) Preliminary pages (i-xxxvi)
Part 1 Attitudes and Standards
Part 2 Language in the Early Years
Part 3 Reading
Part 4 Language in the Middle and Secondary Years
Part 5 Organisation
Part 6 Reading and Language Difficulties
Part 7 Resources
Part 8 Teacher Education and Training
Part 9 The Survey
Part 10 Sumary of Conclusions and Recommendations
Appendix A (561-576)
|
The Bullock Report (1975) A language for life Report of the Committee of Enquiry appointed by the Secretary of State for Education and Science under the Chairmanship of Sir Alan Bullock FBA London: Her Majesty's Stationery Office 1975
Chapter 25 continued [page 502 (cont.)] Analysing the Data 25.33 The survey had two main aspects: provision for English teaching in the schools and practice in the classes. Our aim was to make simple statements about the proportions of schools and classes having specified facilities or working on specific activities. In the main, therefore, the analysis of both primary and secondary data has been a simple matter of tabulating frequencies and calculating percentages, with occasional cross-tabulations. In the usual way, mean values derived from the samples have been taken to provide estimates of mean values within the population, and in all instances we have provided information upon the range of responses. This is presented either in full tables within the text and the commentaries or in the reproductions of the questionnaires in paragraph 25.32. In paragraph 25.36 we supply the means to determine the limits of confidence which are appropriate in interpreting any proportion or percentage derived from the data; paragraph 25.37 assists in deciding whether differences in proportion are significant. Certain other statistical tests of significance have been used, and these are described in paragraph 25.40. 25.34 In the secondary section the data on the actual English teaching which takes place could not be analysed in the same manner. The combined effect of having many subdivisions and the possibility of zero or 'nil' returns led us to present the data in two ways. Firstly, we have calculated the average time devoted to each specific activity by all teachers and rendered this as a percentage of the time allocated by all teachers to the main head from which it came (see table 97 in paragraph 25.31). For example, the time devoted to debates, lecturettes and mock interviews by all teachers of 12 year olds was 7.8 per cent of the total time given to Oral English activities. Secondly, however, it was necessary to acknowledge that NOT ALL teachers would have covered every specific activity. Therefore we have also provided the proportion of teachers who did record the specific activity (12.1 per cent in Table 96) during the week in question and have used this to calculate an [page 503] average teaching time. Thus 25 minutes was the average time spent on "debates, lecturettes and mock interviews" by those teachers who included them in their work during the week of recording. 25.35 Two points had to be considered before we decided to present the data on activities in this fashion. The first was the apparently wide time intervals of 30 minutes provided. The second was the pattern of responses evoked. The data incorporated in the reproduction of the questionnaires in paragraph 25.32 show that the distribution of response was highly skewed, even if the use of the 'nil return' category is ignored. We had to ask whether the width of the time intervals had forced the pattern of responses and rendered suspect our method of calculating average times, i.e. using the mid-point of each interval. However, width of time intervals - 30 minutes - does not appear to have operated in this way if we consider that the overall average English time calculated from these returns matches closely the values obtained from an independent question. (See paragraph 25.13.) It thus appears that 30 minutes was a reasonable choice in the context of a week's activities. The Precision of Estimates Proportions and Percentages 25.36 Since we wished to be able to state what proportion of schools had certain resources and what proportion of classes were taught in various ways, the results have been quoted in percentage terms, e.g. Table 30 in paragraph 25.18 shows that 59.5 per cent of 6 year olds' classes used Alphabetic Analysis in their approach to reading. If 59. 5 per cent is regarded as an estimate of the percentage of all such classes in our sample using this method, it must be understood that a degree of error attends this and all similar stated percentages. The magnitude of the error is dependent upon the size of the sample and upon how extreme the percentage is, and Table 98 sets out the sizes of error that are possible. The above example can be used here to show how the magnitude of possible error is determined. The total number of classes upon which the 59.5 per cent is based is 1,417. The nearest sample size quoted in Table 98 is 1,500 and the nearest percentage quoted is 60 per cent. The table shows the 95 per cent confidence limits for this particular combination of sample size and percentage as being 60 per cent ±2.5 per cent. This may be interpreted as meaning that were a census of all schools to be undertaken then there are 19 chances in 20 that the population percentage would lie between 57.5 per cent and 62.5 per cent. In our example, 59.5 per cent of classes of 6 year olds using Alphabetic Analysis was an estimate, based on 1,417 classes, of the proportion in the whole population which used this method. This is sufficiently near the 60 per cent of the 1,500 sample shown in the table to enable the statement to be made that there are 19 chances in 20 that the population percentage would lie between 57.0 per cent and 62.0 per cent were a census of all schools to be undertaken and the proportion were measured of 6 year olds' classes using Alphabetic Analysis in their approach to reading. [page 504] Differences of Proportions 25.37 The analysis of the data has, in places, been in terms which permit the comparison between differently defined groups. For example, Table 31 shows that 68.9 per cent of deliberately vertically grouped classes with 6 year olds use Alphabetic Analysis compared with 55.6 per cent of classes that are not vertically grouped. The question arises as to whether these two percentages indicate that Alphabetic Analysis is used more in deliberately vertically grouped classes than in classes that are not vertically grouped or whether these two different percentages have resulted merely by chance. The first step in assessing this is to calculate the weighted average of the two samples, i.e. __________ n1+n2 which in this example becomes ____________________ 322 + 781 = 59.5 per cent, i.e. the overall proportion of 6 year olds' classes using Alphabetic Analysis in these two groups. The next step is to consult Table 99 and locate under the column headed 40/60 per cent the pair of sample sizes nearest to 322 and 781. In this case sample sizes of 1,000 and 400 are shown as having a significant difference (at the 95 per cent probability level) at 5.7 per cent. The example shown above has a difference of 13.3 per cent (68.9-55.6). Since this greatly exceeds the 5.7 per cent, we may safely conclude that a difference of this magnitude would not have arisen by chance and therefore that deliberately vertically grouped classes are more likely to use Alphabetic Analysis than are classes which are not vertically grouped. The Basis of the Tables 25.38 Table 98 has been based on the formula for the standard deviation in simple sampling of attributes i.e.  The ± percentages in Table 98 have been calculated as follows:-  and these percentages have then been added and subtracted from the example percentages at the top of each column. 25.39 Table 99 has been prepared by applying the sample numbers and proportions to the formulae for testing the significance of the differences between proportions. (1) The percentages shown in the table represent the differences between two sample proportions which could arise from random sampling in 1 in 20 occasions on the assumption that the two samples had been drawn from [page 505] the same population. It follows that if the differences between two proportions exceed the level shown in the table it may be stated that the difference is significant at the 95 per cent level of significance. This level is commonly taken to mean that larger differences would have been obtained from different populations and therefore that the proportions quoted are different and not merely sampling fluctuations about the same joint proportion. Conversely, smaller differences may well have arisen from sampling fluctuations and thus do not necessarily imply that the two proportions have come from different populations. An example of the application of the formulae is given below for samples of size 1,000 and 200, where 35 per cent of the 1,000 sample (1) and 25 per cent of the 200 sample (2) exhibited a particular characteristic.
A difference between two proportions exceeding (1.96 x 3.55 per cent) 7.0 per cent would be significant at the 95 per cent level of confidence. Any increase in the difference above 7.0 per cent would increase this level of confidence. [page 506] RANGES OF PERCENTAGES WITHIN WHICH THERE IS A 95 PER CENT CHANCE THAT THE POPULATION PERCENTAGE WILL LIE PERCENTAGE DIFFERENCES BETWEEN TWO SAMPLES FROM THE SAME POPULATION THAT COULD BE GIVEN BY 5 PER CENT OF PAIRS OF SAMPLES [page 507] Other Testing 25.40 Elsewhere in the report where figures are provided it has been appropriate to apply one of two other statistical tests of significance to ascertain that apparent differences and relationships are unlikely to be due to chance. Where we have compared mean values - for example, the analysis of different times spent on English (Table 91, paragraph 25.31, Secondary Commentary) - the difference between the means has been tested using the standard t-test. Where 2-way relationships have needed to be tested - for example, the use of teachers' centres by teachers from different sizes of school (Table 27, in paragraph 25.17ii) - the chi-square test has been employed. (2) The Validity of the Sample 25.41 In order to be assured that the results of this survey may be taken to be representative of all schools in England, we have compared certain characteristics of the schools in the sample with known characteristics of all schools in England. By so doing, and confirming that the characteristics that were checked are unbiased, we may not unreasonably infer that the results of the survey will represent equivalent results for England as a whole, should a census be undertaken. The comparisons with all schools in England in January 1973 were as follows: (a) Type of school.Table 100 A. A COMPARISON OF THE DISTRIBUTION OF THE TYPES OF SCHOOL IN THE SAMPLE AND IN THE TOTAL IN ENGLAND January 1973
[page 508] January 1973
The questionnaires for the primary schools were to cover the two age groups, 6 years and 9 years. In order to avoid overburdening the sample schools we selected twice as many Infants with Junior and First and Middle Schools: half were required to complete questionnaires for 6 year olds and the other half for 9 year olds, i.e. 964 different schools of this type took part in the survey and are included in the class analysis but only 480 were included in the sample of schools. Table 101 B. A COMPARISON OF THE REGIONAL DISTRIBUTION OF SCHOOLS IN THE SAMPLE AND IN THE TOTAL IN ENGLAND
[page 509] Table 102 C. A COMPARISON OF THE AVERAGE SIZE OF SCHOOL IN THE SAMPLE AND AVERAGE SIZE OF SCHOOL IN ENGLAND
Table 103 D. A COMPARISON OF THE SIZES OF SCHOOL IN THE SAMPLE AND IN THE TOTAL IN ENGLAND
Table 104 E. A COMPARISON OF THE PUPIL-TEACHER RATIO OF SCHOOLS IN THE SAMPLE AND IN THE TOTAL IN ENGLAND
[page 510] In all the above respects the sample of schools was an unbiased sample. It was also possible to check on the proportions of boys arid girls selected for the secondary schools questionnaire. The survey response gave a higher proportion of boys than would have been expected from a random sample of 1,991 secondary school pupils aged 12 and 14. 54 per cent of the sample pupils were boys, whereas the national proportion at this age is only 51 per cent. The probability of selecting 54 per cent for boys as random sample from the population is less than 1 per cent. The causes of this bias towards boys are not known, but it may result from (a) the tendency of schools to place boys above girls on registers, (b) the higher rates of absenteeism for girls in the 12-14 year old age group, and (c) the possibility of there being a higher proportion of boys than girls with a forename beginning with an A, B or C. Despite the tendency for the class data to have favoured boys rather than girls, the effect on the results will be minimal. Reweighting the results to compensate for this small bias by applying 51/54 to the 'boys' data and 49/46 to the 'girls' data would not materially alter any of the findings. REFERENCES 1. D. G. Lewis: Statistical Methods in Education: U.L.P.: 1967, and M. J. Moroney: Facts from Figures: Penguin: 1951.
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
