The sampling scheme

The purpose of the sample was to establish a baseline for the indices related to opportunity to learn. This baseline would give an indication of the level and range of provision for “ordinary needs children” in New Zealand schools, with which to compare the provision for learners with vision impairment. For this reason the sample needed to be big enough to include a variety of schools. Factor analysis would be important in the construction of an instrument of this type, so this also guided the choice of sample size. As a general rule (see Hair #563 page 99) it is best to have at least ten subjects per variable, and a sample of over 1000 is thought to be “excellent”. As there were about 100 variables, a sample of over 1000 would be sufficient for sensible use of factor analysis and similar multivariate techniques.

There was a limited time frame before the end of the school year in which to arrange and administer the questionnaire in schools. The experience of the pilot study indicated the need to administer the questionnaire in person in order to get the best response rate and quality. (This was later reinforced in the few cases where it was necessary to leave questionnaires to be completed under the supervision of the classroom teacher, which resulted in a poorer quality of response.)

Twenty schools were sampled. With twenty schools it was possible to cover urban and rural, co- educational and single-sex, and the full range of deciles (See Appendix 1 for a discussion on deciles). As the pilot study had showed up differences in scores between the year groups, one class was sampled from each of the three years at each school in the baseline study. This led to an estimated sample size of 20 schools × 3 classes × 25 pupils = 1500 pupils (actual size of 1300).

A purposive convenience sample was taken. The time and funding available allowed for sampling from twenty schools in three regions. Three regions were chosen: Canterbury, Auckland, and Waikato. The candidate schools were chosen in order to make the sample approximately representative of the population with regard to ethnicity, socio-economic background as indicated by the decile rating, school size and gender. If a principal did not wish the school to take part, as happened in five instances out of twenty-five, another school as similar as possible was chosen. The important aspects of the schools within the sample are summarised in Table 6.

Table 6. Characteristics of the twenty schools in the baseline sample. School ID No 2002 Decile School roll Rural/City Percentage Pakeha on the school roll Percentage Maori on the school roll Percentage other (Asian or Pasifika) on the school roll

A 4 400 Rural 88% 11% 1% B(G) 6 400 City 90% 7% 3% C(B) 7 1300 City 88% 8% 4% D 9 300 Rural 91% 7% 2% E 8 800 City 66% 4% 30% F 5 500 City 83% 12% 5% G 9 1000 City 84% 6% 10% H 6 1100 City 66% 10% 24% I 1 600 City 4% 17% 79% J 2 1200 City 13% 42% 45% K 1 400 City 1% 18% 81% L(G) 10 2000 City 66% 5% 29% M(B) 10 2000 City 59% 3% 38% N 10 >2000 City 71% 3% 26% O 5 650 City 54% 22% 24% P 2 450 Rural 37% 40% 23% Q 1 350 Rural 30% 70% 0% R 1 300 Rural 37% 57% 6% S 9 1400 City 82% 6% 12% T 3 1100 City 64% 26% 10%

Note. “B” indicates a boys’ only and “G” a girls’ only school. The school rolls have been rounded to maintain anonymity.

The participating schools were from Auckland (7 schools), Waikato (4 schools) and Canterbury (9 schools). There were sixteen co-educational schools and four single sex schools, of which two were high decile (10) and two were medium decile (6 and 7). There were five rural and fifteen city schools. The schools were chosen as much as possible to obtain a representative sample overall with regard to ethnicity. Thus some schools had high Maori populations and others had low. On average the proportions were 60:20:20 (Pakeha:Maori:Other), whereas the population at that age group has the ratio 62:25:13. Only state funded secondary schools were included. The range of deciles of the schools was as follows (2002 deciles):

Table 7. The number of schools in the baseline sample from each decile.

Decile 1 2 3 4 5 6 7 8 9 10 Schools 4 2 1 1 2 2 1 1 3 3

More schools were sampled from the extremes of the range (deciles 1,2,9 and 10) as it was thought that this is where most variation between deciles would appear. See Appendix 1: Explanation of the Decile system for further explanation.

School size may well affect the opportunities that students have. Thus schools of various sizes were included. It was not practical to go to very small schools as there would not be sufficient pupils at each year level to get a worth-while sample. The intention was to get a sample that roughly represented the population of New Zealand to compare with the learners with vision impairment.

School roll size

0 1 2 3 4 5 6 7 8 <400 401-800 801-1200 1201-1600 1601-2000 >2000 School size N u m b e r of s c hools 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 P ropor ti on

Schools in sample proportion in population

Figure 5. School roll sizes in the population and the ESA sample.

Figure 5 illustrates the school roll sizes in the sample, compared with the population. The solid line in Figure 5 shows the proportion of the population of secondary school students in years 9 to 15 by size of school. About 8% of such students are in schools of fewer than 400 pupils, while 34% of high school students are in schools with between 801 and 1200 pupils. The green bars show the number of schools in the sample within each size category. There is not a perfect fit, and schools under 400 are over-represented, while there are too few schools in the 801 to 1200 range. This is partly due to the

limited number of schools from which to pick, with a large number of criteria to satisfy. Each size range was represented, so it was possible to explore some effects of school size.

In each school I administered the survey to a Year 9, a Year 10 and a Year 11 class, (students typically aged 13 to 16 years – the first three years of secondary school). The classes were selected from those available in a core subject (English, Mathematics, Science, Social Studies) at the time of the visit. Principals were encouraged not to choose “the better classes”, but where there was a choice, to choose according to the alphabetical placement of the teacher’s name.

My experience as a secondary school teacher was useful. In a few schools I was left to administer the questionnaire for a few minutes without the teacher present. I really enjoyed meeting the students and talking to them. They were interested in the purpose of the work. The teachers generally were supportive and interested. I also found it instructive to note how different schools “felt”. There were some schools where the staff and pupils were obviously happy to be there. In another school the year eleven class was quite obstructive, which was not helped by a drug-dog visit in the middle of administering the questionnaire. I later received a written apology for the students’ behaviour.

The survey was well received by the students, possibly as an escape from “work”, and they seemed pleased to be asked their opinion. The questionnaire took between 15 and 20 minutes to complete, and was well within the reading level of all but a few of the respondents. My presence at nearly all of the classes encouraged a high quality of response. The response rate was 100%. There were 1388 returned questionnaires. There were 88 exclusions: those from students outside the year range (4), overseas fee- paying students (51), students with special educational needs (11), students who had changed schools recently (20), and incomplete responses (2). The resulting sample had 1300 observations, about 600 from girls and 700 from boys.

Frequency data for the individual school and for the whole reference group was sent to each participating school in acknowledgement of their contribution. The summary data for the whole sample is given in Appendix