Equipo de carburización de rampas moderadas (MTCVD).

4.4.2.1 Sample size

The school sample for HBSC was drawn under the requirements of the 2002 HBSC Study protocol. In HBSC, samples are drawn from within schools, often using whole classes as the sampling unit. In such circumstances, pupils have a shared experience of the school environment; often come from a range of very similar socio-economic backgrounds and social groups/circles and are exposed to similar educational strategies and local teaching. For these reasons, the behaviour o f respondents (and consequently their responses) cannot be assumed to be independent, and so we have a clustered sample. In other words, these commonalities mean that the responses of pupils in each class and/or school are more likely to be similar to one another, than to the general population (Roberts et al, 2002b :29). In these circumstances, the sample size must be increased in order to achieve the same precision as a random sample. In order to achieve this, the HBSC protocol recommends a minimum of 1536 pupils in each target age group (Roberts et al, 2002b :30).

4.4.2.2 Sample stratification

The Welsh schools selected for HBSC formed a stratified sample, with schools being sampled from within 23 strata2. This stratification of the sample ensured a geographically representative sample of schools from across Wales, and was allowed within the guidelines of the HBSC 2001/2 international research

2

Data on Welsh schools were provided for HPD by the Statistical Directorate (SD) o f the Welsh Assembly Government. This internal database was provided on a Microsoft® Excel spreadsheet, with the data split into two sheets labelled “[State] Secondary Schools” and “Independent Schools”. In order to achieve the school socio-economic stratification o f the sample within each UA, the most recent data on the total number o f pupils entitled to free school meals in each school was also obtained from SD and added to the database (discussed later in this se c tio n ).

protocol (Roberts et al, 2002b :29). In order to achieve this representative geographical dispersal, the first 22 strata consisted o f the 22 Unitary Authorities (UA’s) of Wales (Figure 4.1) with all state secondary schools in Wales being allocated to the strata representing the UA to which they belonged.

Figure 4.1 Map o f the 22 Unitary Authorities o f Wales

1 Abertawe - Sw ansea 2 Blaenau Gwent - Blaenau Gwent 3 Bro Morgannwg - the Vale of Glamorgan 4 Caerdydd - Cardiff

5 CaerfRli - Caerphilly 6 Casnewydd - Newport

7 Castell-nedd Port Talbot - Neath Port Talbot 8 Conwy - Conwy

9 Gwynedd - Gwynedd 10 Merthyr Tudful - Merthyr Tydfil 11 Pen-y-bont ar Ogwr - Bridgend 12 Pow ys-Pow ys

13 Rhondda, Cynon, Taf- Rhondda, Cynon, Taff 14 Sir Benfro - Pembrokeshire

15 Sir Ceredigion - Ceredigion 16 Sir Ddinbych - Denbighshire 17 Sir Fynwy - Monmouthshire 18 Sir Gaerfyrddin - Carmarthenshire 19 Sir y Fflint - Flintshire

20 Sir Ynys Mon - Isle of Anglesey ■ 21 Tor-faen - Torfaen

22 Wrecsam - Wrexham

© Crown Copyright/database right 2006.

An Ordnance Survey/(Datacentre) supplied service (Wales and Unitary Authority maps supplied as Boundary data provided by Ordnance Survey via Digimap. Boundary data merged and legend added by author using ArcGIS software.

It was then necessary to add a 23rd strata consisting o f all the independent schools in Wales. The reason for treating these as a separate stratum was in order to maintain the national ratio of state (n=227) to independent (n=38) schools within the HBSC sample. Due to the relatively few number of independent schools which are spread across Wales, maintaining this ratio necessitated the sampling of independent schools separately. This was

complicated however, by the fact that some independent schools were removed from this stratum before sampling occurred. This was necessary because some of the independent schools in Wales have only a very small number o f 11-16 year old pupils on their rolls (in some cases as few as 5), which would be far too few pupils to create a valid sample. Anecdotal evidence from browsing these schools’ websites, suggests that most commonly schools with very few pupils in the 11-16 age range tended to be schools with registration based on a highly defined core educational objective or ethos, and which selected pupils based on these principles. Mainly these were denominational religious schools, where specific theologies underpinned the curriculum, and which only accepted pupils from families who shared these beliefs, and wanted to opt into a curriculum promoting these central tenets. However, such high selectivity was also seen in schools providing for specific special educationa 1 needs. In all cases, the small number o f pupils on the roll appeared to be partly due to the specific curricula of these schools which fewer parents may be choosing to opt in to, and which restrict the number of pupils qualifying for enrolment. In addition, the small numbers of pupils aged 11+ in these schools was compounded by the fact that not only do these schools have small numbers of pupils in total (in some cases less than 30), but they are also often spread over a large age range (e.g. 3-18 years old).

Due to the problematic nature of these small numbers of pupils in producing a valid sample size, any school from the independent strata with less than 50 pupils aged 11-16 on the roll was removed before selection. This resulted in the removal of 17 schools from this stratum. There were no state secondary schools that had less than 50 pupils registered.

Another problem to consider when examining roll size in independent schools is the fact that some employ a different age structure within their organisation than that found in most state secondary schools. For example, one of the independent schools in the sample took pupils from ages 3 to 18 years old, split into three schools, a lower school (3-7 year olds); a middle school (7-13 years old) and an upper school (13-18 years old). The middle and upper school are located on the same site, treating pupils aged 6-13 years old as one cohort.

This contrasts with state secondary schools which tend to take pupils aged from 11 to either 16 or 18 years old as one cohort. If not recognised, such disparities could lead to a selected independent school appearing to have enough pupils to sample, but actually falling short of a number of 11-16 year olds which would be practically useful to sample. However, for sampling, data for all independent schools, like for state schools was presented as the number of 11-16 year olds on the role.

As mentioned above, the national ratio of state to independent schools in Wales is 227:38, or 0.167. The original sample drawn for recruitment to HBSC was 62:6 (0.097). After the initial recruitment o f schools to HBSC (including replacement schools for refusals), this ratio was 55:6 (0.109). However, after two schools dropped out during the survey, the final HBSC sample had a ratio o f 54:5 (0.093) state to independent schools. While this is lower than the national ratio, it can be explained by the removal of the 17 schools from the independent school strata prior to sampling as discussed. Allowing for this, the population of Welsh schools actually sampled (with 17 removed) had a ratio of 227:21 state to independent schools, or 0.093. This is just slightly lower than the ratio of state to independent schools as originally selected for recruitment to HBSC, and exactly the same as the final sample of schools participating in HBSC. Hence, by sampling independent schools from within a separate stratum, the HBSC sample, even after non-participation and drop-out, maintained a ratio of state to independent schools representative of the population of Welsh schools actually sampled from.

Once schools were placed within these geographical strata, they were then subjected to a secondary, socio-economic stratification, in order to achieve a cross section of the different socio-economic catchments of schools within each authority. Free School Meal (FSM) entitlement is widely used as an indicator of the socio-economic status of school catchments. Although problematic as an indicator, die precedent for this is evident in the widespread use o f FSM entitlement in this way across many studies and policy documents (e.g. Sharp & Croxford, 2003; Gorard et al, 2001; National Audit Office, 2003) Consequently, calculating the proportion of pupils entitled to FSMs in

each school, is a practical way of comparing estimates of the socio-economic status of the catchment of each school. In order to achieve a comparison of school socio-economic status within each UA, the most recent data available on the total number of pupils entitled to FSMs in each school was used to calculate the percentage of pupils in each school entitled to FSMs. Within each strata, schools were then listed in ascending order of the proportion of pupils with FSM entitlement in each school. As FSM entitlement is a good indicator of socio-economic status, by listing the schools this way, and selecting schools down through this list using the cumulative roll for each UA (see below), the selection of schools should achieve a sample across the socio-economic spectrum within each UA. Entitlement to FSMs has been used rather than actual take up o f this entitlement among pupils, as it provides a more accurate picture of the socio-economic character of the school. This is because not every pupil who is entitled to FSMs may take them up.

It should be noted that the independent schools are not listed on the basis of FSM, as they do not have this provision. Instead, independent schools are listed in order of size. There is an assumption made that the independent schools are of more similar socio-economic status than the state schools. This is due to the fact that, as fee-paying schools, they tend to attract pupils from families who are both affluent enough to afford these fees, and who share similar preferences, values and beliefs on education choices.

4.4.2.3 School selection

Once each stratum had been organised in this way, it was necessary to select the schools from each stratum to form the HBSC sample. It was decided, on the basis of previous HBSC studies in Wales, that a sample of 70 schools would be both manageable, and provide a sample well above the HBSC recommended minimum of 1536 pupils at each age group (Roberts et al, 2002b:30). This would allow for the possibility of school drop out during HBSC, while still producing a final sample size above 1536 pupils. This sampling of 70 schools from the population of 248 Welsh schools (excluding

the 17 independent schools removed due to small roll size) equates to a sample of 28.2% of schools.

Schools were then selected using Probability Proportional to Size (PPS) sampling. This method produces randomness within the sampling of the 11-16 year old population of Wales, giving each pupil in each UA the same probability o f being selected as any other pupil. This is in contrast to sampling by school, in which case pupils from smaller schools are over-represented, with individual pupils standing a greater chance of selection than those in larger schools. By allowing all pupils within a strata an equal chance of selection, and selecting every nth pupil rather than every nth school, all members of the pupil population stand an equal chance o f selection, which they would not do if the sample was selected by school.

In order to make this selection, having listed the schools in each UA in ascending order of FSM entitlement, the number of pupils on the register was used to construct a cumulative roll next to the list of schools. This effectively allocated a number to each pupil within the strata. Using these numbers, pupils were then selected at random dependent on the size of the UA.

To make this selection, it was necessary to calculate a sampling interval for each strata which would achieve a sample of 28.2% of schools. To calculate this, the following equation was used:

Sampling Interval - Total roll in strata / (Number o f schools in strata/3.543)

W here 3.543 is the sampling fraction needed to obtain the sample o f 28.2%, i.e. the reciprocal o f 0.282.

Using this formula, the necessary interval between selected pupils which should achieve the desired sample size was calculated.

To ensure randomness, the number of the first pupil to be selected was decided using the random number generator in Microsoft® Excel, programmed to generate an integer between 1 and the value of the sampling interval (SI).

Using the cumulative roll, the number pupil to which this corresponded was then selected, and their school was selected for the sample. The SI was then used to select every rih pupil whose school would be selected for the study. This was repeated until the SI took the pupil number above the number of pupils on the cumulative roll. This was repeated for each of the 23 strata. The schools selected in this way constituted the initial HBSC sample.

4.4.2.4 Selecting replacement schools

Before schools were approached for participation, a replacement strategy was designed for those schools that declined to participate. For each school, a replacement school was designated. This school, as far as possible, was selected to be of similar size and socio-economic status to the original. In order to achieve this, the following rules for the selection o f replacement schools were designed:

1. As far as possible, the replacement school size should be within ±33% of the size of the original school.

2. In order to select a school as near as possible in socio­ economic status of catchment area, as well as size, to the original school, the following process will be adopted. Starting with the first school on the list in each UA, the next unselected school down the list whose roll falls within ±33% of the size of the first school will be selected as the replacement. If the bottom of the list is reached and no appropriate school found, then the replacement school is selected upwards from the original school in the same manner.

3. If no school in the UA lies within ±33% o f the size of the original school, then the next unselected school down the list will be selected as the replacement. As before, if the

bottom of the list is reached and no unselected school is found, the next school upwards will be selected.

4. Independent schools are not listed by FSM, but by size. Selecting the next school on the list would give you the school of most similar size to the original anyway. As discussed earlier, there is an assumption made that the independent schools in the sample are all of similar socio­ economic status. Consequently, in the independent school stratum, replacement schools will be selected just by choosing the next unselected school down the list. As with the state schools, should the bottom of the list be reached, and no unselected school is available, the next school upwards of the original will be selected as the replacement instead. This should produce a replacement school of similar socio-economic status and size.

Each time one of the initial school selections declined the offer to participate in the research, this procedure was implemented. If the replacement school also declined to take part, then no further replacement school was sought, the number of participating schools being reduced by one. Replacement schools were only selected prior to commencement of data collection. If schools dropped out during data collection, no replacement school was selected.

4.4.2.5 School recruitment and retention

Once the sample had been drawn, members of HPD staff recruited schools within the protocols for HBSC. Schools were provided with a booklet detailing the work of HBSC and invited to participate. The booklet gave information on the history of HBSC, it’s current size, it’s importance as a research tool, and what participation involved. A financial incentive was also offered by HPD to encourage a higher response rate.

Once a response had been obtained from all schools and any replacement schools, those agreeing to take part consisted the final list of HBSC schools for the 2001/2 cycle. Teacher survey questionnaires were also distributed to all of these schools at the same time. Once HBSC data collection was completed, apart from two schools that dropped out during data collection (see below), this was also the list of schools that I approached to ask if they would take part in the smoking policy research. Due to drop out 61 schools began taking part in HBSC Wales, with a further 2 dropping out during data collection giving a total set of complete data from 59 schools. Although this was well below the target sample size, it still provided enough respondents for HBSC. Data collected on smoking behaviour as part o f this study would be matched to policy data from the teacher survey and interviews with staff in these schools. It is this that is the fundamental association of this study with the 2000/2001 HBSC survey in Wales.

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5

Discussion of methods