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8 APPENDIX A: TECHNICAL NOTES
8.1 Percentages
The percentages shown in tables have all been rounded to the nearest whole number. Consequently, the percentages in one column will not necessarily add to exactly 100.
Figures of 0.5% or less are shown as 0. A dash (-) indicates no respondents at all. Percentages in brackets (5%) are based on unweighted base sizes of less than 30.
All figures are column percentages, except where otherwise indicated.
8.2 Bases
Each table shows the weighted and unweighted bases corresponding to each percentage. The data were weighted to compensate for differential non-response across subgroups. The weighted bases can be used to (approximately) combine two different columns in a table. The unweighted bases can be used to calculate the precision of estimates. These uses of the bases are described below.
8.3 Estimating the precision of estimates
Each percentage quoted in this report has an associated margin of error, due to the fact that it is based on only a sample, rather than all school leavers. This margin can be estimated for each proportion, p (where p is the percentage divided by 100) by:
where n is the unweighted sample size (base). This margin corresponds to 95% confidence. In other words, there is a 95% chance that the true value across all leavers in the subgroup (as opposed to just those in the sample) falls within this margin.
For example, in Table 2-9, the proportion of respondents with a job working in hotels/restaurants is estimated as 4% and the unweighted base is 1,159. The margin of error around this estimate can be calculated as:
which comes to 0.01. In other words, there is a 95% chance that the true value is within the range 0.04 ± 0.01, i.e. between 0.03 and 0.05 or between 3% and 5%.
In general, the larger the base, the more accurate the estimate is likely to be.
[If a very accurate estimate of the margin of error is required for a particular purpose, then expert help should be sought. The approximate formula shown above may need to be amended to allow for the sampling fraction and the effect of the weighting.]
8.4 Combining columns of a table
One may sometimes want to estimate a proportion for two (or more) columns of a table combined. The combined proportion can be estimated as:
Where P 1 is the proportion for the first column, and n 1 the weighted base for that column, and P 2 and n 2 are the corresponding values from the second column.
For example, you might want to combine the 'professional and inter-mediate' parental class columns in Table 2-4, in order to estimate the proportion of young people with parents in these social classes whose main activity was part-time work. Then:
which comes to 0.07, or 7%.
Note that this method of combining columns will only give approximate estimates for the combined category, because the percentages presented have been rounded to the nearest whole number. If more precision is required, it would be necessary to access the data set, and combine the categories before rounding the estimate.
8.5 School type
For each member of the sample, the type of secondary school that they attended (state, grant-maintained, independent) is known. However, this variable has not been used for analysis in this report, partly because it is of little intrinsic interest (it is highly correlated with other factors), and partly because the sample sizes in the non-state school categories are very small.
8.6 Social Class
The Social Class variables used in this report are based on occupation. Parental class was coded using the SOC-2000 code frame - and is shown using a classification that has been developed from the original Registrar-General's social class classification. The scale - developed and maintained by the Office for National Statistics - classifies people into one of eight groups, and is widely used in censuses, surveys, and other research. It is derived by grouping occupational categories (based on the Standard Occupational Coding), and making further discriminations by reference to the job-holders status in employment (self-employed, supervisor, etc.). For ease of analysis we have combined some of the groups and derived a variable with the following five groups:
I Higher managerial & professional
II Lower professional & managerial/ higher technical & supervisory
IIIN Intermediate occupations & self employed
IIIM Lower supervisory & technical
IV Routine & semi-routine occupations
8.7 Sample size
The survey sample was selected in 1998-1999 by identifying all pupils who were in the fourth year of secondary schooling in Scotland (S4) during the relevant academic year (1997-98) and whose birthday fell on one of six dates in the month. This was done in two stages. At the first stage, the Scottish Qualifications Agency ( SQA) provided a list of all S4 pupils on their data base with the relevant birth-dates. This should include all those who were entered for at least one examination or who received at least one qualification administered by SQA (Standard Grades or National Certificate Modules) in fourth year. At the second stage, this list was then sorted by school and every secondary school was sent a list of its pupils identified by the SQA. Schools were asked to add to the list any other S4 pupils with the relevant birth-dates. It was pointed out to them that this would include any who had not been entered for any SQA examination. Schools with no pupils on the initial list were also sent a letter and form asking for details of any relevant pupils.
For this, the final follow-up survey at age 23-24, questionnaires were only mailed to those sample members who had returned their questionnaire at the time of the previous contact, two years ago at age 21-22. Full details of the procedures used for sampling, mailing and up-dating addresses, appear in the survey technical report.
8.8 Survey non-response
Obviously, not all members of the selected sample returned a completed questionnaire. The nature of any non-response bias was analysed, and corrective weighting introduced. Weighted figures are not likely to be seriously biased. Non-response, and the corrective weighting, are described in the survey technical report.
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