Appendix 5 – Standard errors
The figures presented in this report are produced from surveying a sample of holdings rather than a census of all the holdings in Scotland. Therefore the figures are estimates of the total pesticide use for Scotland and should not be interpreted as exact. To give an idea of the precision of estimates, the report includes relative standard errors ( RSE) ( Table 47). Standard errors are produced using the raising factors. An overall variance is calculated by summing the variance estimates for individual strata (region and size group) multiplied by the square of their raising factors. These variance estimates include a finite population correction. The overall standard error is calculated from the overall variance by taking its square root. This method of standard estimation was implemented as it is both relatively straightforward and has advantages over ratio estimator methods when within-strata sample sizes are small.
Standard errors are expressed as percentage relative standard errors ( Table 47) for both total pesticide use by area treated and for weight applied. Larger relative standard errors mean that the estimates are less precise. A relative standard error of 0 per cent would be achieved by a census. A relative standard error of 100 per cent indicates that the error in the survey is of the same order as the measurement. Relative standard errors may be reduced with larger sample sizes. However, larger relative standard errors can also result from greater variability in pesticides among holdings.
The RSE for estimates of total pesticide use on vegetable crops was seven per cent for area and eight per cent for quantity ( Table 47). For constituent crop groups, the RSE varied from one to 18 per cent for area and one to 14 per cent for weight, varying with sample size and uniformity of pesticide regime encountered. For cauliflower, leeks, lettuce, other vegetables and rhubarb, a standard error could not be calculated due to too few active ingredients being recorded; therefore pesticide estimates for these crops should be treated with caution.
Table 47 Relative standard errors
Relative standard errors ( RSE) for the area treated (ha) with pesticide and for weight of active substance (kg) applied
|Crops||Area SE (%)||Weight SE (%)|
|Broad beans (1)||7||4|
|Brussels sprouts (1)||18||11|
|Other vegetables (2)||NC||NC|
|Turnips & swedes (1)||14||11|
|All vegetable crops||7||8|
(1) For these crops standard errors could not be calculated for all strata due to insufficient data in the sample, as these strata have not been used in the aggregate totals for the region and the overall RSE values should be treated with caution
(2) Standard errors could not be calculated ( NC) for cauliflower, leeks, lettuce, other vegetables and rhubarb because there were too few active ingredients recorded. Therefore estimates for these crops should be treated with caution