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 31). 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 31) 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 pesticide use among holdings.
The RSE for estimates of total pesticide use on vegetable crops (Table 31) was five per cent for both area and weight, compared with ten per cent for area and seven per cent for weight in 2017. For constituent crop groups, the RSE varied from four to 29 per cent for area and three to 40 per cent for weight, varying with sample size and uniformity of pesticide regime encountered. Standard errors could not be calculated (NC) for cauliflower, leeks, lettuce, other vegetables and rhubarb because there were too few active substances recorded. Therefore, estimates for these crops should be treated with caution. However, the standard errors that could be calculated are lower than the past two vegetable reports. This may be due to increased grower participation leading to an improved sample size. Higher standard errors mean that there is more uncertainty associated with estimates of pesticide use.
|Area SE (%)||Weight SE (%)|
|Turnips & swedes||29||40|
|All vegetable crops||5||5|
(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 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 substances recorded. Therefore, estimates for these crops should be treated with caution