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 50). 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 error 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 50) 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 arable crops was three per cent for area and four per cent for quantity (Table 50). For constituent crop groups, the RSE varied from three to 20 per cent for area and four to 36 per cent for weight, varying with sample size and uniformity of pesticide regime encountered. For triticale and dry harvest peas, a standard error could not be calculated due to too few active substances being recorded; therefore pesticide estimates for these crops should be treated with caution.