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 was calculated by summing the variance estimates for individual strata (region and size groups) 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 29) 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 grassland crops (Table 29) was 11 per cent for both area and weight. The RSE for total pesticide use for fodder crops was eight per cent for area and 12 per cent for weight. Rough grazing estimates have a particularly high RSE (60 per cent for both area and weight) due to the very low pesticide use on this type of grassland. Total estimates of pesticide use for fodder and grassland have lower standard errors than those for their constituent crops as sample sizes are greater.
Table 29: Relative standard errors
Relative standard errors (RSE) for the area treated (ha) with pesticide and for weight of active substance (kg) applied
|Area SE||Weight SE (%)|
|Grass over 5 years old||12||12|
|Grass under 5 years old||13||14|
|Kale and cabbage(1)||11||10|
|Turnips and swedes||23||49|
|Other stock-feeding crops(2)||18||28|
(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) Other stock-feeding crops include arable silage as well as other fodder crops (fodder rape, kale, stubble turnips and fodder crop mixes) all recorded under 'other stock-feeding crops' in the June 2021 Agricultural Census
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