Sampling Design of the Pesticide Survey at Statistics Lithuania

1. Sampling Design of the Pesticide Survey at Statistics Lithuania Danutė Krapavickaitė Senior Statistician Sample design of the pesticide survey

2. Population characteristics • Survey population – farms growing up wheat • Sampling frame – list of the farms that have declared their land under the wheat in 2007 • Population size: N=34 533 Sample design of the pesticide survey

3. Distribution of the farms by the area of land under the wheat is skewed Sample design of the pesticide survey

4. Number of farms by the group Sample design of the pesticide survey

5. Land under the wheat by the farm group Sample design of the pesticide survey

6. Sampling design • sample size n=500, • stratified simple random sample, • stratification variable – land under the wheat in the farm, • „take all“ stratum is defined empirically, • rule is used to define the boundaries of the strata, • Neyman optimal allocation of the sample size, • number of strata is defined empirically minimizing the coefficient of variation of the estimator of the total land under the wheat. Sample design of the pesticide survey

7. rule • Land under the wheat in the farm – variable x. • Values of this variable are divided into K=200 intervals of the equal length, M=kH-1<N • Relative frequency of the elements in the k-th interval, k=1,2,…,K • Total , define “take all” stratum • Define H-1 strata by the points of division such that The elements belonging to the first intervals are appointed to the 1st stratum, and so on ….. Sample design of the pesticide survey

8. Simulation study 1. Determination of the number of strata (z – land under the crop) Sample design of the pesticide survey

9. The boundaries of the strata Sample design of the pesticide survey

10. Land under the wheat by the strata Sample design of the pesticide survey

11. Land under the crop by the strata Sample design of the pesticide survey

12. Results of the simulation study 2 Sample design of the pesticide survey

13. The alternatives • Simple random sampling, n=500 For the land under the wheat =0,201 (0,012 when stratified) For the total land =0,162 (0,036 when stratified) • Geometric stratification (P. Gunning, J.M. Horgan ) by geometric progression of the auxiliary variable. Simulation show that this stratification method is less effective than rule. • Ratio estimator allows us to get gain in precision Sample design of the pesticide survey

14. Conclusion To userule to determine the number of strata and the stratum boundaries, empirical determination of the size for the “take all” stratum, Neyman allocation of the sample size to the strata, ratio estimator of the total with the auxiliary: area under the crop describes the most suitable sampling strategy for the pesticide survey Sample design of the pesticide survey

15. References • P. Gunning, J.M. Horgan. A new algorithm for the construction of stratum boundaries in skewed populations. Survey methodology, 30, 2004, 159-166. • D. Krapavickaitė, A. Plikusas. Tikimybinių imčių teorijos pagrindai. Vilnius: Technika, 2005. • C.-E. Särndal, B. Swensson, J. Wretman. Model Assisted Survey Sampling. New York: Springer-Verlag, 1992. Sample design of the pesticide survey