1. Partial Ranked Set Sampling Design By Abdul Haq Ph.D. Student, Department of Mathematics and Statistics, University of Canterbury, Christchurch, NZ. 1

2. Outline 2 Simple random sampling. Ranked set sampling. Examples. Partial ranked set sampling. Simulation and case study. Main findings.

3. Estimate the mean height of Arabidopsis Thaliana (AT) plants 3

4. AT Population 4

5. Simple Random Sampling (SRS) 5

6. Simple random sampling (Estimation of population mean) 6

7. 7 Ranked set sampling (Estimation of population mean) Actual measurements are expensive. Ranking of sampling units can be done visually and cheaper. It provides more representative sample. Examples: Estimating average height of students in NZ university. Estimating average weight of students in NZ university. Estimating average milk yield from cows in a farm. Bilirubin level in jaundiced neonatal babies.

8. Ranked set sampling procedure 8

9. 9 After ranking

10. 10 Sample values Cycle123 1 2 Now apply the RSS procedure to these 3 sets of 2 cycles.

11. 11 Judgment ranks Cycle123 1 2

12. Some Elementary Results 12

13. Partial Ranked Set Sampling (PRSS) Design 13 PRSS scheme is a mixture of both SRS and RSS designs. It involves less number of units compared with RSS. RSS design becomes a special case of PRSS design.

14. 14 Diagram: Partial ranked set sample with 36 units Judgment ranks Cycle123456 1

15. Judgment ranks Cycle123456 1 Diagram: Partial ranked set sample with 26 units

16. 16 Judgment ranks Cycle123456 1 Diagram: Partial ranked set sample with 16 units

17. Estimation of population mean 17

18. Simulation study: Symmetric populations (perfect ranking) 18

19. 19 Simulation study: Asymmetric populations (perfect ranking)

20. 20 Simulation study: Bivariate Normal Distribution (imperfect ranking)

21. An application to Conifer trees data 21 Relative efficiencies of the estimators of population mean RSSPRSS 4 1.920371.38698 _______ 4 1.912471.38545 _______ 5 2.217371.516411.15711 _______ 5 2.203841.515531.15685 _______ 6 2.523421.612531.26187 _______ 6 2.492671.609681.26067 _______ 7 2.809671.689971.323221.10689 7 2.770111.688981.320211.10399 See Platt et al. (1988).

22. Main Findings 22 PRSS requires less number of units, which helps in saving time and cost. RSS is special case of PRSS design. Mean estimators under PRSS are better than SRS for perfect and imperfect rankings. PRSS can be used as an efficient alternative to SRS design.