Forest Mensuration II

1. Forest Mensuration II Lecture 6 Double Sampling Cluster Sampling Sampling for Discrete Variables Avery and Burkhart, Chapter 3

2. Double Sampling (two-phase sampling) • Double sampling with regression and ratio estimator • Double sampling for stratification

3. Double Sampling with Regression and Ratio Estimators • Remember: regression and ratio estimators require known • Take a large sample in which x alone is measured – allow a good estimate of • Establish a regression or ratio relationship between paired x and y

4. Double Sampling with Regression • Estimate of the population mean of y

5. Complete enumeration of x vs. a large sample of it Both gain precision from using regression estimators Double sampling with regression vs. regression estimation

6. where Double Sampling With Ratio

7. Double Sampling for Stratification • Recall: stratified random sampling requires that the strata size (Nh) be known in advance of sampling • Double sampling for stratification applies when • Nh is not known, but can be estimated by sampling

8. Estimate overall population mean Double Sampling for Stratification • Estimate Nh using a large sample How is this different from that in stratified random sampling?

9. Cluster Sampling • A practical problem • A forester needs to estimate average seedling heights or root collar of a nursery. Seedlings are grown on benches, blocks, or clusters of styrofoam How are you going to sample?

10. A cluster sample is a sample in which each sampling unit is a collection, or cluster, of elements Reasons A list of elements is not available, but a list of clusters is Even when a list of elements is available, it is more economical to randomly select clusters than individual elements Cluster Sampling

11. Cluster Sampling • We need to know: • How many clusters in the population (N) • How many clusters selected (n), often by simple random sampling • How many elements in a cluster (m) • Measured value for sampled elements (yij), e.g., seedling height • Estimation of population mean

12. Two-stage Sampling • What if there are too many elements in a cluster? For examples, • You want to know seedling dry weight of the previous example

13. Sampling for Discrete Variables • For qualitative attributes such as dead or alive, deciduous or evergreen – binomial distribution • Species composition – multinomial distribution

14. Estimate standard error of the proportion • Estimate confidence interval Sampling for Discrete Variables • Estimate proportion

15. Sampling for Discrete Variables • Use Cluster Sampling for Attributes – recall how we calculate mean, variance, and standard error of the mean for simple random sampling

16. Relative Efficiencies of Sampling Plans • Measure by cost or time with the same level of accuracy (not precision, why?) • When samples are unbiased, standard error of mean can serve as a measure of accuracy • Most efficient plan is: • min { (standard error)2×cost (time) } Remember: The objective of sampling design is to obtain a specified amount of information about a population parameter at minimum cost