1. Lecture 4 Forestry 3218 Avery and Burkhart, Chapter 3 Shiver and Borders, Chapter 5 Forest Mensuration II Lecture 4 Stratified Random Sampling

2. Lecture 4 Forestry 3218 What is Stratified Random Sampling? A population is subdivided into subpopulations of known sizes A simple random sample (or systematic sampling) of at least two units is drawn from each subpopulation

3. Lecture 4 Forestry 3218 Why Stratified Random Sampling? To obtain a more precise estimate of the population mean when –Sample size is the same –The variations within subpopulations are smaller than the total population variance To obtain an estimate of the subpopulations

4. Lecture 4 Forestry 3218 How to stratify? Assign each sampling unit to one and only one stratum Defining strata can be easy or difficult; normally done prior to sampling, but can be reassigned/re-classified

5. Lecture 4 Forestry 3218 Stratification examples in forestry practices? Stand type Stand age Site class – site quality Climate region Ecosite (ecosystem type)

6. Lecture 4 Forestry 3218 Design Example

7. Lecture 4 Forestry 3218 Definition L = number of strata (h = 1, 2, L) N h = total number of sampling units in strata h N = total number of units in entire population y h,i = an observed value of the variable y on sampling unit i in stratum h

8. Lecture 4 Forestry 3218 How to calculate means The sample mean for stratum h (exact same as in SRS) The sample mean for overall population (weighted average)

9. Lecture 4 Forestry 3218 Example: Stratumacresmean dbh 11012.2 21231.6 3720.1 Estimate the overall population mean

10. Lecture 4 Forestry 3218 1. Compute variance within each strata Estimate the overall population standard error of the mean

11. Lecture 4 Forestry 3218 (with replacement or infinite population) (without replacement) OR Estimate the confidence intervals: Estimate the overall population standard error of the mean 2. Compute population standard error of the mean

12. Lecture 4 Forestry 3218 Additional Reading for Lecture 5 Chen, H.Y.H., and K. Klinka. 2003. Aboveground production of mixed-species western hemlock and redcedar stands in British Columbia. Forest Ecology and Management 184: 46-55. You can download from: flash.lakeheau.ca/~hchen