1. Lecture 3 Forestry 3218 Avery and Burkhart, Chapter 3 Shiver and Borders, Chapter 2 Forest Mensuration II Lecture 3 Elementary Sampling Methods: Selective, Simple Random, and Systematic

2. Lecture 3 Forestry 3218 Sampling vs. Complete Enumeration Why sampling? Measuring all units (trees, birds, etc.) is sometimes impractical, if not impossible –Some measurements are destructive Sampling saves money and time Complete Enumeration Measure every feature of interest; a highly accurate description of the population. Drawbacks: only viable with small populations; only cost-effective with high-valued features.

3. Lecture 3 Forestry 3218 Sampling Design The method of selecting non-overlapping sample units to be included in a sample

4. Lecture 3 Forestry 3218 Sampling Frame The list of all possible sampling units that might be drawn in a sample Developing a reliable frame may be difficult –Jack pine trees in Crown forest (infinite population) –In most field situation, differences between the sampling frame and the population are inconsequential

5. Lecture 3 Forestry 3218 Elementary Sampling Methods Selective Simple Random Sampling Systematic Sampling

6. Lecture 3 Forestry 3218 Selective Sampling The method involved selecting areas that appeared to be reprehensive of the average stand condition to the sampler (cruiser) Was widely used in forestry, is still… Depends on skill of the cruiser, biased No valid variance, and therefore no confidence interval, could be calculated Because sampled areas appeared to be average, their variability would be smaller than the true variability

7. Lecture 3 Forestry 3218 Simple Random Sampling (SRS) Sampling units are chosen completely at random Every possible combination of sampling units has an equal and independent chance of being selected SRS is the fundamental method for other sampling procedures Other procedures are simply modifications to achieve better precision or greater economy

8. Lecture 3 Forestry 3218 SRS Procedure Requires the development of a frame, implying the need of aerial photographs, or maps Select random numbers between one and the total number of sampling units in the population Samples are either chosen with replacement or without replacement, the latter means that once a sampling unit is chosen it may not been chosen again

9. Lecture 3 Forestry 3218 SRS Estimators Mean Variance Coefficient of variation

10. Lecture 3 Forestry 3218 SRS Estimators Standard error of the mean –With replacement or infinite population –without replacement from a finite population Confidence limit

11. Lecture 3 Forestry 3218 Sampling Intensity How many samples to take? Depends on: –The variability of the population –Desired confidence interval –Acceptable level of error

12. Lecture 3 Forestry 3218 Sampling Intensity With replacement or infinite population Without replacement from a finite population

13. Lecture 3 Forestry 3218 Calculating sample size Standard deviation (120 m 3 /ha) 95% confidence (t=2) Acceptable level of error ±40 m 3 /ha

14. Lecture 3 Forestry 3218 Calculating sample size from CV and A Example: Allowable percent error of mean

15. Lecture 3 Forestry 3218 Relationship between sample size and allowable error for different CVs n 5 205 405605805 Allowable error (%) CV=100 CV=20 0 20 10 30 40

16. Lecture 3 Forestry 3218 Can we use SRS all the time? - problems Locating some sample units on the ground may be very time-consuming –Reference point to sample units –Access

17. Lecture 3 Forestry 3218 Systematic Sampling The initial sampling unit is randomly selected. All other sample units are spaced at uniform intervals throughout the area sampled

18. Lecture 3 Forestry 3218 Systematic Sampling Pros: Sampling units are easy to locate Sampling units appear to be “representative” Generally acceptable estimates for the population mean Cons: Impossible to estimate the variance of one sample Accuracy can be poor (i.e., bias) if a periodic or cyclic variation inherent in the population

19. Lecture 3 Forestry 3218 Arguments of systematic sampling Against –SRS statistical techniques can’t logically be applied to a systematic design unless populations are assumed to be randomly distributed For –There is no practical alternative to assuming that populations are distributed in a random order

20. Lecture 3 Forestry 3218 Summary for Systematic Sampling Use systematic sampling to obtain estimates about the mean of populations Numerical statement of precision should be viewed as an approximation Use SRS formulas

21. Lecture 3 Forestry 3218 Summary Selective sampling SRS Systematic sampling