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Forest Mensuration II

Forest Mensuration II. Lecture 3 Elementary Sampling Methods: Selective, Simple Random, and Systematic. Avery and Burkhart, Chapter 3 Shiver and Borders, Chapter 2. Why sampling? Measuring all units (trees, birds, etc.) is sometimes impractical, if not impossible

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Forest Mensuration II

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

  2. 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. Sampling vs. Complete Enumeration

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

  4. 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. Elementary Sampling Methods • Selective • Simple Random Sampling • Systematic Sampling

  6. 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. 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 Simple Random Sampling (SRS)

  8. 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. SRS Estimators Mean Variance Coefficient of variation

  10. SRS Estimators • Standard error of the mean • With replacement or infinite population • without replacement from a finite population • Confidence limit

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

  12. Sampling Intensity • With replacement or infinite population • Without replacement from a finite population

  13. Standard deviation (120 m3/ha) 95% confidence (t=2) Acceptable level of error ±40 m3/ha Calculating sample size

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

  15. CV=100 CV=20 405 605 805 5 205 n Relationship between sample size and allowable error for different CVs 40 30 Allowable error (%) 20 10 0

  16. 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. Systematic Sampling The initial sampling unit is randomly selected. All other sample units are spaced at uniform intervals throughout the area sampled

  18. 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 Systematic Sampling

  19. 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. 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. Summary • Selective sampling • SRS • Systematic sampling

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