Forest Mensuration II Lecture 3 Elementary Sampling Methods

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

Sampling vs. 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. Why sampling? • Measuring all units (trees, birds, etc. ) is sometimes impractical, if not impossible – Some measurements are destructive • Sampling saves money and time

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

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

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

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

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 Lecture 3 Forestry 3218 • SRS is the fundamental method for other sampling procedures • Other procedures are simply modifications to achieve better precision or greater economy

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 Lecture 3 Forestry 3218

SRS Estimators Mean Variance Coefficient of variation Lecture 3 Forestry 3218

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

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

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

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

Relationship between sample size and allowable error for different CVs Allowable error (%) 40 30 20 CV=100 10 CV=20 0 Lecture 3 Forestry 3218 5 205 405 n 605 805

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 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 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 Lecture 3 Forestry 3218 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

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 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 Lecture 3 Forestry 3218

Summary • Selective sampling • SRS • Systematic sampling Lecture 3 Forestry 3218