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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

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
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
sampling design
Sampling Design
  • The method of selecting non-overlapping sample units to be included in a sample
sampling frame
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
Elementary Sampling Methods
  • Selective
  • Simple Random Sampling
  • Systematic Sampling
selective 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

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)
srs procedure
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
srs estimators
SRS Estimators

Mean

Variance

Coefficient of variation

srs estimators1
SRS Estimators
  • Standard error of the mean
    • With replacement or infinite population
    • without replacement from a finite population
  • Confidence limit
sampling intensity
Sampling Intensity
  • How many samples to take? Depends on:
    • The variability of the population
    • Desired confidence interval
    • Acceptable level of error
sampling intensity1
Sampling Intensity
  • With replacement or infinite population
  • Without replacement from a finite population
calculating sample size

Standard deviation (120 m3/ha)

95% confidence (t=2)

Acceptable level of error

±40 m3/ha

Calculating sample size
relationship between sample size and allowable error for different cvs

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

can we use srs all the time problems
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
systematic sampling
Systematic Sampling

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

systematic sampling1
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
arguments of systematic sampling
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
summary for systematic sampling
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
summary
Summary
  • Selective sampling
  • SRS
  • Systematic sampling