1. Appropriate Sampling Ann Abbott Rocky Mountain Research Station
Moscow Forestry Sciences Laboratory

2. Outline What is Appropriate Sampling How do we do it Questions to Ask
Sampling Designs
Sample Size
Northern Region Protocol

3. What is appropriate sampling?
Meets the objectives of the research question
Representative of the population
Feasible
Cost effective

4. Appropriate Sampling is the RESULT
Of answering a series of questions
The answers to the appropriate questions lead naturally to the appropriate Sampling Design and Data Analysis/Interpretation

5. Questions to Ask Objectives of the Research Population for inferences
Sampling Units
Translation of the objectives
Preliminary Information
Choice of Sampling Design

6. Questions to Ask Determination of Sample Size Auxiliary Variables
Randomization
Recording Results
Analysis

7. Stating the Objectives
Have the objectives of the investigation been clearly and explicitly stated, along with the reasons for undertaking it?
Have the objectives been translated into precise questions that sample determinations can be expected to answer?

8. Defining the Population
Has the population about which inferences to be made been carefully defined?
What constraints are to be placed on the population?
Are the units to be measured or counted representative of the population?
If not, what changes must be made to ensure representativeness?

9. Defining the Population
Is there a logical framework for the choice of sample units from the defined population?
If not, what steps can be taken to impose a logical sampling frame?

10. Sampling Units
A successful sampling scheme involves the selection of an appropriate sampling unit
Quadrat
Leaves of a plant
Individual organism
Belt transect
Point

11. Sampling Units Are the sampling units naturally defined?
If not, how will they be defined?
Is the number of sampling units finite?
If it is finite, is the total number of units in the population large enough to ignore finite sampling considerations?
Is the definition of the sampling units appropriate to the objectives

12. Choice of Sampling Unit
Must be the unit upon which you wish to make inferences and estimates
Defined to be “nonoverlapping collections of elements from the population that cover the entire population”
Sampled without replacement

13. Choice of Sampling Unit
Point versus Area
Point samples allow inferences based on the number of observations in the sample
Inferences are made on means or percentages from the sample observations
Area samples are generally measured with densities or percent of the area covered
Inferences are made by extrapolating the sample density to the entire area

14. Choice of Sampling Unit: Point vs Area
Point samples are quicker, can potentially give a more cost effective coverage of the area
Area samples can yield more detailed information but may be more time consuming
Area sampling assumes that counts are made without error

15. Translating the Objectives
What exactly is to be estimated or tested?
Are the required estimates proportions, totals, means, totals or means over sub-populations, or something else?
Have blank data sheets been constructed?
What is the smallest subset of data from which estimates are to be made?
What precision is required of the estimates for the various subsets?

16. Preliminary Information
Is information about the population available that may be helpful in designing the sampling scheme?
Are estimates of the likely variability available?
Is a pilot study feasible or desirable?
Are there any known factors that help stratify the population?

17. Variability
The variation that is inherent in soils data must be accounted for during the design phase of a soil sampling plan, including
Sampling design
Data collection procedures
Analytical procedures
Data Analysis

18. “One of the key characteristics of the soil system is its extreme variability.” (Mason 1992)
Researchers have long been cautioned about failing to consider the variability in soil sampling when dealing with any study of the soils system (e.g. Cline 1944).

19. Accounting for Variability
Ensuring that the sample adequately covers the entire population
Reporting variability estimates along with central tendency estimates
Reporting interval estimates

20. Use an interactive approach to balance the data quality needs and resources with designs that will either control variation, stratify to reduce variation, or reduce the influence of variation on the decision process

21. Precision, Bias and Accuracy
Precision is a measure of the reproducibility of measurements of a particular soil condition or constituent
The statistical techniques seen in soil sampling are designed to measure precision and not accuracy
Bias is a systematic error that contributes to the difference between the mean of a large number of test results and an accepted reference value.

22. Precision, Bias and Accuracy
Accuracy is the correctness of the measurement and cannot be directly measured: it is the sum of precision and bias
Red dots are precise but biased
Blue dots are unbiased but imprecise
Yellow dots are biased and imprecise
Green dots are unbiased, precise
and therefore accurate

23. Sampling Designs Simple Random Sampling Stratified Random Sampling
Systematic Random Sampling
Cluster Sampling
Other
Combinations

24. Sampling Designs
Can the population as defined be broken into naturally occurring groups, where the grouping variable affects the measured variable(s)?
If it cannot, Simple Random Sampling or Systematic Sampling can be effective
If it can, Stratified Random Sampling or Cluster Sampling

25. Simple Random vs Systematic
Simple Random Sampling: If there a “list” (sampling frame) of all sampling units in the population
Randomly selects from units on the list
Systematic Random Sampling: If there is no sampling frame available but there is an estimate of the total number of sampling units
Randomly selects starting point

26. Simple Random Sampling
Used when there is inadequate information for developing a conceptual model for a site or for stratifying a site
Any sample in which the probabilities of selection are known
Sampling units are chosen by using some method using chance to determine selection

27. Simple random sampling is the basis for all probability sampling techniques and is the point of reference from which modifications to increase sampling efficiency may be made
Alone, simple random sampling may not give the desired precision

28. Simple Random Sampling
Advantages
Prior information about population is not necessary
Easy to perform, easy to analyze
Disadvantages
May not give desired precision
Need a sampling frame

29. Computation Simple Random Sample-continuous variable Mean Variance
Confidence Interval
Sample Size

30. Computation Simple Random Sample-Binomial variable Proportion Variance
Confidence Interval
Sample Size

31. Systematic Random Sampling
Attempt to provide better coverage of the study area or population than that provided by a simple random sample or a stratified random sample
Is a simple random sample based on spatial distribution over the site
Does not require a complete list of sampling units
Can give better coverage than a simple random sample

32. Systematic Random Sampling
Requires some estimate of the total number of sampling units in the population
Required sample size must be calculated
Determine sampling interval between units
Randomly select starting point
Transect sampling is a version of Systematic Random Sampling

33. Systematic Random Sampling
Collects samples in a regular pattern over the area in the investigation
Grid
Line Transect
Orientation of grid or transect starting point should be randomly selected

34. Systematic Random Sampling
Considerations
Sample size and population size estimates
Some knowledge of the population to avoid sampling along periodicities

35. Stratified vs Cluster Sampling
Used when the population can be broken into naturally occurring groups or segments
Stratified Random Sampling: when there is more variability among groups than within groups
Cluster Sampling: when there is more variability within groups than among

36. Stratified Random Sampling
Prior knowledge of the sampling area and information obtained from background data may be used to reduce the number of observations necessary to attain specified precision
Goal is to increase precision and control sources of variability in the data

37. Stratified Random Sampling
Variability between strata must be larger than variability with strata for any benefit to be seen
Sampling within each stratum is done with a Simple Random Sample

38. Stratified Random Sampling
Advantages
Gives estimates for subgroups
Can be more precise than Simple Random Sampling
Can be more convenient to implement
Disadvantages
Requires prior information about the population
More complicated computation

39. Computation Stratified Random Sample-continuous variable Mean Variance
Confidence Interval

40. Stratified Random Sample
Sample Size Calculation
Requires information about the relationship between the individuals among strata
Can be calculated by weighting strata
Can allocate sampling based on minimizing the variance for a fixed cost
Other ways to allocate sampling among strata (optimal, Neyman)

41. Post Stratification
Can be used when stratification is appropriate for some key variable, but cannot be done until after the sample is selected
Often appropriate when a simple random sample is not properly balanced according to major groupings

42. Post Stratification
Mean
Variance

43. Cluster Sampling
Used when there is more variability within groups than among
Groups are randomly sampled
Units within groups are sampled
Can sample every element within the group
Can take a second random sample within the group

44. Questions to Ask in Choosing a Sampling Design
If there is no information on population groupings, will simple random or systematic random sampling better meet the objectives?
Is Simple Random Sampling likely to be effective?
If not, have the reasons for not using simple random sampling been clearly stated?

45. Questions to Ask in Choosing a Sampling Design
If Systematic Random Sampling is chosen, what interval will separate units?
Is there a likelihood that the interval will coincide with periodicity in the data?
If so, what steps will be taken to avoid the resulting bias in the estimates?

46. Questions to Ask in Choosing a Sampling Design
If there is a grouping in the population, will stratification improve the precision of the estimates?
Has the efficiency of the stratification been calculated?
What is the basis of the stratification?
How will the sampling units be allocated?

47. Questions to Ask in Choosing a Sampling Design
If there is a grouping in the population, is there an advantage to cluster sampling?
Has the efficiency been calculated?

48. Sample Size
Calculated based on variability (standard deviation) within the population and desired precision of the estimate (confidence level)
Simple Random Sample and
Systematic Random Sample
Stratified Random Sample (complicated) but still needs variance

49. Sample Size Specific sampling design considerations
Systematic: is the sample size required to uniformly cover the population consistent with the expected precision?
Stratified: has the efficiency of the stratification been tested in reducing the sample size or in obtaining the largest number of observations from the part of the population of greatest interest?

50. Sample Size Sample design considerations, continued
Multistage: has the efficiency of various combinations of sample units at different stages been tested?
Cluster: has the efficiency of various size clusters been tested?

51. Sample Size Cost considerations
Must the number of observations be modified to account for variation in cost in different parts of the sampling procedure?
If so, can the design be improved for better cost efficiency?

52. Randomization
Have the sampling units been selected by an explicit randomization procedure?
Has the randomization procedure been documented?
Were any constraints correctly applied?

53. Sample Design Example Northern Region Soil Monitoring Protocol
Goal: Develop an easy, cost effective and statistically defensible monitoring protocol for disturbance
Stating the objectives: Characterize the activity area in terms of management related disturbance

54. Northern Region Protocol
Defining the population: All possible ‘points’ within the Activity Area
Sampling units defined as ‘points’
Infinite number of possible ‘points’ in the population so finite sample correction factors do not need to be used

55. Northern Region Protocol
Sample Design
Stratification may be desirable but variability information is unavailable
Simple Random Sampling may not give the appropriate coverage
Systematic Random Sampling (Transect) was chosen to give the best coverage of the area

56. Northern Region Protocol Translating the objectives What exactly will be measured or tested:
Forest floor depth
Forest floor missing
Topsoil displacement
Mixed topsoil/subsoil
Erosion
Rutting (3 depths)
Burning (light, moderate, severe)
Compaction (3 depths)
Platy/massive structure (3 depths)
5 forest floor variables

57. Northern Region Protocol
Translating the objectives: Blank data tables

58. Northern Region Protocol
Translating the objectives: what exactly is to be estimated or tested?
What proportion of points in the sample have the characteristic of the indicator variable?
What is the variability associated with the proportion?

59. Northern Region Protocol
Translating the objectives: What is the required precision of the estimates?
Confidence intervals within ± 5% of the estimate
Confidence levels are determined by the line officer, allow choice from 70% to 95%

60. Northern Region Protocol
What preliminary information is available about the activity area?
Approximate size and shape
Harvest history
Variability estimates generally unknown
A pilot would be best
Stratification potential exists

61. Northern Region Protocol
Problem:
Variability estimates are unavailable
Pilot studies are not feasible due to time and cost constraint
Statistically valid sample sizes are required

62. Sequential Sampling
An alternative approach to sampling in which the sample size is not fixed in advance
Observations are collected individually or in small batches
After each observation or batch, the data are examined to determine whether or not a decision may be made from the accumulated data

63. Sequential Sampling
Combines data collection and data analysis into a single process or sampling plan
Can considerably reduce the sample size requirements and data processing overheads

64. Sequential Sampling
Best used in situations where classification of a population is useful and where the emphasis is on decision making
In the simplest and most frequently used form, it is used to make binary classifications but can be extended into other applications

65. Northern Region Protocol
Use a combination of sequential and systematic random sampling to obtain variability information for sample size calculation at the same sampling visit as the full data collection trip
First 30 observations are used to calculate initial sample size, then sample size is continually updated as sampling continues

66. Northern Region Protocol
Indicator variables are binomial (0,1)
Binomial variables converge to a normal distribution when n ≥ 30
Attractive for sampling since the maximum variability can be computed

67. Northern Region Protocol
When sampling is complete for the activity area, the estimates and confidence intervals are computed
Protocol allows field crews to sample an activity area with a statistically valid sample size in one visit