1. Statistical Concepts Breda Munoz RTI International

2. Outline Probability sampling or convenience sampling. How to select the sample? Sample size Inflating your sample size to account for possible non-access to sites, missing data, etc Data analysis methods

3. Basic Definitions Judgmental or convenience sampling: selection of sampling units based on professional judgment alone, without any type of randomization. Probability-based sampling designs apply sampling theory and involve random selection of sampling units. An essential feature of a probability-based sample is that each member of the population from which the sample was selected has a known probability of selection.

4. Probability vs Convenience Sampling Probability SamplingConvenience Sampling Ability to calculate uncertainty associated with estimates Can reproduce results within uncertainty limits Ability to make statistical inferences Can account for sampling and non sampling errors Can be less expensive Can be very efficient Easy to implement Random sites may be difficult to locate An optimal design depends on an accurate conceptual model More expensive and takes more time Depends upon expert knowledge Cannot reliably evaluate precision of estimates Depends on personal judgment to interpret data relative to study objectives Pros Cons

5. Convenient/Expert Sampling Some environmental data can not be collected using probability samples because of expense, time constraints, or other impediments (expensive instruments) When to use it? –Relatively small-scale features or conditions are under investigation. –An extremely small number of samples will be selected for analysis –Evaluate new methods/instruments –Knowledge of the feature of interest

6. Examples If you want to determine the success of a wetland mitigation program. –Will you use a probability sample or a convenience sample? –What is the problem with a convenience or random sample? If you want to study the hydrological connectivity of isolated wetlands –Will you use a probability sample or a convenience sample? –What is the problem with a convenience or random sample?

7. Convenience Sampling and Bias Suppose that you want to investigate the occurrence rate of rare plant species in wetlands. You have funding to examine 10 sites. Wetlands range from pristine to disturbed. How do you select the 10 sites? A. 10 sites at random B. 10 pristine sites C. 5 pristine and 5 disturbed D. More pristine than disturbed (e.g. 8 and 2)

8. How to select the sample? Identify your population –Define the region of interest: watershed, county, etc –Define your population: type of wetlands Identify population frame: –Map/GIS model showing location of polygons Identify your study objectives –Want to compare sub-regions –Provide state, county, region estimates Identify clustering/strata –Counties, watersheds, HUCs, etc.

9. Issues in Environmental Sampling Population elements close to one another tend to be more similar than widely separated elements Good sampling designs tend to spread out the sample points more or less regularly Patterned response (gradients, patches, periodic responses) Pattern in population occurrence (density ) Unreliable frame material

10. NC and SC isolated wetlands Population Frame Example of GIS frame

11. Example Listing Frame Mitigation Programs: –listings of mitigation projects can be used as population frame –Mitigation projects are classified by institution, size, years, etc

12. Basic Concepts Strata: Population is divided in mutually exclusive groups such that every element of the population belongs to one and only one stratum –Samples must be selected from each of the stratum Clusters: Groupings of sampling units, e.g. based on geography proximity –Clusters are selected at random, and we can sub- sample within clusters

13. Strata or Clusters?

14. Strata or clusters? Columbus

15. Selection of HUCs at random

16. Simple Random Sampling Easy to implement and understand Sample size calculations are straight forward No restrictions in randomization

17. Systematic Systematic sampling, also called grid sampling or regular sampling, consists of collecting samples at locations or over time in a specified pattern

18. Random or Systematic? Presence of gradients or systematic ordering in the frame Sampling units Confounding variable

19. GRTS Sampling Basic randomization (Stevens and Olsen; 2004): 0 n 14 23 4312 1 2 3 4 2 1 3 4

20. Frame Imperfections Sampling units that do not belong to the population (over coverage) Missing units: visit the field and found not only one wetland but three in neighborhood of sampling site Documentation: Adjust all these problems at the analysis stage

21. Sample Size Considerations –type of variable (continuous or discrete) –sampling design –Budget –Time constrains –Other constraints You don’t need a big sample!!