1. Sampling in i-Tree Concepts, techniques and applications

2. Introduction Sampling is so pervasive in i-Tree that we have factored it out for a separate discussion Overview Concepts Techniques Applications

3. Concepts I Random sample Data collection in which every member of the population has an equal chance of being selected Population = the set of people or entities to which findings are to be generalized. The population must be defined explicitly before a sample is taken Can sometimes break population into subgroups (stratification) for better numbers Mind tricks easily, so need rigorous method

4. Source: http://www.negrdc.org/counties/madison/comprehensive- plans/newcomp/maps/8_01ExistLandUseMadisonCo.jpg

5. Concepts II Variance = (SD) 2 Measure of how spread out the distribution is, i.e., how much individual samples vary The less the individual measurements vary from the mean (average), the more reliable the mean In an urban forest, different traits to investigate (variables) may have different variances Species distribution (high?) vs. population size (low) Hurricane debris (high?) vs. ice storm debris (low)

6. Source: Dave Nowak and Jeff Walton, personal communication (DRG data)

7. Concepts III Sample size Will need to be larger the weaker the relationships to be detected the higher the significance level being sought the smaller the population of the smallest subgroup the greater the variance of the variables Can be smaller as these factors change, especially as variance goes down

8. Source: Dave Nowak, personal communication

9. Standard error (SEM) The Standard Error (Standard Error of the Mean) calculates how accurately a sample mean estimates the population mean. Formula: SEM = SD/  N, where SD = “standard deviation” of the sample, and N = sample size. Note that as SD goes down or N goes up, SEM gets smaller—i.e., estimate becomes better. Commonly represented by “±” after a number. Concepts IV

11. Source: blogaloutre http://www.ontabec.com/fatigue.jpg

12. Techniques I Get random numbers Tables Telephone book (final digits!) Electronic randomizers Online Desktop PDA

13. Techniques II Select plots Use map techniques Grid overlay for maps/photos Simple edge rulers also work Pick randomly from list Street, with replacement Block number Create random coordinates Spreadsheet GIS

14. Techniques II Easy way to get random list of street segments Bring TIGER/Line files as shape file from ESRI into a GIS Details in Appendix B of the Manual

15. Techniques III Reserve Create more plots than needed Something like 10% Take replacements from list in order when plot must be thrown out Non-existent Unfindable Inaccessible No bias!

16. Application I Inventory types Complete Inventory Costly, time-consuming Partial Inventory Complete inventory of some forest segment Sample Inventory Randomly-selected trees inventoried for large- scale interpretation  Cost-efficient  Good for planning  Not suitable for day-to-day field management

17. Application I Sample inventory benefits Increase public safety Facilitate short- and long-term planning Improve public relations Justify budgets Estimate tree benefits Large gain for small investment i-Tree promotes the value of sampling

18. Applications II Manual sampling techniques valid, but tedious for larger areas i-Tree v. 1.0 will include applications to automate the process for two types of plots: Linear (street) plots/segments STRATUM/MCTI, SDAP Spatial (park, any area) plots UFORE

19. Applications II Linear plot selector STRATUM/MCTI SDAP Final testing Requirements ArcMap 8.3 or 9.0 Polygon file delimiting study area boundary Road shape file (TIGER/Line data)

21. Applications II Spatial plot selector UFORE Final testing Requirements ArcMap 8.3 or 9.0 Polygon file delimiting study area boundary Raster-based file of strata (e.g., land uses) within study area Digital aerial photos (optional)

23. Final sampling thoughts Sampling is our friend Both tool and product in i-Tree Understanding of validity of what i-Tree offers will depend critically on understanding the process and capability of sampling