Arboriculture & Urban Forestry 41(6): November 2015 tion, but requires the extra step of pre-sampling of the zones to determine how to distribute the sample and requires that a certain number of trees be sampled. This methodology was used to esti- mate street tree population structure and functions in Davis, California, U.S., and Lisbon, Portugal (Maco and McPherson 2003; Soares et al. 2011). Various studies have investigated simple ran- dom samples of street tree populations. Sun and Bassuk (1991) recommended a minimum sample size of between 5% and 50% of the population based on computer simulations of hypothetical tree populations. Percent of the population need- ing to be sampled varied with total population size and species diversity. Alvarez et al. (2005) compared simple random and stratified ran- dom sampling (i.e., random sampling within predefined zones) of street trees in a neighbor- hood of Piracicaba, Brazil. Random sampling of 20 blocks produced a relative standard error (ratio of standard error to total) of 47%. Strati- fication of the 20 blocks into four zones revealed relative standard errors for the zones that varied between 32% and 70%. The advantage of sim- ple random sampling lies in its simplicity, but more complex designs can reduce standard errors of the estimate (e.g., Cochran 1977). The purpose of this paper is to demonstrate a simple random sampling technique of trees within block segments (i.e., road segments between inter- sections) for assessing street tree populations. In particular, this paper will use street tree data from several cities to: a) determine the sample size (percent of block segments) needed to attain a 10% relative standard error for the street tree population total and b) illustrate how informa- tion on length of block segment can improve the precision of the population estimates. This simple method does not require pre-sampling or pre- existing data and will allow for easy and accurate estimates of the street tree population that can be stratified into various zones of the city if desired. All that is required for this sampling is a list- ing of the individual block segments that make up the study area. If the length of these block segments are also known, then ratio estimates can be used. The ease of this procedure should increase efficiency in collecting street tree popu- lation data and improve street tree management. METHODS The approach used in this paper is a simple ran- dom sampling of block segments to determine street tree population characteristics. Complete street tree inventory data (100% of the street tree population) from six U.S. cities were obtained from the Davey Resource Group: Buffalo, New York (2010 population = 261,310 people, 105.15 km2 , 2,485 people/km2 (114,297 people; 87.80 km2 (31,492 people; 29 km2 people; 27.97 km2 ); Lansing, Michigan , 1,301 people/km2 Livonia, Michigan (96,942 people; 92.46 km2 1,048 people/km2 acuse, New York (145,170 people; 65 km2 people/km2 ); , ); Parkersburg, West Virginia , 1,086 people/km2 ); Syr- , 2,233 ); and Wilmington, Delaware (70,851 , 2,533 people/km2 ). These cit- ies were selected based on available complete street tree inventory data with geographic coor- dinates so that tree locations could be located on street maps in a geographic information system (GIS) to aid in sample selection and analysis. Number and length of block segments in each city were determined using TIGER/Line files (U.S. Census Bureau 2013) within a GIS. Block seg- ments were randomly selected, and all trees on the segment (both sides of the road) were assigned to that block segment. Each block segment was then considered a sampling unit or plot. To determine street tree population characteristics and total, plot calculations were done with and without know- ing the block segment length. The following text illustrates the calculations. For these examples, suppose the goal of the sampling was to deter- mine the total number of street trees within a city. (i=1, 2, ..., N). The total number of trees in the popula- tion is: [1] where Y is the population parameter of interest (the total number of trees). Now suppose a simple random sample of n block segments is selected without replacement (i.e., the plot is not put back in the sample pool aſter being ©2015 International Society of Arboriculture Simple Random Sampling (Block Segment Lengths Unknown) In a city there are a total of N block segments with the number of trees labeled yi for the i-th block segment 347
November 2015
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