Arboriculture & Urban Forestry 41(6): November 2015 DISCUSSION Street tree sampling is a good option, when 100% inventories are not feasible, to provide data to aid in street tree management. With the exception of Parkersburg, West Virginia, which had a substan- tially smaller number of block segments, trees per block segment, and total tree population, a sample size of about 3% of the block segments (with un- known block length), or between 89 to 185 block segments in a city produced a relative standard error of 10% (Table 1). Adding block length informa- tion to a sample increased precision and reduced the sample size needed to gain desired precision, making sampling more efficient (Figure 3). Increas- ing the number of block segments sampled also reduced the variability of the estimate (Figure 2). Urban foresters could begin by sampling 3% of the block segments to try and attain an estimate of total number of trees with a relative standard error of 10%. If the data are not adequate (e.g., 10% RSE is not attained), then an additional block seg- ments could be sampling to help reach the desired precision level. However, the decreasing reduc- tion in RSE with additional plots (Figure 4) illus- trates that at some point the cost of an increased sample outweighs the gain in precision by taking this additional sample (e.g., Stanovick et al. 2002). Desired sampling precision and costs need to be considered in determining the sampling size. To increase precision to a 5% relative standard error for most cities (excluding Parkersburg, West Virginia), an average of 11%, or 462 block seg- ments, were sampled (Table 2). To increase preci- sion to a one-percent relative standard error, an average of about 75%, or 3,240 block segments, were sampled. At this point of precision, it would likely be best to complete a whole street tree inven- tory with locations and attain 100% precision. Full inventories can provide more essential data for street tree management than street tree samples. Buffalo, 0.6 2.4 9.1 71.3 New York % 20% 10% 5% 1% No. 37 145 539 4,248 Lansing, Michigan % 0.6 2.2 8.0 68.6 Livonia, 116 433 3,691 0.7 2.7 9.7 73.0 No. 30 Michigan % 351 In cities with small tree populations (e.g., less than 2,000 trees) or for sub-classes within a larger tree population (e.g., individual species), a larger proportion of block segments will be needed to attain a desired relative standard error. However, smaller street tree populations may have a lower absolute standard error than a larger street tree population with a lower RSE. For example, in Lan- sing, Michigan, a 10% RSE produces a standard error of 5,790 trees (Table 1). In Parkersburg, West Virginia, a 10% RSE equates to a standard error of only 173 trees. Thus, Parkersburg could a have a RSE of 100% (1,734 trees) and still produce an absolute standard error less than Lansing, Michi- gan. An urban forester must decide what level of precision is desired by the sample and whether the precision is relative to the total (RSE) or an abso- lute number in terms of Simple random sampling or trees (standard error). ratio estimates are only one of many possible ways of sampling street tree populations. Although relatively simple, there are other means of sampling that could pro- duce lower relative standard errors. For example, sampling with probability proportional to size, where larger blocks have a higher chance of being selected (compared with equal probabilities of selection as in simple random sampling) could produce lower standard errors, but require addi- tional work in selecting samples (Cochran 1977). Other (Cochran 1977) enhancements to existing methods could also maximize reduc- tions in standard error for a fixed cost. These techniques consider that getting to a particular randomly selected block is the biggest cost and sampling neighboring blocks can be done at little additional cost. While these approaches can add complexity to the sample design, they can be more cost-effective and produce lower standard errors than simple random sampling. The advantage of simple random sampling lies in its simplicity, Table 2. Comparison of sample sizes needed to attain various relative standard errors (RSE) for analyzed U.S. cities. RSE No. 23 89 327 2,449 Parkersburg, West Virginia % 10.5 31.8 65.1 98.8 No. 92 279 570 858 Syracuse, New York % 1.2 4.5 16.1 82.7 Note: % - Percent of total block segments sampled to attain RSE; No. - Number of block segments sampled to attain RSE. No. 26 98 343 1,764 0.9 3.6 13.0 78.9 Wilmington, Delaware % No. 48 185 668 4,043 ©2015 International Society of Arboriculture
November 2015
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