210 Alvarez et al.: Sampling Methods for Estimating Tree Density other hand, evaluating the density does not mean that the quality of the urban forest is analyzed (i.e., there could be an excess of nonappropriate species and/or low diversity). Therefore, the Shannon diversity index (SDI) was selected to describe species diversity in relation to the total number of trees (Pielou 1975). Simple Random Sampling The number of trees per kilometer of sidewalk was estimated according to Cochran (1977), who defines population ratio as R X Y = where XT Figure 1. Map of Santa Cecília district, Piracicaba, São Paulo, Brazil. The district of Santa Cecília contains parcels of land that were occupied gradually. The urban district is relatively new. In 1970s, urbanization began with intensity and continues. This fact has contributed to the diversity of urban characteristics with regard to human population, socioeconomic level, and presence of vegetation. This heterogeneity must be analyzed in full. The block was the sampling unit chosen, and the data records were expressed as number of trees per lineal kilometer of sidewalk. The variable definition was the ratio of the total number of existing trees on the sidewalks to the total of kilometers of sidewalk. AutoCAD software mea- sured these values to obtain a district map. The total number of blocks in Santa Cecília district is 57, excluding public free spaces. An initial 10 random blocks were sampled, with the later addition of 11 more random blocks. One block was dropped from the total of 21 because it had no trees and would thereby exert undue influence on the analysis. For the stratified random sampling, the same 20 blocks were divided into four strata. The sampling strata were divided to achieve homogeneity, based on date of initial occupancy, physical proximity to other blocks in the stratifi- cation group, and purchasing power of residents. The typical sampling unit was a four-sided block, but other clearly defined shapes were acceptable, especially in stratum 3, which had cul-de-sacs. The measured variables were number of trees per lineal kilometer of sidewalk and total number of trees in the district. The estimate of the total number of trees in the district (57 blocks) is important, even though it does not express a difference in the tree density. The number of trees per kilometer of sidewalk gives a clearer measure of the presence of the trees per human-occupied space. On the ©2005 International Society of Arboriculture formula is s T , T is the number of existing trees in the blocks, and YT is the number of lineal kilometers of sidewalk in the blocks. The sampling ratio is represented by r n = = = where xi and yi ∑ ∑ i 1 n i 1 represents number of trees in the selected block, represents the total number of kilometers of the selected block. The interval of 95% of trust for each one of the population ratios is given by [r – 2s(r), r + 2s(r)]. The variation coefficient is represented by x , s where x is the sample average, and s2 2 = ny n xr x yiii y ⎟. ⎜ 1− f 2 () ∑ − 2 ∑ −1 ⎛ ⎝ i=1 f n = N , where N is the total number of blocks in the studied area, and n is the number of blocks selected for the sample. The median value of the total number of kilometers variable is represented by n y = =i 1 ∑yi n , and the sampling error, expressed as a percentage, is represented by Sampling error (%) = ⋅⋅ tsx 100 x n n 22 2 1 + r ∑ i= The sampling fraction is represented by i ⎞ ⎠ is the variance, whose 2 x y i , i
September 2005
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