236 urban forestry, but it can also be used when referring to the total survey made using an image, as Dekker (2001) explains about census survey techniques. A census created using image analysis requires accuracy validation in the field; sam- pling can be used as a way of validating image data. When it comes to street trees, the sam- pling may consider blocks and the number of trees per linear kilometer (Alvarez et al. 2005). Alvarez et al. (2005) used random sampling of blocks and number of trees per linear kilo- meter of sidewalk, and detected significance for evaluating street trees. However, the het- erogeneity of a population may lead to sam- pling errors when random sampling is used. In this context, grouping peculiarities is an efficient method to improve sampling accuracy. The population may be divided into subpopu- lations which are homogeneous when consid- ered individually, in a process called stratification (Cochran 2007). Couto (1994) reports that strati- fied sampling can be very useful for urban forestry inventories. The strata may be the neigh- borhood, the street density, or a set of blocks. To obtain consistent results, the strata must have Alvarez et al.: Street Tree Inventory of Campinas, Brazil of measured values. Thus, a precise median value of any stratum estimate can be obtained using a small sample of that stratum. According to Cochran (2007), those estimates can be combined to produce an accurate estimate of the total popu- lation. The formula for this ratio is the following: H Equation 01 Equation 01 [1] Equation 02 Equation 02 [2] x =∑x ∑x nh Equation 01 Equation 03 Equation 03 Equation 01 Equation 04 h i=1 Equation 02 Equation 04 block of thhe h-tjhh stratum, and yih y ∑xih [3] where xih y ∑y ∑xih = nh h = i=1 Equation 05 Equation 05 Equation 03 Equation 02 Equation 04 Equation 03 homogeneity, so that the measured values do not vary much from one unit to another. Alvarez et al. (2005), in comparative studies between random sampling and stratified sampling, showed it is neces- sary to establish reliable criteria for the grouping of blocks in strata based on the knowledge of the area. The density of trees was obtained by means of the image’s census and expressed as trees per lin- ear kilometer for the perimeter of the block. The final number of trees per linear kilometer was grouped into nine classes of different densities (Figure 3), which were validated in the field by sampling. The adequate number of blocks for each class (stratum) was defined based on the sampling sufficiency test. First, 10 blocks of each class by tree density were randomly selected for the validation. Subsequently, the data collected at the field level were compared with the data obtained from the image. The error was calculated and used to estimate the total number of trees. The assessment of the number of trees per kilometer in stratified sampling was estimated according to Cochran (2007). To obtain a coher- ent survey, the strata should have a homogeneity ©2015 International Society of Arboriculture in linear kilometers, of sidewalk of the block in the h-th stratum. The total number of kilometers of sidewalk in the h-th stratum is: Y ∑Y ∑Y h = nh h = Nh j =1 Y =∑ = Hi=1 H T h=1 T Equation 04 Equation 05 and Yjh Y =∑Y Y ∑Yjh [4] where Nh T of j-th block in h-th stratum; the total population of the linear kilometers of sidewalk variable is: H is thHe total of blocks from h-th stratum, is the toht.al linear kilometers of sidewalk h = i=1 Nh j h=1 =1 Equation 05[5] Y =∑Yh . T h=1 The data collected were compared to those of the 2010 census of the Brazilian Geography and Statistics Institute (IBGE 2010a). A neighborhood by neigh- borhood comparison was made. Once the propor- tions of tree individuals by number of inhabitants was obtained, the Gini coefficient was calculated, which means the ‘measurement of concentration degree of a distribution whose value ranges from zero (perfect equality) to 1 (maximum inequality)’ (IBGE 2007). RESULTS The total number of street trees found for Campinas was 120,730 individuals; all arboreal elements effectively deployed in the urban area (trees, shrubs, and palm trees) were consid- ered. If the seedlings were include, the number rises to 127,367. The average sampling decimal Y ∑Yjh y ∑xih h = Nh j =1 Y = jh j=1 nh Y =xY ∑x h = nh h ∑ ih , and h . i=1 Yh . h=1 nh xih= h x ∑R , and i=1Nh i=1 nh h is thihe num tber of trees in the i-th is the value, ˆxes = Y nh ih i=1 R ˆ es = R ˆ ∑ h=1 = hh=1 Y t es y Y x h h H ∑yh Y t xh Y h The components of the formula are: H xh =, and ih = es R ˆ , andh=1 ∑ H ∑ h=1 y Y x h h Y t y Y x h h h h
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