Arboriculture & Urban Forestry 36(1): January 2010 and that the row and column totals are fixed (Sokal and Rohlf 1995). Given the fact that this test is impossible to perform for most data sets as the total number of cases increases rapidly (Raymond and Rousset 1995), different methods were proposed to obtain an unbiased estimate of the exact P-values (Guo and Thompson 1989; Guo and Thompson 1992). In the research presented here, whenever Fisher’s test was required because of small cell frequencies, the Metropolis algorithm was utilized. Related probabilities were computed by analyzing 20 succes- sive batches, each composed of 2,500 replicates, for an overall total of 50,000 replicates. In order to obtain unbiased estimates, a random arbitrary start state was set after 1,000 dememorization steps. Statistical analyses were performed using Systat® 2004), and Statistica® (Systat (StatSoft 2006). The Fisher's exact test was computed using the program developed by Miller (2009). RESULTS AND DISCUSSION considered not influenced by specific local environmental con- ditions) are marked. Overall, presence/absence of metal grating, urban zone type, surficial deposit, presence/absence of aerial and Table 2. Pearson χ2 conditions.zyx Parameters parameters, according to a null hypothesis H0 Norway maple Metal grating (Yes/No) Soil Cover (Yes/No) Urban zones (5 Classes) Surficial deposit (3 Types) Aerial obstacles (Yes/No) Underground obstacles (Yes/No) Irradiation (5 Classes) Street width (3 Classes) Distance from tree to curb (3 Classes) Tree pit soil volume (4 Classes) Penetration resistance at surface (4 Classes) Penetration resistance at 15 cm (5.9 in) (4 Classes) Penetration resistance at 30 cm (11.8 in) (4 Classes) Penetration resistance at 45 cm (17.7 in) (4 Classes) Soil K – (5 Classes) Soil Ca – (4 Classes) Soil Mg – (4 Classes) Soil Na – (5 Classes) Soil Zn – (5 Classes) Soil Cu – (5 Classes) Soil Fe – (4 Classes) Soil Mn – (4 Classes) Soil P – (5 Classes) pH – (5 Classes) Soil organic matter (5 Classes) z 0.00 a 0.25 a 0.00 a 0.00 a 0.00 b 0.39 b 0.00 a 0.02 a 0.01 b 0.28 b 0.01 a 0.02 a 0.22 b 0.19 b 0.47 b 0.74 b 0.67 b 0.44 b 0.03 b 0.41 b 0.68 b 0.06 b 0.27 b 0.51 b 0.83 b x Fisher’s exact test probabilities are followed by “b”. ©2010 International Society of Arboriculture Silver maple 0.00 a 0.08 a 0.02 b 0.10 a 0.16 b 0.17 a 0.00 a 0.04 a 0.53 b 0.05 b 0.03 a 0.00 b 0.00 b 0.00 b 0.54 b 0.37 b 0.38 b 0.31 b 0.40 b 0.13 b 0.07 b 0.31 b 0.52 b 0.04 b 0.42 b Contingency results are presented in Table 2 as probabilities as- sociated either with the Pearson chi-square statistic or Fisher’s exact test. Significant results (rejection of H0 : tree growth being 5 underground obstacles, irradiation, street width, distance from tree to curb, tree pit soil volume, and penetration resistance were central parameters for many or all species. On the other hand, soil nutrients were only sporadically identified as significant elements thereby their importance as explaining factors for tree growth sta- tus is relatively low. This outcome is most likely related to the fact that, when sidewalks are present, soil samples can only be collect- ed within the transplantation pit opening which is usually 1.5 m (4.9 ft) x 1.5 m (4.9 ft) or less. With their extensive perennial root systems, trees integrate nutrient bioavailability not only near their trunk but mostly throughout the soil profile (Brady and Weil 2002). Originally, the purpose of noting the presence of metal grat- ings over tree pits was to test their potentially positive influence on tree-pit soil compaction. Within the limits of the soil com- paction methodology and apparatus utilized, one can infer that there is no quantifiable impact. Their presence obviously limits pedestrian compaction but probably cannot prevent detrimental vibrational forces due to heavy and dense urban traffic on com- mercial streets (Craul 1992; Craul 1999). This statement is il- lustrated by a contingency analysis between presence/absence of metal grating and the different classes of penetration resistance at the surface, and at depths of 15 cm (5.9 in), 30 cm (11.8 in), and 45 cm (17.7 in). These two variables are independent (Table 3). Nonetheless in the overall analysis (Table 2), presence of protec- and Fisher’s exact test results on the significance of the relationship between growth classes and abiotic where tree growth is considered not influenced by specific local environmental Hackberry 0.00 a 0.12 b 0.00 b 0.07 b 0.00 b 0.06 b 0.00 b 0.00 b 0.04 b 0.07 b 0.04 a 0.00 b 0.00 b 0.01 b 0.03 b 0.45 b 0.28 b 0.13 b 0.04 b 0.18 b 0.01 b 0.08 b 0.68 b 0.37 b 0.45 b Green ash 0.00 a 0.01 a 0.00 b 0.00 a 0.04 b 0.01 b 0.00 b 0.00 a 0.46 b 0.04 b 0.00 a 0.00 a 0.03 b 0.13 b 0.33 b 0.78 b 0.18 b 0.66 b 0.19 b 0.51 b 0.83 b 0.01 b 0.28 b 0.26 b 0.08 b Probabilities where H0 is rejected (significance level α ≤ 0.02) are highlighted in bold type. y Pearson chi-square probabilities are followed by “a”. Honeylocust 0.00 a 0.07 b 0.00 b 0.00 a 0.46 b 0.00 b 0.00 a 0.00 a 0.00 b 0.02 b 0.05 a 0.00 b 0.00 b 0.02 b 0.25 b 0.67 b 0.05 b 0.02 b 0.00 b 0.01 b 0.28 b 0.06 b 0.10 b 0.81 b 0.00 b Littleleaf linden - 0.25 b 0.00 b 0.04 b 0.00 b 0.00 b 0.01 b 0.00 b 0.05 b 0.01 b 0.96 a 0.00 b 0.18 b 0.36 b 0.25 b 0.11 b 0.19 b 0.99 b 0.06 b 0.00 b 0.10 b 0.15 b 0.71 b 0.29 b 0.43 b Siberian elm 0.31 b 0.01 a 0.00 a 0.23 a 0.07 b 0.02 b 0.00 b 0.00 a 0.75 b 0.00 b 0.00 b 0.00 b 0.00 b 0.01 b 0.00 b 0.05 b 0.41 b 0.52 b 0.77 b 0.28 b 0.36 b 0.00 b 0.46 b 0.12 b 0.00 b All-species 0.00 a 0.04 a 0.00 a 0.00 a 0.07 a 0.00 b 0.00 a 0.00 a 0.01 b 0.00 b 0.00 a 0.00 a 0.00 a 0.00 b 0.56 b 0.09 b 0.31 b 0.02 b 0.07 b 0.12 b 0.46 b 0.01 b 0.53 b 0.52 b 0.01 b
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