Mark Breunig
WATR 755
Discriminant Analysis
Please note the height of nest in tree appears to be duplicated in the original data set, so it appears twice in all the tables.
Introduction
Expectations
This exercise will involve using discriminate analysis to observe differences in the nesting habitat of sharp-shinned and Cooper’s hawks. Discriminate analysis is a useful multivariate technique that uses a series of linear combinations (ordinations) to maximize separation between groups and minimize variance within groups. The associated discriminate function can be used to assign observations to groups, which may or may not be the same as the a priori classification scheme.
Considering the nature of discriminate analysis, I expect it will offer a more thorough analysis than using a T-test or ANOVA. The T-test can be used to compare means across groups, but lacks the “multidimensional power” to analyze all observations simultaneously. The successive ordination of variables in multidimensional space allows the observer to observe differences between grouping that are not possible using T-tests and multiple range tests. The reclassification aspect of discriminate analysis offers further advantages. The benefit of discriminate analysis would be even more pronounced if these data involved more than 2 groupings, which presents an even more complicated interpretation.
Based on a literature review, it is suggested that Cooper’s Hawks nest close to water, in mature trees with high canopy cover and sparse ground cover. Therefore I expect DIST_WAT(-), TOT_UN(+), TOT_CA (-)to have strong loadings. It is also known that Cooper’s Hawks prefer deciduous forests, and Sharp-shinned Hawks prefer coniferous forests. Therefore CAN_DE (+) and CAN_CON (-) should have strong loadings as well.
Summary Statistics
Summary statistics can be found in Appendix A. This table was used to insure the data were imported into SAS correctly, and to identify potential issues with the data. The number of observations and variables is important to consider when analyzing how confident one can be in the results. In this case the number of observations vary from 71-74 per variable and there are 25 variables, which is satisfactory.
If a variable has the same minimum and maximum, one would expect the variable to have a very low loading (it does not vary). The same could be said for the standard deviation relative to the mean. If the standard deviation is considerably smaller than the mean, a low loading would be expected. The summary statistics indicate all variables have an adequate amount of variance to have utility in discriminate analysis.
Correlation Matrix
The pearson correlation matrix can be found in Appendix B. Several variables are cross correlated. Some examples of this include DIST_OPEN (distance to nearest forest opening) and TREE_HT (Nest tree height) [α = 0.10, p =0.0005, r = 0.40]; TREE_HT and DBH [α = 0.10, p =<0.0001, r = 0.70]; TREE_HT and NEST_HT (height of nest in tree) [α = 0.10, p =<0.0001, r = 0.75]. These correlations make intuitive sense, and will be included in the analysis.
Data Standardization
Data are assumed to be normal. Data were standardized using SAS to have a mean of zero and a standard deviation of 1.
Results
T-Tests
The results of the T-Tests can be found in Appendix C. Several significant differences in means were found using this analysis (α = 0.10). These include TREE_HT, DBH, NEST_HT, DEG_SLOP, AVG_CAN, AVG_SH_D, CAN_DE, CAN_CON, TOT_CA, UND_DEC, UND_CON, DENS, and AVG_DBHC. These variables should have the loadings with the greatest magnitude (could be either positive or negative). Based on these results, it would appear that tree size, type (conifer or deciduous), and density are the factors that differentiate the nests of the two species.
The Wilks' Lambda value (<0.0001) indicates the discriminate analysis is statistically significant, so it is appropriate to proceed with further analysis.
Coefficients of Canonical Discriminant Axes
Table 1 presents the total canonical structure coefficients calculated in the discriminate analysis. As was expected, the same variables found to be have significant differences in means in the T-Test show the strongest loadings. However, this analysis offers a more thorough examination of the data because it allows one to see how the variables that have significant differences in means rank amongst themselves. Based on this, it can be seen that NEST_HT (0.66) has the strongest influence on the discriminate function. CAN_DE (0.62), AVG_CAN (0.62), AVG_DBHC (0.61), DENS (-0.58) have the next highest loadings. Based on this, it appears that the height of the nest in tree, % deciduous trees, mean plot diameter breast height, and tree density provide the most distinction between the two species nests.
Table 1. Total Cononical Structure Coefficients for nesting habitat characteristics of sharp-shinned hawks and Cooper’s hawks calculated using discriminant analysis.
Variable / Total Cononical Structure Coefficients / Variable / Total Cononical Structure CoefficientsNEST_HT / 0.66 / TOT_UNDS / -0.11
__CAN_DE / 0.62 / __GRN_CO / -0.20
AVG_CAN / 0.62 / AVG_SH_I / -0.28
AVG_DBHC / 0.61 / AVG_SH_D / -0.46
DBH / 0.54 / _UND_CON / -0.53
TREE_HT / 0.53 / _CAN_CON / -0.53
_NEST_HT / 0.40 / DENS / -0.58
_UND_DEC / 0.37
TOT___CA / 0.36
DEG_SLOP / 0.29
_GRN_DEC / 0.22
TOT___GR / 0.21
DIST_WAT / 0.19
DIST_OPE / 0.08
BA / 0.07
TOT___UN / 0.06
TREE_SP / -0.04
Correct Classification Table
The correct classification table is shown in Table 2. The original classifications performed very well when compared to the groups calculated by the discriminate analysis (98% and 95% success). There doesn’t appear to be a significant difference between the success rate of reclassification between species (2% vs 5%).
Table 2. Correct classification (cross-validation) table based off of nesting habitat characteristics of sharp-shinned hawks and Cooper’s hawks calculated using discriminant analysis.
1 / 2 / Total1 / 39 / 8 / 47
98% / 2% / 100%
2 / 2 / 18 / 20
5% / 95% / 100%
Total / 41 / 26 / 67
70% / 30% / 100%
Priors / 0.5 / 0.5
Discussion
Interpretation of Model Structure
Some of my a priori expectations were correct, while others were not. I expected DIST_WAT, TOT_UN, TOT_CA to have strong loadings but they turned out to be weak. For this particular data set, those variables provide little distinction among groups.
The literature states that Cooper’s Hawks prefer deciduous forests, and Sharp-shinned Hawks prefer coniferous forests, which is supported by the discriminate analysis (CAN_DE = 0.62, CAN_CON = -0.53). These two variables would have an inverse relationship anyways, but the magnitude of their loadings supports the importance of coniferous versus deciduous forest. It can also be observed that Coopers hawks nest in stands of lower densities (DENS = -0.58) of taller (TREE_HT = 0.53) and larger trees (DBH = 0.54) than Sharp-shinned Hawks.
Utility of Discriminate Analysis
The utility of discriminate analysis is apparent from this exercise. While T-Tests can tell you which means are statistically different between 2 groups (and multiple range tests between more than 2 groups), the multidimensional ordination utilized by discriminate analysis allows one to analyze the magnitude and direction of structure coefficients. This provides a more powerful analysis and interpretation of the significance and meaning of variables, and a more contrasting separation of groups. The correct classification table offers additional utility, enabling the analyst to check the validity of a priori classifications.
Appendix A: Summary Statistics
Variable / N / Mean / Std Dev / Minimum / MaximumSPECIES / 74 / 1.30 / 0.46 / 1.00 / 2.00
DIST_WAT / 72 / 356.92 / 415.03 / 0.50 / 1700.00
DIST_OPE / 71 / 58.58 / 68.22 / 2.00 / 320.00
TREE_SP / 74 / 7.05 / 4.51 / 1.00 / 20.00
TREE_HT / 74 / 17.84 / 4.26 / 9.10 / 31.80
DBH / 74 / 30.00 / 8.91 / 10.16 / 49.50
NEST_HT / 74 / 11.90 / 3.29 / 4.88 / 20.80
NEST_HT / 74 / 67.02 / 12.81 / 32.08 / 102.41
DEG_SLOP / 72 / 3.08 / 6.44 / 0.00 / 41.00
AVG_CAN / 74 / 18.16 / 4.04 / 8.44 / 30.10
AVG_SH_D / 74 / 9.85 / 9.93 / 0.00 / 52.50
AVG_SH_I / 74 / 19.60 / 15.77 / 0.00 / 70.25
CAN_DE / 74 / 42.53 / 35.98 / 0.00 / 100.00
CAN_CON / 74 / 40.00 / 34.27 / 0.00 / 97.50
TOT_CA / 74 / 82.53 / 10.79 / 52.50 / 100.00
UND_DEC / 74 / 27.40 / 27.16 / 0.00 / 95.00
UND_CON / 74 / 8.95 / 16.31 / 0.00 / 70.00
TOT_UN / 74 / 36.35 / 26.70 / 0.00 / 95.00
GRN_DEC / 74 / 44.66 / 25.23 / 0.00 / 97.50
GRN_CO / 74 / 0.34 / 1.82 / 0.00 / 15.00
TOT_GR / 74 / 45.00 / 25.18 / 0.00 / 97.50
TOT_UNDS / 73 / 13.03 / 10.17 / 0.00 / 48.00
BA / 74 / 30.87 / 18.60 / 2.19 / 146.00
DENS / 74 / 758.78 / 434.66 / 200.00 / 2050.00
AVG_DBHC / 74 / 23.25 / 7.06 / 10.10 / 47.40
Appendix B: Correlation Matrix
SPECIES DIST_WAT DIST_OPE TREE_SP TREE_HT DBH NEST_HT _NEST_HT DEG_SLOP
SPECIES 1.00000 -0.17709 0.02210 0.09786 -0.42879 -0.44621 -0.57423 -0.38285 -0.23054
0.1367 0.8549 0.4068 0.0001 <.0001 <.0001 0.0008 0.0514
74 72 71 74 74 74 74 74 72
DIST_WAT -0.17709 1.00000 0.06917 -0.21362 0.07967 -0.06542 0.01008 -0.03320 -0.08806
0.1367 0.5723 0.0716 0.5059 0.5851 0.9331 0.7819 0.4685
72 72 69 72 72 72 72 72 70
DIST_OPE 0.02210 0.06917 1.00000 0.12946 0.40428 0.35674 0.18004 -0.16958 0.17092
0.8549 0.5723 0.2819 0.0005 0.0023 0.1330 0.1574 0.1603
71 69 71 71 71 71 71 71 69
TREE_SP 0.09786 -0.21362 0.12946 1.00000 0.19736 0.04705 0.17216 -0.05417 0.40859
0.4068 0.0716 0.2819 0.0919 0.6906 0.1424 0.6467 0.0004
74 72 71 74 74 74 74 74 72
TREE_HT -0.42879 0.07967 0.40428 0.19736 1.00000 0.70415 0.75065 -0.10000 0.29942
0.0001 0.5059 0.0005 0.0919 <.0001 <.0001 0.3966 0.0106
74 72 71 74 74 74 74 74 72
DBH -0.44621 -0.06542 0.35674 0.04705 0.70415 1.00000 0.62363 0.08832 0.31381
<.0001 0.5851 0.0023 0.6906 <.0001 <.0001 0.4543 0.0073
74 72 71 74 74 74 74 74 72
NEST_HT -0.57423 0.01008 0.18004 0.17216 0.75065 0.62363 1.00000 0.55838 0.39309
<.0001 0.9331 0.1330 0.1424 <.0001 <.0001 <.0001 0.0006
74 72 71 74 74 74 74 74 72
_NEST_HT -0.38285 -0.03320 -0.16958 -0.05417 -0.10000 0.08832 0.55838 1.00000 0.16810
0.0008 0.7819 0.1574 0.6467 0.3966 0.4543 <.0001 0.1581
74 72 71 74 74 74 74 74 72
DEG_SLOP -0.23054 -0.08806 0.17092 0.40859 0.29942 0.31381 0.39309 0.16810 1.00000
0.0514 0.4685 0.1603 0.0004 0.0106 0.0073 0.0006 0.1581
72 70 69 72 72 72 72 72 72
AVG_CAN -0.50129 0.12465 0.35861 0.26752 0.92539 0.71120 0.76512 0.03004 0.27130
<.0001 0.2968 0.0021 0.0212 <.0001 <.0001 <.0001 0.7994 0.0212
74 72 71 74 74 74 74 74 72
AVG_SH_D 0.36654 -0.18917 -0.17929 0.00661 -0.25139 -0.26207 -0.30291 -0.21691 -0.08021
0.0013 0.1115 0.1346 0.9554 0.0307 0.0241 0.0087 0.0634 0.5030
74 72 71 74 74 74 74 74 72
AVG_CAN AVG_SH_D AVG_SH_I __CAN_DE _CAN_CON TOT___CA _UND_DEC _UND_CON TOT___UN
SPECIES -0.50129 0.36654 0.16932 -0.53010 0.44956 -0.33986 -0.31271 0.38432 -0.08333
<.0001 0.0013 0.1492 <.0001 <.0001 0.0031 0.0067 0.0007 0.4803
74 74 74 74 74 74 74 74 74
DIST_WAT 0.12465 -0.18917 0.12510 0.03005 0.00107 0.10315 -0.11429 -0.05125 -0.14787
0.2968 0.1115 0.2951 0.8022 0.9929 0.3885 0.3391 0.6690 0.2151
72 72 72 72 72 72 72 72 72
DIST_OPE 0.35861 -0.17929 -0.13551 0.16995 -0.10942 0.21160 0.02231 -0.23294 -0.11479
0.0021 0.1346 0.2598 0.1565 0.3637 0.0765 0.8535 0.0506 0.3405
71 71 71 71 71 71 71 71 71
TREE_SP 0.26752 0.00661 -0.06395 0.13836 -0.11136 0.10770 0.23938 0.05066 0.27443
0.0212 0.9554 0.5883 0.2397 0.3449 0.3611 0.0400 0.6682 0.0180
74 74 74 74 74 74 74 74 74
TREE_HT 0.92539 -0.25139 -0.05516 0.40692 -0.29197 0.42955 0.24513 -0.36036 0.02922
<.0001 0.0307 0.6406 0.0003 0.0116 0.0001 0.0353 0.0016 0.8048
74 74 74 74 74 74 74 74 74
DBH 0.71120 -0.26207 -0.02980 0.49247 -0.40857 0.34454 0.38364 -0.38728 0.15367
<.0001 0.0241 0.8010 <.0001 0.0003 0.0026 0.0007 0.0007 0.1912
74 74 74 74 74 74 74 74 74
NEST_HT 0.76512 -0.30291 -0.01039 0.32357 -0.19809 0.44973 0.15507 -0.40714 -0.09097
<.0001 0.0087 0.9300 0.0049 0.0907 <.0001 0.1871 0.0003 0.4408
74 74 74 74 74 74 74 74 74
_NEST_HT 0.03004 -0.21691 0.07230 0.02525 0.03444 0.19351 -0.09332 -0.19407 -0.21347
0.7994 0.0634 0.5404 0.8309 0.7708 0.0985 0.4291 0.0976 0.0678
74 74 74 74 74 74 74 74 74
DEG_SLOP 0.27130 -0.08021 0.06939 0.22727 -0.17399 0.20493 0.21525 -0.20504 0.09365
0.0212 0.5030 0.5625 0.0549 0.1438 0.0842 0.0694 0.0840 0.4340
72 72 72 72 72 72 72 72 72
AVG_CAN 1.00000 -0.26513 -0.10643 0.45742 -0.32799 0.48353 0.31503 -0.40949 0.07031
0.0224 0.3668 <.0001 0.0043 <.0001 0.0063 0.0003 0.5517
74 74 74 74 74 74 74 74 74
AVG_SH_D -0.26513 1.00000 0.29100 -0.22019 0.16386 -0.21378 0.06678 0.24964 0.22042
0.0224 0.0119 0.0594 0.1630 0.0674 0.5719 0.0319 0.0591
74 74 74 74 74 74 74 74 74
_GRN_DEC __GRN_CO TOT___GR TOT_UNDS BA DENS AVG_DBHC
SPECIES -0.17118 -0.03980 -0.17439 0.02524 -0.05700 0.48499 -0.51800
0.1448 0.7363 0.1373 0.8322 0.6296 <.0001 <.0001
74 74 74 73 74 74 74
DIST_WAT -0.13950 -0.04300 -0.14037 -0.08748 0.02747 -0.02456 0.10455
0.2425 0.7199 0.2396 0.4682 0.8188 0.8378 0.3821
72 72 72 71 72 72 72
DIST_OPE -0.15427 0.02938 -0.15246 -0.00785 0.07372 -0.15614 0.24690
0.1990 0.8079 0.2043 0.9486 0.5412 0.1935 0.0379
71 71 71 70 71 71 71
TREE_SP 0.22857 -0.03569 0.22643 -0.04461 0.09863 0.01759 0.04685
0.0501 0.7627 0.0524 0.7078 0.4031 0.8817 0.6918
74 74 74 73 74 74 74
TREE_HT -0.01879 0.09184 -0.01219 -0.08883 0.06087 -0.45813 0.62609
0.8737 0.4365 0.9179 0.4548 0.6064 <.0001 <.0001
74 74 74 73 74 74 74
DBH -0.02664 0.08847 -0.02030 -0.07566 0.09768 -0.59113 0.72589
0.8217 0.4535 0.8637 0.5246 0.4077 <.0001 <.0001
74 74 74 73 74 74 74
NEST_HT -0.06520 0.12358 -0.05639 -0.09285 0.17707 -0.38515 0.62765
0.5810 0.2942 0.6332 0.4346 0.1312 0.0007 <.0001
74 74 74 73 74 74 74
_NEST_HT -0.09274 0.05056 -0.08927 -0.04511 0.20857 -0.00438 0.21567
0.4319 0.6688 0.4494 0.7047 0.0745 0.9705 0.0650
74 74 74 73 74 74 74
DEG_SLOP 0.12321 -0.00820 0.12288 -0.11201 0.08159 -0.16228 0.26948
0.3025 0.9455 0.3038 0.3489 0.4957 0.1732 0.0221
72 72 72 72 72 72 72
AVG_CAN -0.01754 0.05207 -0.01381 -0.16026 0.11923 -0.50699 0.71478
0.8821 0.6595 0.9070 0.1756 0.3116 <.0001 <.0001
74 74 74 73 74 74 74
AVG_SH_D 0.26322 -0.04553 0.26044 -0.11330 -0.18166 0.01754 -0.27464
0.0235 0.7001 0.0250 0.3399 0.1214 0.8821 0.0179
74 74 74 73 74 74 74
SPECIES DIST_WAT DIST_OPE TREE_SP TREE_HT DBH NEST_HT _NEST_HT DEG_SLOP
AVG_SH_I 0.16932 0.12510 -0.13551 -0.06395 -0.05516 -0.02980 -0.01039 0.07230 0.06939
0.1492 0.2951 0.2598 0.5883 0.6406 0.8010 0.9300 0.5404 0.5625
74 72 71 74 74 74 74 74 72
__CAN_DE -0.53010 0.03005 0.16995 0.13836 0.40692 0.49247 0.32357 0.02525 0.22727
<.0001 0.8022 0.1565 0.2397 0.0003 <.0001 0.0049 0.8309 0.0549
74 72 71 74 74 74 74 74 72
_CAN_CON 0.44956 0.00107 -0.10942 -0.11136 -0.29197 -0.40857 -0.19809 0.03444 -0.17399
<.0001 0.9929 0.3637 0.3449 0.0116 0.0003 0.0907 0.7708 0.1438
74 72 71 74 74 74 74 74 72
TOT___CA -0.33986 0.10315 0.21160 0.10770 0.42955 0.34454 0.44973 0.19351 0.20493
0.0031 0.3885 0.0765 0.3611 0.0001 0.0026 <.0001 0.0985 0.0842
74 72 71 74 74 74 74 74 72
_UND_DEC -0.31271 -0.11429 0.02231 0.23938 0.24513 0.38364 0.15507 -0.09332 0.21525
0.0067 0.3391 0.8535 0.0400 0.0353 0.0007 0.1871 0.4291 0.0694
74 72 71 74 74 74 74 74 72
_UND_CON 0.38432 -0.05125 -0.23294 0.05066 -0.36036 -0.38728 -0.40714 -0.19407 -0.20504
0.0007 0.6690 0.0506 0.6682 0.0016 0.0007 0.0003 0.0976 0.0840
74 72 71 74 74 74 74 74 72
TOT___UN -0.08333 -0.14787 -0.11479 0.27443 0.02922 0.15367 -0.09097 -0.21347 0.09365
0.4803 0.2151 0.3405 0.0180 0.8048 0.1912 0.4408 0.0678 0.4340
74 72 71 74 74 74 74 74 72
_GRN_DEC -0.17118 -0.13950 -0.15427 0.22857 -0.01879 -0.02664 -0.06520 -0.09274 0.12321
0.1448 0.2425 0.1990 0.0501 0.8737 0.8217 0.5810 0.4319 0.3025
74 72 71 74 74 74 74 74 72
__GRN_CO -0.03980 -0.04300 0.02938 -0.03569 0.09184 0.08847 0.12358 0.05056 -0.00820
0.7363 0.7199 0.8079 0.7627 0.4365 0.4535 0.2942 0.6688 0.9455
74 72 71 74 74 74 74 74 72
TOT___GR -0.17439 -0.14037 -0.15246 0.22643 -0.01219 -0.02030 -0.05639 -0.08927 0.12288
0.1373 0.2396 0.2043 0.0524 0.9179 0.8637 0.6332 0.4494 0.3038
74 72 71 74 74 74 74 74 72
TOT_UNDS 0.02524 -0.08748 -0.00785 -0.04461 -0.08883 -0.07566 -0.09285 -0.04511 -0.11201
0.8322 0.4682 0.9486 0.7078 0.4548 0.5246 0.4346 0.7047 0.3489
73 71 70 73 73 73 73 73 72
AVG_CAN AVG_SH_D AVG_SH_I __CAN_DE _CAN_CON TOT___CA _UND_DEC _UND_CON TOT___UN
AVG_SH_I -0.10643 0.29100 1.00000 -0.18374 0.14666 -0.14689 -0.08283 0.10038 -0.02294
0.3668 0.0119 0.1171 0.2124 0.2117 0.4829 0.3948 0.8462
74 74 74 74 74 74 74 74 74
__CAN_DE 0.45742 -0.22019 -0.18374 1.00000 -0.95394 0.30508 0.52646 -0.23574 0.39151
<.0001 0.0594 0.1171 <.0001 0.0082 <.0001 0.0432 0.0006
74 74 74 74 74 74 74 74 74
_CAN_CON -0.32799 0.16386 0.14666 -0.95394 1.00000 -0.00532 -0.50570 0.13545 -0.43165
0.0043 0.1630 0.2124 <.0001 0.9641 <.0001 0.2499 0.0001
74 74 74 74 74 74 74 74 74
TOT___CA 0.48353 -0.21378 -0.14689 0.30508 -0.00532 1.00000 0.14956 -0.35582 -0.06522
<.0001 0.0674 0.2117 0.0082 0.9641 0.2034 0.0019 0.5809
74 74 74 74 74 74 74 74 74
_UND_DEC 0.31503 0.06678 -0.08283 0.52646 -0.50570 0.14956 1.00000 -0.32815 0.81673
0.0063 0.5719 0.4829 <.0001 <.0001 0.2034 0.0043 <.0001
74 74 74 74 74 74 74 74 74
_UND_CON -0.40949 0.24964 0.10038 -0.23574 0.13545 -0.35582 -0.32815 1.00000 0.27705
0.0003 0.0319 0.3948 0.0432 0.2499 0.0019 0.0043 0.0169
74 74 74 74 74 74 74 74 74
TOT___UN 0.07031 0.22042 -0.02294 0.39151 -0.43165 -0.06522 0.81673 0.27705 1.00000
0.5517 0.0591 0.8462 0.0006 0.0001 0.5809 <.0001 0.0169
74 74 74 74 74 74 74 74 74
_GRN_DEC -0.01754 0.26322 0.18132 0.31893 -0.40560 -0.22445 0.41552 -0.02606 0.40674
0.8821 0.0235 0.1221 0.0056 0.0003 0.0545 0.0002 0.8256 0.0003
74 74 74 74 74 74 74 74 74
__GRN_CO 0.05207 -0.04553 0.38170 -0.17677 0.20466 0.06045 -0.14489 -0.06872 -0.18936
0.6595 0.7001 0.0008 0.1319 0.0803 0.6089 0.2181 0.5607 0.1061
74 74 74 74 74 74 74 74 74
TOT___GR -0.01381 0.26044 0.20924 0.30678 -0.39160 -0.22051 0.40586 -0.03107 0.39385
0.9070 0.0250 0.0736 0.0078 0.0006 0.0590 0.0003 0.7927 0.0005
74 74 74 74 74 74 74 74 74
TOT_UNDS -0.16026 -0.11330 -0.02241 0.19462 -0.22663 -0.07111 0.14708 0.22952 0.29223
0.1756 0.3399 0.8508 0.0990 0.0538 0.5500 0.2143 0.0508 0.0121
73 73 73 73 73 73 73 73 73
_GRN_DEC __GRN_CO TOT___GR TOT_UNDS BA DENS AVG_DBHC
AVG_SH_I 0.18132 0.38170 0.20924 -0.02241 -0.04869 0.03360 -0.06995
0.1221 0.0008 0.0736 0.8508 0.6804 0.7762 0.5537
74 74 74 73 74 74 74
__CAN_DE 0.31893 -0.17677 0.30678 0.19462 -0.23728 -0.55020 0.27696
0.0056 0.1319 0.0078 0.0990 0.0418 <.0001 0.0169
74 74 74 73 74 74 74
_CAN_CON -0.40560 0.20466 -0.39160 -0.22663 0.28398 0.54184 -0.19968
0.0003 0.0803 0.0006 0.0538 0.0142 <.0001 0.0881
74 74 74 73 74 74 74
TOT___CA -0.22445 0.06045 -0.22051 -0.07111 0.11054 -0.11393 0.28930
0.0545 0.6089 0.0590 0.5500 0.3484 0.3338 0.0124
74 74 74 73 74 74 74
_UND_DEC 0.41552 -0.14489 0.40586 0.14708 0.10757 -0.32801 0.30790
0.0002 0.2181 0.0003 0.2143 0.3616 0.0043 0.0076
74 74 74 73 74 74 74
_UND_CON -0.02606 -0.06872 -0.03107 0.22952 -0.19787 0.22417 -0.31792
0.8256 0.5607 0.7927 0.0508 0.0910 0.0548 0.0058
74 74 74 73 74 74 74
TOT___UN 0.40674 -0.18936 0.39385 0.29223 -0.01145 -0.19671 0.11899
0.0003 0.1061 0.0005 0.0121 0.9229 0.0930 0.3126
74 74 74 73 74 74 74
_GRN_DEC 1.00000 -0.06278 0.99740 0.03267 -0.28531 -0.26232 -0.05724
0.5951 <.0001 0.7838 0.0137 0.0240 0.6281
74 74 74 73 74 74 74
__GRN_CO -0.06278 1.00000 0.00935 0.04795 0.05950 0.00811 0.02483
0.5951 0.9370 0.6870 0.6146 0.9453 0.8337
74 74 74 73 74 74 74
TOT___GR 0.99740 0.00935 1.00000 0.03629 -0.28156 -0.26224 -0.05556
<.0001 0.9370 0.7605 0.0151 0.0240 0.6382
74 74 74 73 74 74 74
TOT_UNDS 0.03267 0.04795 0.03629 1.00000 -0.14866 0.03241 -0.22917
0.7838 0.6870 0.7605 0.2094 0.7854 0.0511
73 73 73 73 73 73 73
SPECIES DIST_WAT DIST_OPE TREE_SP TREE_HT DBH NEST_HT _NEST_HT DEG_SLOP
BA -0.05700 0.02747 0.07372 0.09863 0.06087 0.09768 0.17707 0.20857 0.08159
0.6296 0.8188 0.5412 0.4031 0.6064 0.4077 0.1312 0.0745 0.4957
74 72 71 74 74 74 74 74 72
DENS 0.48499 -0.02456 -0.15614 0.01759 -0.45813 -0.59113 -0.38515 -0.00438 -0.16228
<.0001 0.8378 0.1935 0.8817 <.0001 <.0001 0.0007 0.9705 0.1732
74 72 71 74 74 74 74 74 72
AVG_DBHC -0.51800 0.10455 0.24690 0.04685 0.62609 0.72589 0.62765 0.21567 0.26948
<.0001 0.3821 0.0379 0.6918 <.0001 <.0001 <.0001 0.0650 0.0221
74 72 71 74 74 74 74 74 72
AVG_CAN AVG_SH_D AVG_SH_I __CAN_DE _CAN_CON TOT___CA _UND_DEC _UND_CON TOT___UN
BA 0.11923 -0.18166 -0.04869 -0.23728 0.28398 0.11054 0.10757 -0.19787 -0.01145
0.3116 0.1214 0.6804 0.0418 0.0142 0.3484 0.3616 0.0910 0.9229
74 74 74 74 74 74 74 74 74
DENS -0.50699 0.01754 0.03360 -0.55020 0.54184 -0.11393 -0.32801 0.22417 -0.19671
<.0001 0.8821 0.7762 <.0001 <.0001 0.3338 0.0043 0.0548 0.0930
74 74 74 74 74 74 74 74 74
AVG_DBHC 0.71478 -0.27464 -0.06995 0.27696 -0.19968 0.28930 0.30790 -0.31792 0.11899
<.0001 0.0179 0.5537 0.0169 0.0881 0.0124 0.0076 0.0058 0.3126
74 74 74 74 74 74 74 74 74
_GRN_DEC __GRN_CO TOT___GR TOT_UNDS BA DENS AVG_DBHC
BA -0.28531 0.05950 -0.28156 -0.14866 1.00000 0.48246 0.47283
0.0137 0.6146 0.0151 0.2094 <.0001 <.0001
74 74 74 73 74 74 74
DENS -0.26232 0.00811 -0.26224 0.03241 0.48246 1.00000 -0.41985
0.0240 0.9453 0.0240 0.7854 <.0001 0.0002
74 74 74 73 74 74 74
_GRN_DEC __GRN_CO TOT___GR TOT_UNDS BA DENS AVG_DBHC
AVG_DBHC -0.05724 0.02483 -0.05556 -0.22917 0.47283 -0.41985 1.00000
0.6281 0.8337 0.6382 0.0511 <.0001 0.0002
74 74 74 73 74 74 74
Appendix C: T-Tests
Variable / DF / t value / Pr>|t|DIST_WAT / 70 / 1.51 / 0.1367
DIST_OPE / 69 / -0.18 / 0.8549
TREE_SP / 72 / -0.83 / 0.4068
TREE_HT / 72 / 4.03 / 0.0001
DBH / 72 / 4.23 / <.0001
NEST_HT / 72 / 5.95 / <.0001
_NEST_HT / 72 / 3.52 / 0.0008
DEG_SLOP / 70 / 1.98 / 0.0514
AVG_CAN / 72 / 4.92 / <.0001
AVG_SH_D / 72 / -3.34 / 0.0013
AVG_SH_I / 72 / -1.46 / 0.1492
__CAN_DE / 72 / 5.3 / <.0001
_CAN_CON / 72 / -4.27 / <.0001
TOT___CA / 72 / 3.07 / 0.0031
_UND_DEC / 72 / 2.79 / 0.0067
_UND_CON / 72 / -3.53 / 0.0007
TOT___UN / 72 / 0.71 / 0.4803
_GRN_DEC / 72 / 1.47 / 0.1448
__GRN_CO / 72 / 0.34 / 0.7363
TOT___GR / 72 / 1.5 / 0.1373
TOT_UNDS / 71 / -0.21 / 0.8322
BA / 72 / 0.48 / 0.6296
DENS / 72 / -4.71 / <.0001
AVG_DBHC / 72 / 5.14 / <.0001
Pooled Method used for all tests
α = 0.10