Cottonwood Burn Recovery

Statistical Analysis

Becky Parker

September 6, 2004

 

The primary study question, for which the following analyses are used to answer, is “Does conifer success (quality of conifer growth) depend on the presence (or absence) of CEVE?”  The quality of conifer growth can be measured by several different quantities.  The total number of conifers per plot, crop tree diameter, height, leader, and whorl sum are all reasonable measures of the quality of conifer growth.  The significance level of 0.10 (10%) was used throughout the analyses.

 

TOTAL NUMBER OF CONIFERS PER PLOT

 

An analysis was performed to determine if the average total number of conifers per plot is significantly related to the height of CEVE and if it significantly differs among the CEVE cover classes.  The natural log (LN) of the total number of conifers was used as the response (dependent) variable and CEVE height and cover were the explanatory (independent) variables of interest.  The assumption of the residuals being normally distributed was violated when the untransformed total number of conifers data was used.  The LN transformation was used to adequately resolve the violation of the normally distributed residuals assumption.  CEVE height is a continuous variable measured in feet and CEVE cover is a categorical variable measured in the percent cover classes of 0-9%, 10-24%, 25-50%, 51-80%, and 81-100%.  Stand, transect within a stand, slope, aspect, and shrub cover were also considered as potential explanatory variables in the model to help reduce the error variability, which in turn allows for an easier detection of a significant dependence on CEVE height or cover.  All explanatory variables in the model (except CEVE height) are categorical.  Please note only the explanatory variables that contributed to reducing the error variability were retained in the model, the others were discarded.

 

MINITAB Output

 

General Linear Model: LN Total Conifers versus Stand, Slope, Aspect, CEVE Height,

    CEVE Cover, and Shrub Cover

 

Factor        Type Levels Values

Stand        fixed      9 610-014 640-024 640-036 640-124 645-129 650-190 655-002

                          655-007 660-003

Slope        fixed      4 < 10%     10% - 19% 20% - 29% > 30%   

Aspect       fixed      8 N  NE E  SE S  SW W  NW

CEVE Cover   fixed      5 1 2 3 4 5

Shrub Cover  fixed      5 1 2 3 4 5

 

Analysis of Variance for LN Total Conifers, using Adjusted SS for Tests

 

Source        DF     Seq SS     Adj SS     Adj MS       F      P

Stand          8     51.637     30.963      3.870    3.48  0.001

Slope          3      7.925      5.375      1.792    1.61  0.190

Aspect         7     10.979     10.185      1.455    1.31  0.252

CEVE Height    1      0.159      0.569      0.569    0.51  0.476

CEVE Cover     4      3.284      4.268      1.067    0.96  0.432

Shrub Cover    4      8.537      8.537      2.134    1.92  0.112

Error        117    130.086    130.086      1.112

Total        144    212.608 

 

Term              Coef   SE Coef        T      P

Constant        2.1163    0.5050     4.19  0.000

CEVE Height     0.1149    0.1606     0.72  0.476

 

Conclusion regarding CEVE Height:

Based on the p-value (p=0.476) for CEVE height, we can conclude that the average total number of conifers per plot is not significantly related to CEVE height.  The estimated slope for the linear relationship between LN total number of conifers per plot and CEVE height was 0.1149.  Based on this estimate, we do not have enough evidence to conclude that there is a significant linear relationship between total number of conifers per plot and CEVE height.  See Figure 1 to view the relationship between the total number of conifers per plot and CEVE height. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1:  This graph shows the relationship between CEVE height and the total conifers per plot.  As found in the statistical analysis, this graph illustrates the conclusion that there is no significant linear relationship between CEVE height and total conifers per plot.

 

Conclusion regarding CEVE Cover:

Based on the p-value (p=0.432) for CEVE cover, we can conclude that the average total number of conifers per plot does not significantly depend on CEVE cover either.  In other words, the average total number of conifer per plot does not significantly differ among the cover classes.  Please note since the LN transformation was used, regular averages cannot be calculated by back-transforming means on the natural log scale.

 

 

 

 

 

 

CROP TREE ANALYSIS

 

Two trees (called ‘crop trees’) were selected from each plot (where available) and were treated as replicates of the most vigorous conifers per plot for the purpose of analyses. 

 

CROP TREE DIAMETER

 

An analysis was performed to determine if the average crop tree diameter is different in the presence versus absence of CEVE.  The crop tree diameter was used as the response (dependent) variable and CEVE and Location were the two explanatory (independent) variables of interest where CEVE has two categories (present and absent) and Location has three categories (within, edge, and outside).  Stand, transect within a stand, slope, aspect, CEVE height, CEVE cover, shrub cover and relevant interactions were also included in the model as potential explanatory variables to help reduce the error variability, which in turn allows for an easier detection of a significant CEVE or Location effect.  All explanatory variables considered in the model are categorical, except CEVE height.  Please note only the explanatory variables that contributed to reducing the error variability were retained in the model, the others were discarded.

 

MINITAB Output

 

General Linear Model: Crop Tree Diameter versus Stand, Transect within Stand,

    Aspect, CEVE, Location

 

Factor            Type Levels Values

Stand            fixed      9 610-014 640-024 640-036 640-124 645-129 650-190

                              655-002 655-007 660-003

Transect(Stand)  fixed     19 A A B C A A B C A B C A B C D E A A A

Aspect           fixed      8 N  NE E  SE S  SW W  NW

CEVE             fixed      2 absent  present

Location         fixed      3 Within  Edge  Outside

 

Analysis of Variance for Crop Tree Diameter, using Adjusted SS for Tests

 

Source            DF     Seq SS     Adj SS     Adj MS       F      P

Stand              8    18.4386    14.3988     1.7998    7.66  0.000

Transect(Stand)   10     6.6631     8.1745     0.8175    3.48  0.000

Aspect             7     5.4898     4.5522     0.6503    2.77  0.009

CEVE               1     0.9358     1.0919     1.0919    4.65  0.032

Location           2     2.8516     2.8516     1.4258    6.07  0.003

Error            178    41.8069    41.8069     0.2349

Total            206    76.1859 

 

Tukey Simultaneous Tests

Response Variable Crop Tree Diameter

All Pairwise Comparisons among Levels of CEVE                                 

 

CEVE = absent subtracted from:

 

Level       Difference       SE of             Adjusted

CEVE          of Means  Difference   T-Value    P-Value

present         0.2451      0.1137     2.156     0.0324

 

Tukey Simultaneous Tests

Response Variable Crop Tree Diameter

All Pairwise Comparisons among Levels of Location                                

 

Location = Within subtracted from:

 

Level         Difference       SE of             Adjusted

Location        of Means  Difference   T-Value    P-Value

Edge              0.2923     0.08415    3.4738     0.0019

Outside           0.1828     0.52700    0.3469     0.9358

 

Location = Edge subtracted from:

 

Level         Difference       SE of             Adjusted

Location        of Means  Difference   T-Value    P-Value

Outside          -0.1095      0.5188   -0.2110     0.9758

 

Conclusion regarding CEVE:

Based on the p-value (p=0.0324) for CEVE and Tukey’s simultaneous test, we can conclude that the average crop tree diameter is significantly greater where CEVE is present compared to where CEVE is absent.  The average crop tree diameter where CEVE is present is 1.546 inches, whereas the average crop tree diameter where CEVE is absent is 1.301 inches, a difference of 0.245 inches. 

 

Conclusion regarding Location:

Based on the p-value (p=0.0019) for Location and Tukey’s simultaneous test, we can conclude that the average crop tree diameter is significantly greater for crop trees located on the edge compared to crop trees located within.  The average diameter of crop trees located on the edge was 1.557 inches and the average diameter of crop trees located within was 1.265, a difference 0.292 inches.  The average crop tree diameter does not significantly differ for crop trees located outside versus edge or for crop trees located outside versus within.

 

Crop Tree Location

Within

Edge

Outside

Crop Tree Diameter  Mean (in.)

1.265

1.557

1.448

 

 

 

 

 

CROP TREE HEIGHT

 

An analysis was performed to determine if the average crop tree height is different in the presence versus absence of CEVE.  The crop tree height was used as the response (dependent) variable and CEVE and Location were the explanatory (independent) variables of interest where CEVE has two categories (present and absent) and Location has three categories (within, edge, and outside).  Stand, transect within a stand, slope, aspect, CEVE height, CEVE cover, shrub cover, and relevant interactions were also included in the model as explanatory variables to help reduce the error variability, which in turn allows for an easier detection of a CEVE significant difference.  All explanatory variables considered in the model are categorical, except CEVE height.  Please note only the explanatory variables that contributed to reducing the error variability were retained in the model, the others were discarded.

 

MINITAB Output

 

General Linear Model: Crop Tree Height versus Stand, Transect within Stand,

   Aspect, CEVE, Location

 

Factor            Type Levels Values

Stand            fixed      9 610-014 640-024 640-036 640-124 645-129 650-190

                              655-002 655-007 660-003

Transect(Stand)  fixed     19 A A B C A A B C A B C A B C D E A A A

Aspect           fixed      8 N  NE E  SE S  SW W  NW

CEVE             fixed      2 absent  present

Location         fixed      3 Within  Edge    Outside

 

Analysis of Variance for Crop Tree Height, using Adjusted SS for Tests

 

Source            DF     Seq SS     Adj SS     Adj MS       F      P

Stand              8     73.313     43.423      5.428    3.37  0.001

Transect(Stand)   10     53.450     50.395      5.039    3.13  0.001

Aspect             7     32.775     28.987      4.141    2.57  0.015

CEVE               1      6.868      7.194      7.194    4.46  0.036

Location           2      3.804      3.804      1.902    1.18  0.310

Error            180    290.170    290.170      1.612

Total            208    460.380

 

Tukey Simultaneous Tests

Response Variable Crop Tree Height  

All Pairwise Comparisons among Levels of CEVE                                 

 

CEVE = absent subtracted from:

 

Level       Difference       SE of             Adjusted

CEVE          of Means  Difference   T-Value    P-Value

present         0.6158      0.2915     2.113     0.0360

 

Conclusion regarding CEVE:

Based on the p-value (p=0.036) for CEVE and Tukey’s simultaneous test, we can conclude that the mean crop tree height is significantly greater where CEVE is present compared to where CEVE is absent.  The average crop tree height where CEVE is present is 4.499 feet, whereas the average crop tree height where CEVE is absent is 3.883 inches, a difference of 0.6158 inches. 

 

Conclusion regarding Location:

Based on the p-value (p=0.310) for Location, we can conclude that the mean crop tree height does not significantly differ among the locations (within, edge, outside).

 

 

CROP TREE LEADER

 

An analysis was performed to determine if the mean crop tree leader is different in the presence versus absence of CEVE.  The square root (SQRT) of the crop tree leader was used as the response (dependent) variable and CEVE and Location were the explanatory (independent) variables of interest where CEVE has two categories (present and absent) and Location has three categories (within, edge, and outside).  The assumption of the residuals being normally distributed was violated when the untransformed crop tree leader data was used.  The SQRT transformation was used to adequately resolve the violation of the normally distributed residuals assumption.  Stand, transect within a stand, slope, aspect, CEVE height, CEVE cover, shrub cover and relevant interactions were also included in the model as explanatory variables to help reduce the error variability, which in turn allows for an easier detection of a CEVE significant difference.  All explanatory variables in the model are categorical.  Please note only the explanatory variables that contributed to reducing the error variability were retained in the model, the others were discarded.

 

MINITAB Output

 

General Linear Model: SQRT Crop Tree Leader versus Stand, Transect within Stand,

   Slope, Aspect, CEVE, Location, Slope*CEVE, Aspect*CEVE

 

Factor            Type Levels Values

Stand            fixed      9 610-014 640-024 640-036 640-124 645-129 650-190

                              655-002 655-007 660-003

Transect(Stand)  fixed     19 A A B C A A B C A B C A B C D E A A A

Slope            fixed      4 < 10%     10% - 19% 20% - 29% > 30%   

Aspect           fixed      8 N  NE E  SE S  SW W  NW

CEVE             fixed      2 absent  present

Location         fixed      3 Within  Edge    Outside

 

Analysis of Variance for SQRT Crop Tree Leader, using Adjusted SS for Tests

 

Source            DF     Seq SS     Adj SS     Adj MS       F      P

Stand              8    13.9844     5.7649     0.7206    2.16  0.033

Transect(Stand)   10     4.6377     4.3323     0.4332    1.30  0.234

Slope              3     1.0303     0.6088     0.2029    0.61  0.610

Aspect             7     5.5040     1.9581     0.2797    0.84  0.556

CEVE               1     0.5707     1.4280     1.4280    4.29  0.040

Location           2     1.2820     1.7260     0.8630    2.59  0.078

Slope*CEVE         3     2.3287     2.5664     0.8555    2.57  0.056

Aspect*CEVE        7     4.0908     4.0908     0.5844    1.75  0.100

Error            166    55.2967    55.2967     0.3331

Total            207    88.7252 

 

 

Tukey Simultaneous Tests

Response Variable SQRT Crop Tree Leader

All Pairwise Comparisons among Levels of CEVE                                 

 

CEVE = absent subtracted from:

 

Level       Difference       SE of             Adjusted

CEVE          of Means  Difference   T-Value    P-Value

present         0.4457      0.2153     2.070     0.0400

 

Tukey Simultaneous Tests

Response Variable SQRT Crop Tree Leader

All Pairwise Comparisons among Levels of Location                               

 

Location = Within subtracted from:

 

Level         Difference       SE of             Adjusted

Location        of Means  Difference   T-Value    P-Value

Edge              0.2186      0.1012    2.1610     0.0811

Outside          -0.2215      0.6666   -0.3322     0.9410

 

Location = Edge subtracted from:

 

Level         Difference       SE of             Adjusted

Location        of Means  Difference   T-Value    P-Value

Outside          -0.4401      0.6568   -0.6700     0.7812

 

Conclusion regarding CEVE:

Based on the p-value (p=0.040) for CEVE and Tukey’s simultaneous test, we can conclude that the mean crop tree leader is significantly greater where CEVE is present compared to where CEVE is absent.  Unfortunately, estimates of the average crop tree leader cannot be generated due to the fact that back-transforming from the square root scale will not give a recognizable measure on the original scale.

 

Conclusion regarding Location:

Based on the p-value (p=0.078) for Location and Tukey’s simultaneous tests, we can conclude that the mean crop tree leader is significantly greater for crop trees located on the edge compared to crop trees located within.  The mean crop tree leader does not significantly differ for crop trees located outside versus edge or for crop trees located outside versus within.  Again, the average crop tree leader estimates cannot be calculated.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2:  This plot shows the interaction between CEVE and Slope.  Based on this data, the combination that maximizes the crop tree leader is CEVE present and <10% slope.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3:  This plot shows the interaction between CEVE and Aspect.  Based on this data, the combination that maximizes the crop tree leader is CEVE present and southeast aspect.

 

 

CROP TREE WHORL SUM

 

An analysis was performed to determine if the mean crop tree whorl sum is different in the presence versus absence of CEVE.  The natural log (LN) of the crop tree whorl sum was used as the response (dependent) variable and CEVE and Location were the explanatory (independent) variables of interest where CEVE has two categories (present and absent) and Location has three categories (within, edge, and outside).  The assumption of the residuals being normally distributed was violated when the untransformed crop whorl sum data was used.  The LN transformation was used to adequately resolve the violation of the normally distributed residuals assumption.  Stand, transect within a stand, slope, aspect, CEVE height, CEVE cover, shrub cover and relevant interactions were also included in the model as explanatory variables to help reduce the error variability, which in turn allows for an easier detection of a CEVE significant difference.  All explanatory variables in the model are categorical.  Please note only the explanatory variables that contributed to reducing the error variability were retained in the model, the others were discarded.

 

MINITAB Output

 

General Linear Model: LN Crop Tree Whorl Sum versus Stand, Transect within

   Stand, Aspect, CEVE, Location

 

Factor            Type Levels Values

Stand            fixed      9 610-014 640-024 640-036 640-124 645-129 650-190

                              655-002 655-007 660-003

Transect(Stand)  fixed     18 A A B C A A C A B C A B C D E A A A

Aspect           fixed      8 N  NE E  SE S  SW W  NW

CEVE             fixed      2 absent  present

Location         fixed      3 Within  Edge    Outside

 

Analysis of Variance for LN Crop Tree Whorl Sum, using Adjusted SS for Tests

 

Source            DF     Seq SS     Adj SS     Adj MS       F      P

Stand              8     2.9972     2.8403     0.3550    2.82  0.006

Transect(Stand)    9     3.1452     3.5920     0.3991    3.17  0.001

Aspect             7     2.8418     2.3845     0.3406    2.71  0.011

CEVE               1     0.5471     0.5972     0.5972    4.75  0.031

Location           2     0.0719     0.0719     0.0360    0.29  0.752

Error            173    21.7642    21.7642     0.1258

Total            200    31.3675 

 

Tukey Simultaneous Tests

Response Variable LN Crop Tree Whorl Sum

All Pairwise Comparisons among Levels of CEVE                                 

 

CEVE = absent subtracted from:

 

Level       Difference       SE of             Adjusted

CEVE          of Means  Difference   T-Value    P-Value

present         0.1835     0.08422     2.179     0.0307

 

Conclusion regarding CEVE:

Based on the p-value (p=0.0307) for CEVE and Tukey’s simultaneous tests, we can conclude that the average crop tree whorl sum is significantly higher where CEVE is present compared to where CEVE is absent. Again, regular averages cannot be calculated since the test was performed on the natural log scale.

 

Conclusion regarding Location:

Based on the p-value (p=0.752) for Location, we can conclude that the mean crop tree whorl sum does not significantly differ among the locations (within, edge, and outside).

 

 

 

 

ASSOCIATIONS BETWEEN CATEGORICAL VARIABLES
 
CROP TREE DOMINANCE and CEVE

 

A chi-square test was conducted to determine if the likelihood of a crop tree being considered dominant depended on whether or not CEVE was present.  The sub-dominant (SD) category was ignored because there were not enough occurrences to include it in the analysis.

 

MINITAB Output

 

Chi-Square Test: Crop Tree Dominance vs. CEVE

 

Expected counts are printed below observed counts

 

        absent  present    Total

    D       22      113      135

         21.14   113.86

 

   CD        9       54       63

          9.86    53.14

 

Total       31      167      198

 

Chi-Sq =  0.035 +  0.007 +

          0.076 +  0.014 = 0.131

DF = 1, P-Value = 0.717

 

Conclusion:

Based on the data, the proportion of conifers that were considered dominant is similar in the presence and absence of CEVE.

 

 

 

 

 

 

 

 

CROP TREE DOMINANCE and LOCATION

 

A chi-square test was conducted to determine if the likelihood of a crop tree being considered dominant depended on its location relative to the CEVE.  The sub-dominant (SD) category was ignored because there were not enough occurrences to include it in the analysis.

 

MINITAB Output

 

Chi-Square Test: Chi-Square Test: Crop Tree Dominance vs. Location

 

Expected counts are printed below observed counts

 

        Within     Edge  Outside    Total

    D       56       78       77      211

         71.58    75.30    64.12

 

   CD       40       23        9       72

         24.42    25.70    21.88

 

Total       96      101       86      283

 

Chi-Sq =  3.390 +  0.097 +  2.587 +

          9.933 +  0.283 +  7.582 = 23.871

DF = 2, P-Value = 0.000

 

Conclusion:

Based on the data, the proportion of conifers that were considered dominant depends on the crop tree’s location relative to the CEVE, where the conifers are more likely to be dominant on the outside and less likely to be dominant within.