Statistical Soil Moisture Analysis by hcj

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									Statistical Soil Moisture Analysis
Kelly Wilhelm and David Smith
    Statistical Methods (105)
           Project Report
            May 5, 2008
Introduction:
        Soil, the weathered remains of rocks and organic matter provides both faunal and floral
organisms a medium for ecological growth. A specific characteristic of soil is the pore space
between nodules of clay, silts and clastic rock grains that allow for percolation of water from
precipitation events. This critical attribute allows for the aqueous migration of nutrients to the
roots of plants which are processed as inputs into the biological cycle. Thus, soil moisture is
defined as the amount of water one can evaporate, by weight percent, of an original soil sample.
        Interestingly, soil moisture is highly variable and is influenced by many surface
characteristics included topography changes, slope declination, vegetation cover, and potentially
the amount of solar radiation received creating evaporative surface conditions. The focus of this
project is to find and statistically represent the variability of soil moisture content within the
grade of surface topography. Our goal is to analyze the changes in soil moisture content on three
sections of a hill: summit, slope and foot (see figure 1). Then repeat the sampling system and
compare the three sections between an east facing and west facing slopes for statistical
differences (see figure 2).


       [ Figure 1]

                                                               East Facing Hill
                                                                Sample Field
                        Summit



          Slope

                                                                         Transect
       Base                                                                Line
       [ Figure 2 ]




     West Facing Slope




                                                                       East
                                                                       Facing
                                                                       Slope




Methods:
        Initially, two hills were selected for having similar characteristics of slope, vegetation
cover, area and height, but varying in the overall facing direction of East and West (Figure 2). In
order to complete a survey, transect methods of stratified random sampling were implemented.
For each hill, a transect line from summit to base was selected for have traits of smooth surface
transitions and lack of visible disturbance in surface flow down a slope (White line in figure 1).
Samples collected were measured in a fifty foot by fifty foot square (the three locations in figure
1) area of sampling. For the three sampling locations found on a hill, fifteen samples were
chosen to be collected. For each sample the program Microsoft Excel was used to randomly
select the length down the transect line, whether to sample on the left or right side of the transect,
and the overall width away from the transect. An example or our stratified random sample
output can be seen in table 1.
         At each selected location a soil auger was used to extract the sample. The soil samples were
subsequently labeled and stored in individual sandwich bags for further processing and to prevent
evaporation of moisture. Since a direct measure of moisture in the soil is not possible, using a
precise scale we measured the original sample weight, then evaporate all water, and re-measure the
dried sample. Evaporation was accomplished by cooking the samples at 450 degrees for 8 hours.
The potential weight difference will indicate how much moisture was evaporated from each sample
as found in table 2 (appendix).
[ Table 1 ]

           West Facing [Slope]                                   East Facing [Slope]
Sample #    Length Right/Left      Width              Sample #    Length Right/Left      Width
   1          10          R         11                   1            1         R          0
   2           5          L          1                   2           22         R          5
   3          27          R         24                   3           10         R          4
   4          40          R          6                   4            6          L         7
   5          50          R          8                   5           20         R          9
   6          35          L         17                   6            2         R          3
   7          11          R         22                   7           19          L         1
   8           4          R          4                   8           20          L         0
   9          30          L          2                   9           21          L         3
  10          21          L          2                  10           14         R          3
  11           2          L         24                  11           25         R         19
  12          33          L         11                  12            8          L        11
  13           2          R          2                  13           17         R          5
  14          49          R          7                  14            4          L        15
  15           3          R         13                  15           23          L        20

Statistical Analysis:
        The soil sampling analysis was conducted under the hypothesis of finding differences in
variability of soil moisture content within the grade of surface topography. Our initial
hypothesis was to find variation within the three sections of a hill. This occurs as precipitation
follows topography from high to low regions. High gradation of slopes significantly decreases
the moisture holding capacity of the soil therefore yielding potential differences. Therefore, the
mean soil moisture of samples collected from the summit, slope and base of a hill will potentially
have statistically significant differences. This is represented by our Hypothesis:

                                    Ho: µtop = µslope = µbase
                                    Ha: µtop ≠ µslope ≠ µbase

         Another interesting statistical analysis would be the variability of soil moisture content
within topography regions between two similar hills. Thus, by measuring the aforementioned
regions in two hills, a statistical comparison of variation could be made to find a potential
statistical difference between facing hills. This is stated by our second hypothesis:

                    Ho: µtop1 = µtop2: µslope1 = µslope2: µbase1 = µbase2
                    Ha: µtop1 ≠ µtop2: µslope1 ≠ µslope2: µbase1 ≠ µbase2

        The analyses will be entered through SAS statistical software. Initially, means procedure
and box plot will be utilized for an overall statistical analysis. To find statistical differences
between east and west facing locations and compiled means individual t tests will be conducted.
For the comparison of multiple individual location means, ANOVA statistical analysis will be
used to find the variance for more than two means. Tests of regression will be utilized. as
evidence for potential sampling biasness.
                                                                                         [ Table 3 ]
                                        The MEANS Procedure
                                      Analysis Variable : pwet

                                                          Lower 95%   Upper 95%
      hill     Obs N      Mean      Median     Std Dev   CL for Mean CL for Mean    Variance
     _______________________________________________________________________________________
     EastBase 15 15 0.0026350 0.0025980 0.000721298        0.0022355 0.0030344 5.2027049E-7

     EastSlop   15 15   0.0026373   0.0025305   0.000677979   0.0022619   0.0030128   4.5965512E-7

     EastTop    15 15   0.0028267   0.0029243   0.000727137   0.0024240   0.0032294   5.2872833E-7

     WestBase   15 15   0.0021408   0.0022641   0.000434937   0.0018999   0.0023816   1.8917028E-7

     WestSlop   15 15   0.0023937   0.0022049   0.000683253   0.0020154   0.0027721   4.6683402E-7

     WestTop    15 15   0.0025823   0.0025526   0.000539567   0.0022835   0.0028811   2.9113221E-7


Statistical Results:
Means Procedure
        To begin, the analysis from the proc means procedure yielded data that supports the use
of two independent t tests and ANOVA. The data collected is represented by a simple random
sample, all sample locations have the same amount of sample individuals as well. The standard
deviations do not display a high level of variance which ranges from .00043 to .00072. Thus, the
largest standard deviation is smaller than twice the smallest sample standard deviation yielding a
ration of 1.67 which is less than 2. This is a great indication for the data being in compliance
with the rules that satisfy ANOVA. The overall dataset does not appear to have significant
outliers as the mean and median of all samples are approximately equal with little variance. This
data indicates the satisfaction of rules regarding two-sample t procedures and ANOVA statistical
analysis at an alpha level of .05.

Box Plots
         The Slope Location Box plot (appendix Figure 3) displays a comparison of the weight
percent of water for each section of the hills. The analysis required the hill classification: Top,
Slope, and Base. Since there were two hills made for a total of six box plots – three for each of
the two hills. The mean for the weight percent of water was fairly homogenous throughout each
sample; the means ranged from only 0.23%-0.29%. The sample homogeneity is unexpected
since the water should percolate down to the bottom over time. The hill Top is displayed as
contained the largest water weight percent for each individual hill (east or west alone), followed
by Bottom, and slope always contained the least weight percent water. The data
         The East v West Box plot (appendix Figure 4) displays a comparison of the percent of
water was within each sample for all samples between each hill. The mean percent water weight
for the East facing hill was a bit more than 0.25%, while the mean percent water weight for the
West facing hill was slightly less than 0.25%. The near identical mean for the two hills is not
surprising since they were hills of similar slope, thus the same forces should have acted on both.
The East facing hill had a wider range of water weight percentages compared to the West facing
hill, but was generally not different from the West facing hill. The spread of the box plots
satisfies the requirement for two-sample t producers to have equal populations and distributions
in shape.
T-test – Statistical Analysis Tops
        The first t test table (appendix table 4) displays the confidence limits of the mean and
standard deviations between the East and West facing Top locations, and the difference between
the two. The confidence interval for the difference in means is (-0.00023, 0.0007), and the
confidence interval for the difference in standard deviation between the two slopes is (0.0006,
0.0009). With 44 degrees of freedom the p value was 0.2763, much less than the F value of 1.82.
This indicates that the null cannot be rejected; although it does not prove the null either.

t-Test – Slopes:
        The second t test table (appendix table 5) displays the confidence limits of the mean and
standard deviations between the East and West facing Slope locations, and the difference
between the two. The confidence interval for the difference in means is (-0.00027, 0.0008), and
the confidence interval for the difference in standard deviation between the two slopes is
(0.0005, 0.0009). With 44 degrees of freedom the p value was 0.9773, slightly less than the F
value of 1.02. This indicates that the null cannot be rejected; although it does not prove the null
either.

t-Test – Bases:
        The third t test table (appendix table 6) displays the confidence limits of the mean and
standard deviations between the East and West facing Base locations, and the difference between
the two. The confidence interval for the difference in means is (0.0000487, 0.0009), and the
confidence interval for the difference in standard deviation between the two slopes is (0.0005,
0.0008). With 44 degrees of freedom the p value was 0.0684, much less than the F value of 2.75.
This indicates that the null cannot be rejected; although it does not prove the null either.

t-Test - East versus West Total Slope:
         The fourth t test table (appendix table 7) displays the confidence limits of the mean and
standard deviations between the all the samples of each the East and West facing hills, and the
difference between the two. The confidence interval for the difference in means is (0.0000586,
0.0006), and the confidence interval for the difference in standard deviation between the two
slopes is (0.0006, 0.0008). With 44 degrees of freedom the p value was 0.2148, much less than
the F value of 1.46. This indicates that the null cannot be rejected; although it does not prove the
null either.

ANOVA statistical test:
        In order to avoid multiple P-values of lone tests in comparing the six sample areas,
ANOVA was selected to find the differences in parameters of soil moisture means per location.
The box plots help to indication a normal distribution of independent simple random samples,
and identical sample populations per location collected help to reduce and increase the
robustness of the ANOVA analysis. Our original null hypothesis stated no difference between
the means of the top, slope and base. The resulting F-value of 2.08 (appendix table 8) indicates a
value relatively close to 0 thus indicating support for the null hypothesis of the population means
being similar. The total sample collection contained 90 observations from six sample locations
producing 84 degrees of freedom. The completed result of the F-test produced a value of 2.09
with a p value of .0765. Thus, by finding the F distribution critical value with a numerator of 5
and a denominator of 84 the resulting p value is approximately 2.34. Thus, pr >F gives evidence
that the null hypothesis cannot be rejected at the alpha level of 0.05. Being that the F-test is not
significant at 0.05, the individual t-tests of the Bonferroni Correction also displayed each hill
sample location as supporting the null hypothesis without findings of significant differences, as
indicated by the same character value for all locations.

Project Conclusions:
        While the original alternative hypothesis indicated a significant change in the soil
moisture levels based on topography, our final statistical conclusions indicate that at a
significance of 0.05 the multiple t-tests and ANOVA conclude in finding no significant
differences. Thus, the experiment confirms the null hypothesis that the means within slopes and
between two independent hills have approximately the same means at an alpha of 0.05. Though,
the null hypothesis could not be rejected throughout the sampling process, there where many
indications of potential experimental errors, and alterations that would potentially help similar
studies.
        The distribution of the box plots for each individual hill hints at the potential of soil
composition differences. The variation of clay and silts throughout the soil profile and sampling
location can have a dramatic effect on moisture. Clay, having hydrophobic and soil moisture
retention properties, could dramatically decrease the amount of water entrance into the soil. This
could lead to precipitation creating overland flow without percolation into the ground. This
would also allow water to flow on the slopes, and bases and potentially causing similarities in
soil moisture means. In future analyses, the variable of overall soil composition should be
collected and used for statistical comparisons.
        Ideally, more consistent sampling protocol should have been utilized, though time
constraints prevented this in our research. Throughout, the sample procedure taking similar
lengths of soil core was inhibited as varying moisture and soil consolidation made collecting
similar masses unfeasible for our timeframe. One of our overall conclusions is that ground
locations were the soil moisture seemed low yielded samples of lower mass. Also, that sample
locations of extreme surface wetness, samples were surprisingly easy to collect, producing larger
sample cores from the saturated soil. In order to examine potential sampling errors in collecting
a regression analysis was used to examine statistical correlation of the original sample weight
and the percentage of moisture evaporated from the samples and can be found in (figure 5).
        This regression compares the starting weight of a sample to the same sample’s
evaporated water weight. The regression line was negative and had a moderately strong
correlation (R Squared = .7789). It is surprising that that regression line was negative, because
that means that as a sample became larger, a smaller total percentage of water was evaporated.
We expected that even as the weight increased, the overall percentage of water would stay
consistent. A possible reason for the smaller samples having larger percents of water weight is
that the smaller samples could have been from the slopes, which were more soil rich and could
not hold as much water as the more clay rich base and top; so this regression could be showing
differences in sample composition. The second surprising fact about this scatter plot is that it
had such a moderately strong correlation, with a R square of 0.78, it is difficult to deny that there
is a correlation between starting weight and weight percent water. The reason for this
moderately strong correlation is likely caused by the same compositional differences that created
the negative slope.
 pwet                   -   ei
        = 0. 0049 - 238E 7 w ght
   0. 0045
                                                                           Another graphical [ Figure 5 ]                 N
                                                                                                                          90
                                                                                                                          Rsq


   0. 0040
                                                                   representation of our soil                             0. 7814
                                                                                                                           dj sq
                                                                                                                          A R

                                                                   sampling can be found in the                           0. 7789
                                                                                                                           ME
                                                                                                                          R S
                                                                                                                          0. 0003


   0. 0035
                                                                   regression analysis of percent
                                                                   of soil moisture and the overall
   0. 0030
                                                                   change in soil mass from
                                                                   collection to evaporation. This
   0. 0025
                                                                   regression was preformed to
                                                                   examine for potential
   0. 0020
                                                                   correlation between soil sample
                                                                   mass loss and the percentage of
   0. 0015
                                                                   water loss from the samples.
                                                                   The results (Figure 6) yielded
   0. 0010
                                                                   absolutely no correlation
              60        70        80        90        100          between the two factors, being
                                                                 110        120       130       140       150       160

                                                                ei
                                                                   as the R squared statistic is
                                                               w ght



<0.0002. This can be contributed to the nature of weight lost was almost always falling between
20 and 28 grams. With this plot a great visual representation of the variability of sample weight
loss from evaporation.

    pwet                          ei
             = 0. 0026 - 0. 0004 w ght
        0. 0045
                                                                                                     [ Figure 6 ]                  N
                                                                                                                                   90
                                                                                                                                   Rsq
                                                                                                                                   0. 0002


        0. 0040
                                                                                Finally, the time                                    dj sq
                                                                                                                                   A R
                                                                                                                                   - . 0111

                                                                        constraints also made our                                   ME
                                                                                                                                   R S
                                                                                                                                   0. 0007

                                                                        sampling schedule fall 1.5
        0. 0035
                                                                        days after heavy rainstorms
                                                                        in the area. Thus, the time
        0. 0030                                                         needed from the last rain
                                                                        fall event to find statistical
                                                                        differences in soil moisture
        0. 0025
                                                                        may need to be increase to
                                                                        allow for surface processes
        0. 0020
                                                                        to influence soil moisture.
                                                                        Though with the idealized
        0. 0015
                                                                        set of sampling procedures,
                   0. 100    0. 125    0. 150    0. 175     0. 200      we believe significant
                                                                       0. 225     0. 250    0. 275    0. 300    0. 325    0. 350

                                                                      ei
                                                                        difference can be found to
                                                                     w ght



reject the null hypothesis, and perhaps a better understanding of hill surface features could be
explained.
Appendix




  Top Left – Kelly displaying our transect stratified random sample procedure.

  Top Right - An example of our soil weighing procedure.

  Bottom – All 90 samples placed in an oven at 450°F for 8 hours.
                                             [ Table 1 ]


 Facing                 % Soil    Original   Differ        West   Top     0.0017   136.62   0.225
Direction   Location   moisture   Weight     ence
  East        Top       0.0033     67.64     0.236         West   Top     0.0024   101.99   0.244
 East         Top       0.0035     69.11     0.246         West   Top     0.0031   79.78    0.221

 East         Top       0.0024     90.74     0.246         West   Top     0.0026   91.84    0.214
 East         Top       0.0017     128.5     0.234         West   Top     0.0025   100.39   0.238
 East         Top       0.0037     65.13     0.254         West   Top     0.0026    93.1    0.225
 East         Top       0.0017    128.88     0.242         West   Top     0.0026   90.15    0.23

 East         Top       0.0023    100.54     0.234         West   Top     0.003    85.21    0.234
 East         Top       0.0031     76.13     0.252         West   Top     0.0024   96.84    0.258
 East         Top       0.0042     62.06     0.233         West   Top     0.0018   119.3    0.229
 East         Top       0.0029     78.39     0.219         West   Top     0.0018   119.38   0.222

 East         Top       0.0019    117.58     0.218         West   Top     0.0036   68.32    0.239

 East         Top       0.0027     88.67     0.247         West   Top     0.0031   78.75    0.214
 East         Top       0.003      72.3      0.247         West   Top     0.0023   108.54   0.234
 East         Top       0.0033     70.34     0.254         West   Top     0.0031   76.33    0.254

 East         Top       0.0027     93.51     0.239         West   Slope   0.0031   76.35    0.242
 East        Slope      0.0022    112.66     0.233         West   Slope   0.0015   156.94   0.23
 East        Slope      0.0034     68.54     0.234         West   Slope   0.0033   70.75    0.258
 East        Slope      0.002     130.69     0.234         West   Slope   0.0028    82.6    0.225

 East        Slope      0.0031      73       0.233         West   Slope   0.0017   143.32   0.113
 East        Slope      0.0016     68.59      0.24         West   Slope   0.0022   125.65   0.274
 East        Slope      0.0024    116.06     0.277         West   Slope   0.0037   62.26    0.247
 East        Slope      0.0025     98.35     0.233         West   Slope   0.0016   152.65   0.242

 East        Slope      0.0029     82.44     0.247         West   Slope   0.0026   90.24    0.241
 East        Slope      0.0017    141.43     0.238         West   Slope   0.0025   93.61    0.253
 East        Slope      0.0029     86.55     0.229         West   Slope   0.003    81.39    0.231
 East        Slope      0.0025     91.39     0.244         West   Slope   0.0016   143.6    0.243
 East        Slope      0.0031     78.86     0.231         West   Slope   0.0021   112.91   0.229
 East        Slope      0.0025     90.64     0.235         West   Slope   0.0021   116.49   0.243
 East        Slope      0.0025     97.61     0.249         West   Slope   0.0021   121.26   0.344
 East        Slope      0.0043     80.55     0.252         West   Base    0.0023   107.9    0.255
 East        Base       0.002     128.95     0.246         West   Base    0.0017   133.1    0.249
 East        Base       0.0037     67.63     0.225         West   Base    0.0017   122.33   0.259
 East        Base       0.0033     77.3      0.208         West   Base    0.0025   86.25    0.291
 East        Base       0.0028    105.21     0.212         West   Base    0.0016   131.33   0.239

 East        Base       0.0019    128.53     0.207         West   Base    0.0028   81.69    0.238
 East        Base       0.0018    135.68     0.228         West   Base    0.0019   109.63   0.253
 East        Base       0.0036     70.02     0.212         West   Base    0.0023    91.4    0.258
 East        Base       0.0028     92.4      0.214         West   Base    0.0017   124.3    0.266

 East        Base       0.0036     73.54      0.21         West   Base    0.0023   96.17    0.234

 East        Base       0.0022    104.55     0.218         West   Base    0.0025   95.95    0.252
 East        Base       0.0026     97.05     0.237         West   Base    0.0026   85.33    0.238
 East        Base       0.0016     151.8     0.219         West   Base    0.002    117.43   0.241

 East        Base       0.0021    113.47     0.237         West   Base    0.0028   79.53    0.276

 East        Base       0.0032     86.53     0.222         West   Base    0.0015   146.12   0.262
 East        Base       0.0024    108.26     0.226
  0. 0045
                                                                                    [ Figure 3 ]

  0. 0040




  0. 0035




p
w
  0. 0030
e
t




  0. 0025




  0. 0020




  0. 0015

               East Top   E     l
                           ast S op          East Base            West Top   W     l
                                                                              est S op     West Base

                                                         hi l l




            0. 0045

                                                                                    [ Figure 4 ]

            0. 0040




            0. 0035




       p
       w
         0. 0030
       e
       t




            0. 0025




            0. 0020




            0. 0015

                                      East                                   West

                                                             f ace
  [ Table 4 ]

hill=Top t Test
The TTEST Procedure
                                                    Statistics
                               Lower CL             Upper CL Lower CL                Upper CL
Variable       face        N       Mean     Mean        Mean   Std Dev   Std Dev      Std Dev   Std Err
pwet           East       15     0.0024   0.0028      0.0032    0.0005    0.0007       0.0011    0.0002
pwet           West       15     0.0023   0.0026      0.0029    0.0004    0.0005       0.0009    0.0001
pwet           Diff (1-2)        -23E-5   0.0002      0.0007    0.0005    0.0006       0.0009    0.0002
                                                      T-Tests
                  Variable       Method             Variances      DF      t Value     Pr > |t|
                  pwet           Pooled             Equal          28         1.05       0.3049
                  pwet           Satterthwaite      Unequal      25.8         1.05       0.3056


                                                Equality of Variances
                      Variable       Method         Num DF    Den DF     F Value     Pr > F
                      pwet           Folded F           14        14        1.82     0.2763




 [ Table 5 ]

hill=Slope
The TTEST Procedure
                                                     Statistics
                                     Lower CL             Upper CL Lower CL               Upper CL
Variable       face        N        Mean    Mean         Mean    Std Dev Std Dev      Std Dev Std Err
pwet           East       15      0.0023 0.0026       0.003     0.0005   0.0007      0.0011   0.0002
pwet           West       15      0.002 0.0024        0.0028    0.0005   0.0007      0.0011   0.0002
pwet           Diff (1-2)         -27E-5 0.0002       0.0008    0.0005   0.0007      0.0009   0.0002

                                                      T-Tests
                  Variable       Method             Variances      DF      t Value     Pr > |t|
                  pwet           Pooled             Equal          28         0.98       0.3355
                  pwet           Satterthwaite      Unequal        28         0.98       0.3355

                                                Equality of Variances
                      Variable       Method         Num DF    Den DF     F Value     Pr > F
                      pwet           Folded F           14        14        1.02     0.9773
 [ Table 6 ]

hill=Base
The TTEST Procedure
                                                     Statistics
                                    Lower CL              Upper CL Lower CL             Upper CL
Variable       face        N       Mean    Mean          Mean   Std Dev Std Dev     Std Dev Std Err
pwet           East       15     0.0022 0.0026          0.003    0.0005  0.0007      0.0011   0.0002
pwet           West       15     0.0019 0.0021         0.0024    0.0003  0.0004      0.0007   0.0001
pwet           Diff (1-2)        487E-7 0.0005         0.0009    0.0005  0.0006      0.0008   0.0002

                                                      T-Tests
                  Variable       Method             Variances      DF     t Value     Pr > |t|
                  pwet           Pooled             Equal          28        2.27       0.0309
                  pwet           Satterthwaite      Unequal        23        2.27       0.0327

                                                Equality of Variances
                      Variable       Method         Num DF    Den DF    F Value     Pr > F
                      pwet           Folded F           14        14       2.75     0.0684




 [ Table 7 ]

East and West facing mean comparison
The TTEST Procedure
                                                     Statistics
                               Lower CL            Upper CL Lower CL              Upper CL
Variable/face    N               Mean   Mean          Mean   Std Dev Std Dev      Std Dev Std Err
pwet East       45             0.0025 0.0027        0.0029    0.0006  0.0007       0.0009  0.0001
pwet West       45             0.0022 0.0024        0.0025    0.0005  0.0006       0.0007  0.0001
pwet Diff (1-2)                586E-7 0.0003        0.0006    0.0006  0.0006       0.0008  0.0001

                                                      T-Tests
                  Variable       Method             Variances      DF     t Value     Pr > |t|
                  pwet           Pooled             Equal          88        2.42       0.0176
                  pwet           Satterthwaite      Unequal        85        2.42       0.0176

                                                Equality of Variances
                      Variable       Method         Num DF    Den DF    F Value     Pr > F
                      pwet           Folded F           44        44       1.46     0.2148
[ Table 8 ]

The ANOVA Procedure           Class Level Information

          Class         Levels    Values
          hill               6    EastBase EastSlop EastTop WestBase WestSlop WestTop
                            Number of Observations Read          90
                            Number of Observations Used          90
Dependent Variable: pwet
                                              Sum of
      Source                      DF         Squares     Mean Square    F Value    Pr > F
      Model                        5      0.00000425      0.00000085       2.08    0.0765
      Error                       84      0.00003438      0.00000041
      Corrected Total             89      0.00003863

                       R-Square         Coeff Var    Root MSE    pwet Mean
                       0.109947          25.22755    0.000640     0.002536

      Source                       DF          Anova SS    Mean Square   F Value   Pr > F
      hill                          5      4.2470571E-6   8.4941141E-7      2.08   0.0765

                               Bonferroni (Dunn) t Tests for pwet

 NOTE: This test controls the Type I experimentwise error rate, but it generally has a
higher
                                 Type II error rate than REGWQ.

                            Alpha                              0.05
                            Error Degrees of Freedom             84
                            Error Mean Square              4.093E-7
                            Critical Value of t             3.02146
                            Minimum Significant Difference   0.0007

                  Means with the same letter are not significantly different.
                   Bon Grouping          Mean      N    hill

                               A        0.0028267    15   EastTop
                               A
                               A        0.0026373    15   EastSlope
                               A
                               A        0.0026350    15   EastBase
                               A
                               A        0.0025823    15   WestTop
                               A
                               A        0.0023937    15   WestSlope
                               A
                               A        0.0021408    15   WestBase
data soilwet;
input face$ hill$ pwet mass change;
datalines;
East     Top       0.003326653      67.64    0.23561704
East     Top       0.003530009      69.11    0.245514266
East     Top       0.002439958      90.74    0.245675608
East     Top       0.001667853      128.5    0.234429443
East     Top       0.003656366      65.13    0.253909752
East     Top       0.001748941      128.88   0.241568206
East     Top       0.002292178      100.54   0.233721575
East     Top       0.003076378      76.13    0.251731017
East     Top       0.004159479      62.06    0.233064849
East     Top       0.002924332      78.39    0.21860855
East     Top       0.001887153      117.58   0.217540627
East     Top       0.002691301      88.67    0.24721897
East     Top       0.002953729      72.3     0.247492063
East     Top       0.003328809      70.34    0.254376267
East     Top       0.002717255      93.51    0.23922442
East     Slope 0.002151702          112.66   0.23313687
East     Slope 0.003354811          68.54    0.234484516
East     Slope 0.001972497          130.69   0.234204947
East     Slope 0.003085007          73       0.233414044
East     Slope 0.001647328          68.59    0.240440971
East     Slope 0.002360815          116.06   0.277039395
East     Slope 0.002508084          98.35    0.232733697
East     Slope 0.002941283          82.44    0.246708156
East     Slope 0.001704792          141.43   0.237588652
East     Slope 0.002928886          86.55    0.229462664
East     Slope 0.00253109           91.39    0.244010321
East     Slope 0.003082539          78.86    0.231337047
East     Slope 0.002530549          90.64    0.234611638
East     Slope 0.002486431          97.61    0.248776719
East     Slope 0.004273845          80.55    0.252102919
East     Base      0.001975571      128.95   0.245783133
East     Base      0.00367964       67.63    0.224643125
East     Base      0.003345444      77.3     0.207716832
East     Base      0.002767152      105.21   0.211942029
East     Base      0.001857147      128.53   0.207188
East     Base      0.001752398      135.68   0.228424532
East     Base      0.00361834       70.02    0.212076986
East     Base      0.002788788      92.4     0.213785558
East     Base      0.003611229      73.54    0.210297667
East     Base      0.002240478      104.55   0.21773942
East     Base      0.002598022      97.05    0.236685774
East     Base      0.001570092      151.8    0.21938357
East     Base      0.002119539      113.47   0.236821936
East     Base      0.003185334      86.53    0.221803093
East     Base      0.002415482      108.26   0.225636463
West     Top       0.001724616      136.62   0.225014784
West     Top       0.002407239      101.99   0.243958906
West     Top       0.003079413      79.78    0.221401807
West     Top       0.002552585      91.84    0.214319066
West     Top       0.002529234      100.39   0.238139106
West     Top       0.002594718      93.1     0.225403476
West     Top       0.002592585      90.15    0.23045554
West     Top       0.002954243      85.21    0.23420465
West     Top      0.0024067        96.84    0.258137286
West     Top      0.001832427      119.3    0.229238423
West     Top      0.001822254      119.38   0.221891478
West     Top      0.003618545      68.32    0.238637645
West     Top      0.003142756      78.75    0.213554633
West     Top      0.002343618      108.54   0.234148422
West     Top      0.003134081      76.33    0.254090472
West     Slope 0.003053528         76.35    0.242410794
West     Slope 0.001494103         156.94   0.229938722
West     Slope 0.003310317         70.75    0.2577856
West     Slope 0.002825836         82.6     0.225205479
West     Slope 0.001677651         143.32   0.112990232
West     Slope 0.00220485          125.65   0.273996209
West     Slope 0.003738093         62.26    0.246670056
West     Slope 0.001616169         152.65   0.242479379
West     Slope 0.002632853         90.24    0.241108676
West     Slope 0.002451262         93.61    0.25349509
West     Slope 0.002998038         81.39    0.231316337
West     Slope 0.001610982         143.6    0.243089019
West     Slope 0.002077864         112.91   0.229368932
West     Slope 0.002135606         116.49   0.242700543
West     Slope 0.002079028         121.26   0.344258225
West     Base     0.002277879      107.9    0.254749903
West     Base     0.001687777      133.1    0.248854059
West     Base     0.001698004      122.33   0.258602846
West     Base     0.002457299      86.25    0.291132022
West     Base     0.001577614      131.33   0.238699136
West     Base     0.002796236      81.69    0.23776533
West     Base     0.001934479      109.63   0.253356184
West     Base     0.00233901       91.4     0.257683983
West     Base     0.001691856      124.3    0.265569758
West     Base     0.00226411       96.17    0.234241989
West     Base     0.002466762      95.95    0.252138073
West     Base     0.002571002      85.33    0.238339921
West     Base     0.002016707      117.43   0.240504098
West     Base     0.002788924      79.53    0.27562695
West     Base     0.001544186      146.12   0.261500092
;
run;
proc sort data = soilwet ;
by hill;
run ;

proc ttest data = soilwet;
class face;
var pwet;
by hill;
run;
proc ttest data=soilwet;
class face;
var pwet;
run;

proc reg data = soilwet;
model pwet = mass;
plot pwet * mass / symbol = '.';
run;

proc reg data = soilwet;
model pwet = change;
plot pwet * change / symbol = '.';
run;

proc means data=soilwet n mean median std clm alpha = .05 var;
 class hill;
 var pwet;
run;
proc sort data=soilwet;
 by hill*face;
run;
proc boxplot data=soilwet;
 plot pwet*hill / boxstyle=schematic boxwidth=10;
run;
proc boxplot data = soilwet;
plot pwet*face / boxstyle=schematic boxwidth=10;
run;

proc sort data = soilwet ;
by hill ;
run ;
proc means data = soilwet ;
by hill ;
var pwet ;
run ;
proc anova data = soilwet ;
class hill ;
model pwet = hill ;
run ;
proc anova data = soilwet ;
class hill ;
model pwet = hill ;
means hill / bon alpha = .05 ;
run ;

								
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