There were 133 sites on the
Southern Ute Reservation with enough data to permit analysis by the
T-Test. At every significance level,
there were many more sites showing change (both upward and downward trends) in
measured CH4 than could be explained by chance. For example, at the 95% level, 92 of the 133
sites showed a significant trend. The
probability of this happening by chance, assuming that CH4 levels at
the sites were independent and fluctuating randomly, is microscopically
small—less than 10
At every significance level,
sites showing an increase outnumbered sites showing a decrease by a wide
margin. At the 95% significance level,
there were 61 sites with increasing CH4 and 31 sites with decreasing
CH4. The probability of
this happening by chance, if we expected half the sites to be increasing and
half to be decreasing, would be about 0.001.
The tests using Sen’s
estimator and the Mann-Kendall statistic confirmed the results of the T-test,
with even greater disparity between the numbers of increasing and decreasing
sites.
Despite the predominance of
upward-trending sites, the number of downward-trending sites on the reservation
is also significant, and far more than can be explained by chance alone. Any explanation of soil vapor trends at
these sites must account for the surprisingly large numbers of both upward and
downward trending sites. Computing the
chi-squared test for homogeneity of the Mann-Kendall statistics shows that the
probability of a uniform trend across all sites is very nearly zero.
For reasons discussed in the
next section, the T-test was repeated using the logarithm of the observed CH4
levels in place of the observed CH4 , at both reservation and
non-reservation sites. Results were
almost identical. Results for CH4 levels
and their logarithms, at reservation sites, are summarized in Tables 1–3. The
logarithmic transformation was not necessary for the Mann-Kendall and Sen
tests, since these effectively consider only the direction and not the
magnitude of changes.
Table 1. Summary of T-Test
results, CH4_LEL for 133 sites on the Southern Ute Reservation.
|
Significance Level |
U
Number
of Sites with Upward Trend |
D
Number
of Sites with Downward Trend |
U+D
Number
of Sites with Any Trend |
Expected
Number of Sites with Any Trend |
Probability
of U out of U+D Sites Increasing (see
Note 1) |
Probability
of U+D Sites with Any Trend (see
Note 2) |
|
99.9% |
32 |
5 |
37 |
0 |
3.71E-06 |
9.92E-79 |
|
99.0% |
54 |
14 |
68 |
1 |
5.55E-07 |
3.82E-98 |
|
95.0% |
61 |
31 |
92 |
7 |
1.16E-03 |
9.02E-87 |
Table 2. Summary of T-Test
results, log(CH4_LEL) for 133 sites on
the Southern Ute Reservation.
|
Significance Level |
U
Number
of Sites with Upward Trend |
D
Number
of Sites with Downward Trend |
U+D
Number
of Sites with Any Trend |
Expected
Number of Sites with Any Trend |
Probability
of U out of U+D Sites Increasing (see
Note 1) |
Probability
of U+D Sites with Any Trend (see
Note 2) |
|
99.9% |
31 |
6 |
37 |
0 |
2.06E-05 |
9.92E-79 |
|
99.0% |
56 |
7 |
63 |
1 |
6.82E-11 |
3.13E-88 |
|
95.0% |
63 |
10 |
73 |
7 |
7.77E-11 |
2.04E-58 |
Table 3. Sen and Mann-Kendall
statistics, CH4_LEL for 183 sites on
the Southern Ute Reservation.
|
Significance Level |
Sites
with Positive Sen estimator |
Sites
with Negative Sen
estimator |
Sites with Positive Mann-Kendall statistic
|
Sites
with Negative Mann-Kendall statistic |
|
99.0% |
55 |
12 |
52 |
7 |
|
95.0% |
66 |
17 |
61 |
10 |
Chi-square estimate of
homogeneity for the Mann-Kendall scores: less than 0.0001%