Geoscience Reference
In-Depth Information
0.5
0.4
0.3
0.2
0.1
1995
1997
1999
2001
2003
2005
Study Ye ar
FIGURE 11.2
Side-by-side box plots of mercury concentration levels for which the spread in each box cor-
responds to the variability in concentrations across the stations for each study year.
y
−
−
y
2006
1995
~
t
11
,
(
)
se y
y
2006
1995
where
y
2006
and
y
1995
d
e
note the average measurements from 2006 and 1995,
respectively;
(
)
se y
−
y
2006 1995
represents the estimated standard error of the
difference in the measurements; and
~
11
denotes the fact that the test sta-
tistic follows a
t
distribution with 11 degrees of freedom. The test statistic is
t
= 3.81 with a
p
value of 0.0021, showing that the average mercury concentra-
tion was significantly greater in the final year of the study than it was at the
beginning of the study. The observed mean difference in mercury concentra-
tion, comparing 2006 to 1995, is 0.1480 ppm.
Another approach for comparing two time points would be to take the
differences in the measurements across the time points and then bootstrap
the differences to obtain a confidence interval on the difference in average
part-per-million levels. The bootstrap approach is a modern nonparametric
computational approach and is easily accomplished through a variety of sta-
tistical software packages. For more details on this method, see the work of
Manly (2007).
At this point, the graphics considered indicate that mercury concentrations
appear to be trending upward over time, and the paired
t
analysis makes it
possible to compare the values at any two time points. It is also possible to
probe more into the details of the trend to see if, for example, the rate of
