We tested the hypothesis that the transect % TDG values (total dissolved gas as percent
saturation) were greater than the fixed monitor % TDG values using Equation 7. We
hypothesized that H0:D ≤ 0 with alternative H1:D > 0. We rejected H0 if t0 > tα,n1. Again,
using α = 0.05 and υ = n 1 = 7 (determined by the sample size of 8), the value of tα,n1
= t0.05,7 = 1.895.
Also, since 5.9 = t0 > tα,n1 = t0.05,7 = 1.895, we rejected H0 and concluded that the difference
between the transect values and the fixed monitor station values was greater than zero. The fixed
monitor consistently recorded total dissolved gas percent saturation values that were less than the
average of those actually present in the river at this location during this study. Thus, we
conclude that the fixed monitor system does not accurately represent the flux of total dissolved
gas in the river.
To avoid tedious hand calculations, software packages are useful for calculating the paired
t-test statistics for the data sets. Two commonly used packages are SPSS (SPSS Inc., Chicago
IL) and SAS (SAS Institute, Inc., Cary, NC).
Example 2: Columbia and Snake Rivers Fixed Monitoring System
The technique employed in the above example can be used to look at an entire monitoring
system. Though the fixed monitoring system is designed to determine extreme concentrations of
total dissolved gas in spill waters, here we explore the potential of each station for use in
monitoring the average total dissolved gas concentration in the river. The system consists of
monitors at 26 sites. As in example 1, these fixed monitor sites were compared with transect
data collected during 1995.
Again, because the transect study was designed to aid modelers and not strictly to verify the
fixed monitor system, adequate data were not available for each location. The analysis shown
here was intended only to provide insight into the representativeness of the monitoring system.
Details, such as verifying normality, have been omitted. The results presented here might best be
used to design future, more rigorous verification studies.
Transects within 3.5 km of each fixed monitor site were used for comparisons to fixed
monitor data. This created a larger data set than if only transects that were adjacent to
the monitor sites were used. Larger data sets reduce the type II error, that is, the
probability of accepting H0 when H0 is false. The paired test requires at least two pairs
of data for each site. This constraint eliminated three stations, leaving 23 for further
Because of the number of comparisons that were desired, SPSS was used to analyze the data.
A paired t-test was run on each of the 23 fixed monitor sites and their comparable transect data.
The results of these analyses are shown in Table 3.
Water Quality Technical Note AM-03 (January 1998)