Averaging should be carried out for each sampling time. Again, only in the most carefully

designed and executed studies is such information available. More typically, an analyst may have

three to seven lateral measurements along a transect to compare with fixed monitor information.

In this case, the analysis can be performed, but the analyst must be aware that those limited data

lessen the weight that may be given to any conclusions.

At this point, the verification data set should contain *n *pairs of data (*X*m,j , *X*s,j), each

containing a monitor observation *X*mj and an average stream value *X*sj for time *j*, where *m *and *s*

indicate that the observation came from the monitor or stream, respectively. Next, one tests the

relationship between the two locations using a paired t-test (following Hines and Montgomery

1980). This test assumes that the samples each come from a normally distributed, independent

distribution. However, moderate departures from normality should not adversely affect the

analysis (Pollard 1977). The difference between each pair of observations, *D*j = *X*mj *X*sj , should

come from a normally distributed independent distribution.

To verify that the data come from a normally distributed population, either of two methods

can be used. The easiest method is to plot the data on normal probability paper or use a

statistics software package to generate a normal probability graph. A second method is to use a

quantitative test such as the Kolmogorov-Smirnov test or Lillefore's test. Further details of these

tests can be found in Hines and Montgomery (1980) and Pollard (1977). Within this technical

note, normal plots are used; these were generated using SPSS (SPSS, Inc., Chicago, IL), a

statistical analysis software package.

Once it has been determined that the data come from a normal or nearly normal distribution,

one can begin the comparison by stating the hypotheses. The null hypothesis is that the mean of

the differences between pairs, D , is zero. This implies that monitor value agrees with stream

values and is representative. The alternative hypothesis is that the mean of the differences is not

zero; that is, the monitor values do not agree with stream values and are not representative. This

is stated as follows:

(2)

(3)

These hypotheses are tested with the following statistic:

,

(4)

where

∑D

,

(5)

4

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