Statistical Analysis of Trends in the Red River Over a 45 Year Period

The Kruskal-Wallis test statistic, H is;
[
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H =
N(N + 1)
n∑
i=1
]
Ri
2 − 3(N + 1),
N i
where the k seasons are first ordered and assigned ranks (R i ) and
R i is the sum of the ranks of the ith station;
N i is the number of observations in the ith station;
N is the total number of observations; and
k is the number of seasons;
This test statistic has an approximate Chi-Square distribution on k − 1 degrees of
freedom.
Using the seasons defined in Table 3.1, the following table indicates the constituents
exhibiting seasonality at the 5% level of significance. A significant result
indicates at least one season has a significantly different median concentration than
one or more other seasons. The p-value is approximately the probability of a chisquared
random variable with k −1 degrees of freedom exceeding the observed value
of H. At certain stations, there was insufficient data for some constituents and that
is denoted by “n/a”.
Seasonality is evident in all water quality parameters tested (shown in Table 3.3)
and most parameters demonstrate similar seasonal patterns across all sites. Two
basic seasonality patterns emerged; dissolved calcium, sodium, magnesium, total
dissolved solids and specific conductance exhibit peak concentrations in the winter
months. This follows an inverse pattern to the hydrograph, where maximum
concentrations occur during the low flow winter months. Major ions derived from
geological weathering and ground water become more concentrated as flows decrease
in winter and ground water comprises a higher proportion of flow (Glozier, et al.,
2004). Parameters exhibiting the winter pattern tend to be correlated positively
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