Water Quality Assessment of the South Platte River Basin, Colorado , Nebraska, and Wyoming

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(the lines to the boundary points of the boxplot), and the quartile skew (the relative position of the median to the 25th and 75th percentiles). For nutrient- and sedi- ment -data groups that had five to nine data values, only the individual data values were plotted, and only the medians were reported in tables. For pesticides, all val- ues were plotted, but statistical comparisons were not done for groups that had less than five values, and only the medians were reported in tables. For data groups that had 10 to 14 values, the boxes and median line were drawn for boxplots, and the 25th and 75th percen- tiles were added to the tables. For data groups that had 15 or more values, boxplots and boundary lines were drawn, and the 10th and 90th percentiles of the data dis- tributions were added to tables. Where appropriate, a line was drawn on boxplots to indicate the USEPA Maximum Contaminant Level (MCL) for each constit- uent. The Kruskal- Wallis test was used to compare the means of different groups of data. This is a non -para- metric test that compares real and chance differences in groups of data; the null hypothesis states that no real difference exists. For this study, this test was done at the 0.05 level of significance, which represents the maximum probability of rejecting the null hypothesis when it is actually true. Multiple -stage tests (as described in Helsel and Hirsch, 1992) were performed to detect differences between various combinations of groups. The LOWESS, or LOcally WEighted Scatterplot Smoothing method (Cleveland, 1979) was used to highlight trends or patterns of selected nutrient concen- trations over time. To test for statistically- significant trends, the Seasonal Kendall test (Hirsch and others, 1982) was done at the 0.05 level of significance. Water - quality trends were only analyzed for sites with: (1) instantaneous flow data and at least one nutrient sample per month during 1980 -92 and (2) at least one - half of the data present in the first and last thirds of the record. Concentrations were flow- adjusted to remove the variability due to differences in streamflow (Lanfear and Alexander, 1990). Nutrient loads were estimated using nutrient - transport models. Models were based on data collected during water years 1980 -92. Data requirements for load calculation were as follows: (1) 35 or more obser- vations for a nutrient constituent from the period 1980 to 1992; (2) at least 3 of these observations from sam- ples collected during the top decile of flow; and (3) daily streamflow data available for years of interest. Models were developed by multiple regression of nutrient - constituent load on independent variables including: (1) streamflow, because constituent concen- trations often are related to streamflow; (2) time, to compensate for long -term trends; and (3) sine and cosine of time to compensate for seasonal variations. Censored data were modified using the adjusted maxi- mum likelihood estimator (Cohn and Gilroy, 1992). 421 Number of observations p > 0.05 90th percentile 75th percentile- Percentiles are statistics upper quartile which describe the varia- bility in a data set. The nth percentile is the value that has at most n percent of the observations less than that value. For example, 50th percentile - the 25th percentile has 25% median value of the observations less than that value. If 9 or less data points exist, the data points themselves are represented 25th percentile- instead of a box. lower quartile 10th percentile KRUSKAL -WAWS TEST-Hypothesis test to examine real versus chance differences in data. The test involves a null hypothesis stating that no real difference exists. An alpha value, or level of signif- icance, is used in the hypothesis test representing the maximum probability of rejecting the null hypothesis when it is actually true. An alpha value of 0.05 is used. p > 0.05 - Probability represent- ing the attained significance level. If the p -value is smaller than or equal to the alpha value, the null hypothesis is rejected and significant differences are assumed to exist among the data. Figure 11. Description of components of a boxplot and related statistical tests. DATA - ANALYSIS METHODS 33