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INTERPRETATION OF HISTORICAL DATA FROM YAMPA RIVER NEAR MAYBELL This section describes the results of statistical hypothesis tests that were used to examine historical trends in onsite measurements, concentrations of dissolved solids and major ions, and selected thermo- dynamic characteristics of water-quality samples collected from the Yampa River near Maybell (site 8 in fig. 1). For this site, from November 29, 1950, through August 16, 1999, the USGS National Water Informa- tion System (NWIS) data base has 657 water-quality analyses that have sufficient data to allow thermody- namic calculations using PHREEQC. At a minimum, such calculations require pH measurement and concentrations of all major ions (except potassium, which can be neglected because of small concentra- tions). River discharge was not measured for one of these analyses, allowing 656 flow-adjusted analyses for statistical calculations. Through September 1, 1969, sampling times (for 413 analyses) and tempera- tures (for 406 analyses) were not recorded; most of these analyses were for composited samples. Missing temperatures were estimated to be the median water temperature for the month of the sampling date. Alka- linity was measured on unfiltered sample water before October 15, 1986, and on filtered water thereafter; for PHREEQC calculations, unfiltered measurements were used when filtered measurements were not avail- able. For the periods October 9, 1980, through December 20, 1984 (25 samples), and May 15, 1991, through March 5, 1999 (61 samples), neither measure- ment generally was done, so alkalinity was calculated as the amount required to charge balance the solution with other ions, including potassium. For the sample collected on July 12, 1956, the concentration of the sulfate ion was calculated in a similar manner (neglecting potassium). The Wilcoxon-Mann-Whitney rank-sum test, a nonparametric t-test on the joint ranks of two sample sets (Iman and Conover, 1983), was used to compare onsite measurements (including pH), constituent concentrations, and thermodynamic properties of water samples collected from Yampa River near Maybell during 1950-74 with those parameters during 1975-99. These periods of time were chosen to repre- sent the general periods of time before and after onsite measurements of pH were begun and to separate the earlier period of minor coal-mining development from the period beginning in the late 1970's, when coal- mining development grew rapidly. These statistical tests were done to indicate possible water-quality trends associated with the apparent historical increase in measured pH at Yampa River near Maybell and to suggest hypotheses that can be examined as possible causes of that increase. Because concentrations of dissolved water- quality constituents usually vary inversely with discharge, if the data are not flow adjusted for hypoth- esis tests, unequal distributions of flow discharge between two sampling periods can cause apparent significant differences in physical measurements, concentrations of water-quality constituents, and ther- modynamic properties. To adjust for the effects of flow, logarithmic values of these variables (except pH, calcite saturation index, and pH at atmospheric PCOZ) were fitted by linear regression (Iman and Conover, 1983) to logarithmic values of discharge for the entire period of record, and residuals (differences between predicted and measured values) were used to conduct statistical hypothesis tests. Because pH is a loga- rithmic function of H+ concentration, measured pH and pH at atmospheric PCp2 were not converted to logarithms for regression. Because some calcite satu- ration indices are negative and cannot be converted to logarithms and because saturation indices are loga- rithmic quotients, calcite saturation indices were not converted to logarithms for regression. Tests were set up by defining a null hypothesis (Hp) stating that the distribution of flow-regression residuals for measurements, concentrations, and prop- erties was not significantly different for the two periods and an alternative hypothesis (Hl) stating that a significant difference did exist. A test resulting in a two-tailed significance less than or equal to 0.05 indi- cates that the alternative hypothesis was accepted, whereas a significance greater than 0.05 indicates that the null hypothesis was accepted. Accepting the null hypothesis does not necessarily indicate a lack of difference in sample distributions; it merely indicates that the chance of erroneously rejecting a true null hypothesis exceeds 5 percent, given the variability in the data. When the alternative hypothesis was accepted for a variable, the mean ranks of the residuals for the two periods were inspected to determine which period had significantly greater values with respect to that variable. Results of flow-adjusted Wilcoxon-Mann- Whitney rank-sum tests are listed in table 2. INTERPRETATION OF HISTORICAL DATA FROM YAMPA RIVER NEAR MAYBELL 25