Serial correlation in water quality time series invalidates tests of significance, such as seasonal Kendall analysis, that assume independence. One approach to analyzing such data is to estimate the magnitude of the serial correlation and then use the degree of serial correlation to adjust the variance and make valid inferences. Four methods for estimating serial correlation lag parameters are evaluated. R-estimation outperformed the alternative methods considered. In case studies of water quality time series, the nonparametric rank von Neumann's ratio test of randomness is used to test for the presence of serial correlation, and R-estimation is used to estimate the severity of the serial correlation. Case study results demonstrate that serial correlation is common in monthly water quality data and does not disappear when bimonthly intervals are used. Adjustment for flow and seasonal effects generally reduced estimates of serial correlation. However, even after flow adjustment and deseasonalization, the assumption of independence was often unreasonable.