USE OF BOOTSTRAPPING STATISTICS IN CALCULATION OF UNCERTAINTY FOR HYDROBIOGEOCHEMICAL DATA: MEAN VERSUS MEDIAN

Bootstrapping is a statistical method for non-Gaussian-distributed data that randomly samples the data with replacement to estimate summary statistics. These qualities allow bootstrapping to be a suitable method for calculating statistical data of hydrobiogeochemical data. However, a challenge with bootstrapping is knowing when to use the mean or median. In this study, bootstrap analyses were conducted with daily stream flux data for the Loch Vale Watershed (LVW) and the Andrews Creek Watershed (ACW), both located in Rocky Mountain National Park, Colorado USA. For 1993-2008 and the five inclusive triennia, an online bootstrapping calculator (https://www.wessa.net/) was utilized to calculate the mean and median flux values, and their associated standard deviations, from which the standard error was determined to 2σ. The standard errors using the mean and median were compared between the LVW and ACW, with the LVW having a higher measurement frequency (n=720-775) than the ACW (n=50-54). With a higher measurement frequency, the LVW should have a smaller uncertainty than the LVW. However, the median values caused ACW errors to be smaller than LVW errors almost 50% of the time, whereas only 13% of ACW errors were smaller when the mean value was used. Median standard errors were consistently higher than the mean standard errors in both watersheds with some anomalously high values. Median resample distributions were non-Gaussian, displayed clumped/isolated values, or both. Ideally, the outcome of bootstrapping statistical calculations should be a Gaussian curve. Based on these findings it is concluded that the mean data are more favorable when applying bootstrapping statistics to non-Gaussian hydrobiogeochemical data.