Estimating statistical power for detecting long term trends in surface water Escherichia coli concentrations

Abstract

Water quality monitoring programs commonly use the Mann-Kendall test or linear regression to identify statistically significant monotonic trends in fecal indicator bacteria concentrations (typically Escherichia coli [E. coli]). The statistical power of these tests to detect trends of different magnitudes (effect size) is rarely communicated to stakeholders, and it is unlikely they are considered when designing monitoring schedules. The statistical power for detecting trends in surface water E. coli bacteria concentrations using Mann-Kendall and linear regression at water quality monitoring sites across Texas was estimated using Monte Carlo simulation. The probability that an individual water quality monitoring site in Texas had adequate statistical power was also estimated using logistic regression. Mann-Kendall and linear regression trend tests show similar statistical power. Both tests are unlikely to achieve adequate statistical power when E. coli concentrations decrease by 20% or less over 7 years under most sampling frequencies. To adequately detect concentration decreases of 30% to 40% over 7 years, monthly sampling is required. Because many sites across Texas are sampled quarterly, monotonic trends tests will not be powerful enough to detect trends of moderate magnitudes. To better facilitate stakeholder decision-making, it is important to communicate the relative power of statistical tests and detectible magnitudes of changes. I suggest data analysts conduct power analyses to improve monitoring program designs and improve communication of trend test limitations. Software and training for water quality analysts could facilitate communication of power and effect sizes. Alternative trend assessment methods may be more reliable for describing changes in fecal indicator bacteria concentrations.

Keywords

• trend detection
• E. coli
• statistical power
• water quality