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The null hypothesis/significance testing (NHST) analytical paradigm does not produce answers for environmental regulatory decisions because rejecting the null hypothesis (of no difference between data sets) says nothing about why or by how much they differ. The likelihood paradigm overcomes many of NHST’s problems and can be applied to environmental data when its limitations are understood.
The NHST approach tests how well the data fit a single null hypothesis. The Maximum Likelihood Estimation (MLE) approach tests how well multiple hypotheses fit the data and identifies the hypothesis that maximizes the likelihood of explaining the data. The difference between testing data for fit to an explanation and testing explanations for their fit to data are critical for regulatory decisions. Data are collected to understand the whole population because we cannot measure or observe the entire population.
The NHST paradigm assumes the population is normally distributed (the familiar bell-shape curve), yet environmental data almost never are normally distributed. The MLE approach overcomes this limitation by testing a set of probability distributions for how well each describes the data. When the probability distribution with the maximum likelihood is identified it is used to make predictions about the entire population, compare data sets, make predictions, and inform regulatory.
An example is characterizing chemical concentrations when some are below the chemical laboratory’s method detection limits. Since these values are unknown any arbitrary value assigned to them is wrong. One model for these data fits the measured concentrations to several probability distributions and identifies the one with the maximum likelihood of describing those data. The unknown data are then spread along the left side of that curve, below the detection limit. Using the mathematical characteristics of that distribution allows the data to be described, characterized, and compared with other data to look for change over time or space.
Applying the MLE approach to environmental data supports technically sound and legally defensible decisions. However, there is still more information that has value when making these decisions: prior knowledge.
When there is a history of data from a location prior knowledge is used do make decisions and is valuable when examining environmental data for policy and regulatory decisions. The statistical paradigm is called the Bayesian paradigm.
This work was originally published on the Applied Ecosystem Services, LLC web site at https://www.appl-ecosys.com/blog/updating-environmental-regulations-2/
It is offered under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license. In short, you may copy and redistribute the material in any medium or format as long as you credit Dr. Richard Shepard as the author. You may not use the material for commercial purposes, and you may not distribute modified versions.