Statistical Applications for Environmental Analysis and Risk Assessment

Chapter 8Tests of Hypothesis and Decision Making

8.1 Introduction and Overview

A test of hypothesis is a standard statistical procedure for deciding between two competing alternatives or scenarios, based on evidence presented by a data sample collected for the purpose of conducting the test. Most data statistics such as the mean, standard deviation, and percentiles are usually computed from data samples that contain a relatively small number of observations (due to cost and other constraints associated with data collection) when compared to the “universe” or “population” of all possible data values. As would be expected, uncertainties arise when such sample statistics are used as estimates of the true but unknown population parameters such as the population mean and population standard deviation. Tests of hypothesis provide a framework for managing these uncertainties and controlling potential decision errors based on objective and reproducible decision-making procedures.

For example, suppose we suspect or hypothesize that the mean concentration of hexavalent chromium, a known human carcinogen, in the surface soils at a contaminated commercial site exceeds the regulatory standard or allowable concentration for this chemical. To test our hypothesis, we collect a set of, say, 20 randomly selected soil samples from the site and have them analyzed for chromium by a laboratory, thereby obtaining a data sample of 20 chromium concentrations from which we can compute the mean or average ...