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Statistical Applications for Environmental Analysis and Risk Assessment by Joseph Ofungwu

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Chapter 9Applications of Hypothesis Tests: Comparing Populations, Analysis of Variance

9.1 Introduction and Overview

Problems involving decision making are usually addressed by performing tests of hypothesis on the data samples, as described in Chapter 8. Based on the results of the hypothesis tests, decisions are made to either reject the null hypothesis (i.e., the presumed baseline condition) in favor of a specified alternative hypothesis, or fail to reject the null hypothesis due to insufficient contradicting evidence provided by the data sample. As a result of natural variability of environmental data and the inability of typically limited data sample sizes to capture the full range of the data variability, errors of false rejection or false “acceptance” of the null hypothesis are inevitable. This chapter describes several tests of hypothesis-based procedures for comparing one population with a fixed reference or regulatory screening value (i.e., one-sample tests), comparing two populations with each other (two-sample tests), and comparing several populations with one another (using analysis of variance or ANOVA procedures), while controlling potential decision error rates.

The purpose of the comparisons is usually to determine for instance whether the population mean (i.e., true mean) contaminant concentration at a site is higher than the allowable regulatory limit, or whether the site population mean contaminant or other constituent concentration is higher than the background ...

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