Statistical aspects of two measurement problems : defining taxonomic richness and testing with unanchored responses Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/pg15bj60x

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  • Statisticians often focus on sampling or experimental design and data analysis while paying less attention to how the response is measured. However, the ideas of statistics may be applied to measurement problems with fruitful results. By examining the errors of measured responses, we may gain insight into the limitations of current measures and develop a better understanding of how to interpret and qualify the results. The first chapter considers the problem of measuring taxonomic richness as an index of habitat quality and stream health. In particular, we investigate numerical taxa richness (NTR), or the number of observed taxa in a fixed-count, as a means to assess differences in taxonomic composition and reduce cost. Because the number of observed taxa increases with the number of individuals counted, rare taxa are often excluded from NTR with smaller counts. NTR measures based on different counts effectively assess different levels of rarity, and hence target different parameters. Determining the target parameter that NTR is "really" estimating is an important step toward facilitating fair comparisons based on different sized samples. Our first study approximates the parameter unbiasedly estimated by NTR and explores alternatives for estimation based on smaller and larger counts. The second investigation considers response error resulting from panel evaluations. Because people function as the measurement instrument, responses are particularly susceptible to variation not directly related to the experimental unit. As a result, observed differences may not accurately reflect real differences in the products being measured. Chapter Two offers several linear models to describe measurement error resulting from unanchored responses across successive evaluations over time, which we call u-errors. We examine changes to Type I and Type II error probabilities for standard F-tests in balanced factorial models where u-errors are confounded with an effect under investigation. We offer a relatively simple method for determining whether or not distributions of mean square ratios for testing fixed effects change in the presence of u-error. In addition, the validity of the test is shown to depend both on the level of confounding and whether not u-errors vary about a nonzero mean.
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