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

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. / Graduation date: 2002
Date03 April 2001
CreatorsRitter, Kerry
ContributorsUrquhart, N. Scott, Birkes, David
Source SetsOregon State University
Detected LanguageEnglish

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