Duane A. Meeter

On Beale's Measures of Non-linearity

Measures of non-linearity that have been developed by Beale (1960a), are designed to indicate when the degree of non-linearity in a non-linear estimation problem is small enough to justify using the usual linear model theory results as approximations. The validity and usefulness of the measures is examined by means of numerical examples. Explanations for the behaviour of the measures is offered and the results are discussed.

Modifications of estuarine sedimentary microbiota by exclusion of epibenthic predators

Abstract The ability of epibenthic predators (crabs and fishes) to influence biomass and community structure of sedimentary microbiota was investigated in St. George Sound-Apalachicola Bay System, Florida, U.S.A. Replicate areas (4 m 2 ) of mud-flat sediment were caged in the field to confine and exclude predators. Uncaged areas were used as controls. The microbiota (prokaryotes and microeukaryotes) of the sediments was characterized at Weeks 0, 2, and 6 by measuring concentrations of phospholipid and analyzing fatty acids of the microbial lipids extracted from the sediments. Data were analyzed using analysis of variance and step-wise discriminant analysis. After 2 wk, the microbiota of the predator exclusion treatment was significantly different from that in control and predator inclusion treatments. After 6 wk, these differences became more pronounced. There were no demonstrable caging effects that could account for treatment differences. Results indicated that removal of predators had a profound effect on microbial communities in estuarine sediments. Thus, the top trophic level (epibenthic predators) had an important role in regulating the structure of the lowest trophic level (the microbiota).

TESTS FOR AGGREGATION AND SIZE‐BASED SAMPLE‐UNIT SELECTION WHEN SAMPLE UNITS VARY IN SIZE

Previous tests for aggregation of organisms among sampling units that vary in size and tests for size-based sample-unit selection fail to account for variation in the size of the sample unit. When sample units vary in size, tests that assume equal-sized sample units overestimate the degree of aggregation and have a tendency to find selection for large-sized sample units. Previous tests for selection of large or small leaves by phytophagous insects have been biased toward detecting selection for large leaves when no leaf selection or selection for small leaves may actually be present, and toward detecting aggregation even when populations are Poisson random or repulsed. We derive explicitly the population mean and variance of the number of organisms per sample unit when the size of the sample unit is random, and we outline procedures to estimate the degree of aggregation and test for size-based sample-unit selection using a generalized linear model based on a Poisson null hypothesis of independent random placement.

An Expanded Approach to Educating Statistical Consultants

Abstract This article describes an expanded approach to the education of statistical consultants that is being implemented at Florida State University. Our program begins with a preconsulting course in which students first study general problem-solving techniques. Next these techniques are used in solving applied statistics “textbook” problems. Then problem formulation and research methods are studied. Finally the structure of consulting sessions is considered, along with interpersonal issues that arise in consulting. In the supervised consulting course, students work with actual clients in videotaped sessions, attend supervision sessions in which the tapes are reviewed, present case conferences, attend new material sessions, and complete a project. We conclude this article with preliminary evaluation data on the program and observations regarding what we have learned.

The effects of statutory change on the civil commitment of the mentally ill

Several states have revised their civil commitment statutes in recent years. A majority of the recent revisions reflect judicial directives to provide more explicit commitment criteria, but in some instances, criteria have been broadened in reaction to the difficulty of getting some individuals hospitalized under strict criteria. Such statutory changes have impacted considerably on both process and outcome of the civil commitment system. Adoption of explicit commitment criteria has resulted most visibly in substantial reduction of hospital admissions and census. The present study examines the impact of explicit changes in commitment criteria in Florida following the 1982 enactment of amendments to the Baker Act. A total of 80 commitment hearings are reviewed before and after the law took effect to determine procedural effects of the law on degree of defense counsel advocacy, client dispositions, and on the courts adherence to more explicit criteria. State hospital admissions, discharge, and census information is examined in order to identify the larger impact of 1982 statutory changes on the commitment system. Evidence from hearings and state data suggests that changes in the Florida law impacted significantly on both process and outcome of the civil commitment system. Clients referred to commitment hearings are more dangerous, and may represent a new “hard-core” group remaining after more explicit eligibility criteria are applied by local intake, and emergency detention facilities. State hospital admissions and census in Florida declined significantly following enactment of the 1982 law, consistent with findings from other states enacting similar statutory reforms. Implications for deinstitutionalization policy and administration are discussed.

Sequential Experimental Design Procedures

Abstract A new sequential design decision rule is proposed for a statistical multiple decision problem with finite state space and with a finite set of available experiments. Conditions are established under which the proposed rule is asymptotically optimal as c, the cost of a single experiment, tends to zero. The rule is compared to those of Chernoff [6] and Box and Hill [5]. In numerical simulations of a type of drug screening experiment, the proposed procedure yielded estimated risks no larger than, often significantly smaller than, those of procedures [6] and [5].

Long-Term Climatological Cycles and Population Changes in a River-Dominated Estuarine System

River flow and rainfall patterns in the Apalachicola drainage system were analyzed by time-series methods, and a preliminary comparison was made with commercial harvests and trawl-tow collections of organisms taken during a long-term sampling program. Spectral analysis revealed long-term (5–7 year) cycles in river flow ranging over 25% of the mean flow figures. Cross- spectral analysis indicated that these cycles were somewhat correlated with local (Florida) rainfall but were strongly related to upstream (Georgia) rainfall. A two-parameter model gave a satisfactory fit to the monthly series of annual river flow changes. Dam construction and filling did not appear to be related to long-term cyclic patterns, but weekly cycles in river flow, evident during periods of low water, appeared after dam installations were made. A preliminary comparison of annual river flows with commercial harvests showed strong correlations with oyster and crab catches in associated coastal areas. River flow was weakly correlated with shrimp and crab numbers obtained from a long-term sampling program. There were indications that while long-term river fluctuations were closely associated with commercial landings, such correlations should be carefully scrutinized for possible influence of economic and sociological conditions. Cyclic biological changes driven by key climatological factors may be complicated by highly individualistic species strategies which tend to mask direct phase relationships. However, long-term periodic changes in climatological features of drainage systems need to be considered if the biological variability of such areas is to be explained. There are indications that such cycles may differentially influence population changes at various levels of biological organization.

A Comparison of Two Model-Discrimination Criteria

Within the last few years there has been increased research involving a generalization of sequential analysis problems in which the experimenter is allowed to design his experiment sequentially. Two different approaches to this Sequential Design of Experiments or Model Discrimination problem have been made by Chernoff [4] and Box and Hill [3]. This paper compares the two approaches through examples. Some minor modifications of Chernoffs procedures are shown to lead to improved results.

Growth response of Thalassiosira pseudonana Hasle and Heimdal clone 3H to illumination, temperature, and nitrogen source

Exponential phase division rate ofThalassiosira pseudonana Hasle and Heimdal clone 3H was studied in response to illumination intensity, day length, temperature, and nitrogen sources and concentrations. An apparatus is described for performing factorial experiments at three temperatures using day/night cyclic light of varied intensity. Population density was measured without subsampling using nephelometry calibrated with direct cell counts in parallel cultures. Cell division rates were computed by regression analysis of population densities during exponential growth. Exponential phase cell division rate was proportional to day length while division rate saturation intensity was the same with 12 or 24 hours of light per day. However, exponential phase was abbreviated under the more natural discontinuous illumination and ultimate cell yield was achieved by growth occuring during the phase of decreasing relative growth rate. We observed an optimal temperature range which always included 21 C but which varied in size with illumination intensity and with nitorgen source and concentration. Growth rate was affected by interactions among illumination intensity, temperature and nitrogen sources and concentrations. Under continuous illumination and nitrogen limination, the diatom did not respond additively to combinations of nitrogen sources in the growth medium.

A robust bayesian lower limit for the expected number of unobserved classes

Under both simple random sampling and stratified random sampling from a study region, we develop a Bayesian, asymptotic lower limit for the expected number of the regions classes that are not observed in the sample. In practical applications, the classes might be species in a forest or types of defects in a product line. The aforementioned lower limit is extremely robust to the prior on θ, the total number of classes in the region. We also consider a potential lower limit for θ. Both the lower limit on the expected number of unobserved classes and the lower limit on θ were conservative in our simulations.