Sample size calculation methods for ordinal logistic regression are proposed to test statistical hypotheses. The author was motivated to do this work by the need for statistical analysis of the red imported fire ants data. The proposed methods use the concept of approximation by the moment-generating function. Some correction methods are also suggested. When a prior data set is available, an empirical method is explored. Application of the proposed methodology to the fire ant mating flight data is demonstrated. The proposed sample size and power calculation methods are applied in the hypothesis testing problems. Simulation studies are also conducted to illustrate their performance and to compare them with existing methods.

Sample size calculation methods for ordinal logistic regression are proposed to test statistical hypotheses. The author was motivated to do this work by the need for statistical analysis of the red imported fire ants data. The proposed methods use the concept of approximation by the moment-generating function. Some correction methods are also suggested. When a prior data set is available, an empirical method is explored. Application of the proposed methodology to the fire ant mating flight data is demonstrated. The proposed sample size and power calculation methods are applied in the hypothesis testing problems. Simulation studies are also conducted to illustrate their performance and to compare them with existing methods.

Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2010.

Thesis (M.B.A.)--North-West University, Potchefstroom Campus, 2010.

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Covariate quality has been primarily theory driven in propensity score matching with a general adversity to the interpretation of group prediction. However, effect sizes are well supported in the literature and may help to inform the method. Specifically, I index can be used as a measure of effect size in logistic regression to evaluate group prediction. As such, simulation was used to create 35 conditions of I, initial bias and sample size to examine statistical differences in (a) post-matching bias reduction and (b) treatment effect sensitivity. The results of this study suggest these conditions do not explain statistical differences in percent bias reduction of treatment likelihood after matching. However, I and sample size do explain statistical differences in treatment effect sensitivity. Treatment effect sensitivity was lower when sample sizes and I increased. However, this relationship was mitigated within smaller sample sizes as I increased above I = .50.

The purpose of this current study was to evaluate the use of a stimulus equivalence paradigm to teach emerging adults with developmental disabilities to accurately estimate portion sizes. This study also aimed to integrate nutritionally recommended foods to incorporate a socially significant component to promote health related behaviors. Three emerging adults with various developmental disabilities participated in this study. A pre/post-test embedded in a multiple baseline design across food was used to demonstrate experimental control. Results of this study indicated that all participants exhibited accurate portion size estimations following stimulus equivalence direct training trials and test of untrained relations. When asked about their perceptions of the training methods through a social validity questionnaire participants indicated that this training method were effective and acceptable. Limitations and directions for further research are also discussed.

The goal of this study was to establish empirical benchmarks for Cohen's d in child counseling research. After initial review of over 1,200 child intervention research studies published from 1990 to 2016, 41 randomized clinical trials were identified in which intervention and control groups were compared with children 3-12 years old (N = 3,586). Upon identification or calculation of a Cohen's d for each study, I calculated a weighted mean d by multiplying the effect size of each study by the number of participants in that study then dividing by total number of effect sizes. The weighted mean accounted for study sample size and served as the suggested medium effect size benchmark. Results indicated effect size is impacted in large part by type of reporter, with parents apparently most sensitive to improvement and yielding higher effect sizes overall; teachers relatively less sensitive, perhaps due to difficulty observing change in a classroom setting; and children self-reporting lowest levels of improvement, perhaps reflecting a lack of sufficient measures of child development. Suggested medium benchmarks for Cohen's d in child counseling literature are .70. for parent report, .50 for teacher report, and .36 for child self-report. Small and large benchmarks are suggested based on the use of standard deviations of the mean Cohen's d for each reporter.

Current rates of extinctions are estimated to be around 1000 times higher than background rates that would occur without anthropogenic impacts. These extinction rates refer to the traditional view of extinctions, i.e. numerical extinctions. This thesis is about another type of extinctions: functional extinctions. Those occur when the abundance of a species is too small to uphold the species’ ecologically interactive role. I have taken a theoretical approach and used dynamical models to investigate functional extinctions and threshold values for species’ mortality rates in ecological networks. More specifically, I have derived threshold values for focal species mortality rates at which another species or the focal species itself goes numerically extinct (Paper I-II), or transgresses some predefined threshold abundance (Paper III). If an increased mortality rate of a focal species causes another species to go numerically extinct, the focal species can be regarded as functionally extinct, since its abundance is no longer large enough to uphold its ecologically interactive role. Such functional extinctions are investigated in the first papers (Paper I-II). In the following paper, limits for both increased and decreased mortality rates of species are explored (Paper III). Paper III also extends the basic theoretical idea developed in paper I-II into a more applied setting. In this paper I develop a time series approach aimed at estimating fishing mortalities associated with a low risk that any species in a community transgresses some predefined critical abundance threshold. In the last paper (Paper IV) the community wide effect of changes in the abundance of species is investigated. In the first paper (Paper I) I investigate threshold levels for the mortality rate of species in ecological networks. When an increased mortality rate of a focal species causes another species to go extinct, the focal species can be characterized as functional extinct, even though it still exists. Such functional extinctions have been observed in a few systems, but their frequency and general patterns have been unexplored. Using a new analytical method the patterns and frequency of functional extinctions in theoretical and empirical ecological networks are explored. It is found that the species most likely to be the first to go extinct is not the species whose mortality rate is increased, but instead another species in the network. The species which goes extinct is often not even directly linked to the species whose mortality rate is increased, but instead indirectly linked. Further, it is found that large-bodied species at the top of food chains can only be exposed to small increases in mortality rate and small decreases in abundance before going functionally extinct compared to small-bodied species lower in the food chains. These results illustrate the potential importance of functional extinctions in ecological networks and lend support to arguments advocating a more community-oriented approach in conservation biology, with target levels for populations based on ecological functionality rather than the mere persistence of species. In Paper II I use the approach developed in Paper I to explore the frequency and patterns of functional extinctions in ecological networks with varying proportions of mutualistic and antagonistic (predator-prey) interactions. The general results from Paper I are also found in Paper II; that is, an increased mortality rate of one focal species often first leads to an extinction of another species rather than to an extinction of the focal species itself. Further, the frequency of functional extinctions is higher in networks containing a mixture of interaction types than in networks with only antagonistic interactions. Overall, this study generalize the findings of paper I for networks containing a variety of interaction types. To make the theoretical approaches developed in paper I-II operational in a management setting I develop a time series approach aimed at estimating ecologically sustainable fishing mortalities in a multispecies fisheries context (Paper III). An ecologically sustainable fishing mortality is here defined as a long-term fishing mortality associated with a multispecies objective which infers a low risk that any species, either the focal species itself or another species, in a community transgresses a critical biomass limit, below which the risk of recruitment failure is high. The approach is exemplified using a statistical food web model of the dominating fish stocks in the Baltic Sea. For the most abundant fish stock a counterintuitive result is found; it is more likely that the multispecies objective is met if its mortality caused by fishing is increased compared to if it is decreased. Further, simultaneous changes of the fishing mortality of a number of interacting species in the food web model shows a much narrower region of possible sustainable fishing mortalities than a single species approach, something that is not captured by current stock assessment models. Altogether these results are governed by indirect effects propagating in the community and pinpoints the need to adopt community dynamical approaches in fisheries management. The population sizes of many species in the world are declining. Negative population trends are particular pronounced in large-bodied herbivores and carnivores, species known to play important regulatory roles in many ecosystems. Although this indicates that the ecological consequence of declining populations of species might be profound, its impact on ecosystem stability remains largely unexplored. In paper IV it is therefore explored how declining populations of rare and common species affects the resilience – recovery rate – of ecological networks. An analytical approximation shows that network resilience is a function of the harmonic mean of the species’ abundances. This means that network resilience is especially sensitive to declining abundances of rare species. Consistent with this analytically derived result, a clear and positive relationship between resilience and the abundance of the rarest species in a broad spectrum of dynamical models of ecological networks is found. Together these results illustrate the potentially negative consequences of declining populations of rare species for the stability of the ecological systems in which they are embedded, and provide ecological arguments for the protection and management of rare species.

This study examined the statistical consequences of employing various methods of computing and cumulating effect sizes in meta-analysis. Six methods of computing effect size, and three techniques for combining study outcomes, were compared. Effect size metrics were calculated with one-group and pooled standardizing denominators, corrected for bias and for unreliability of measurement, and weighted by sample size and by sample variance. Cumulating techniques employed as units of analysis the effect size, the study, and an average study effect. In order to determine whether outcomes might vary with the size of the meta-analysis, mean effect sizes were also compared for two smaller subsets of studies. An existing meta-analysis of 60 studies examining the effectiveness of computer-based instruction was used as a data base for this investigation. Recomputation of the original study data under the six different effect size formulas showed no significant difference among the metrics. Maintaining the independence of the data by using only one effect size per study, whether a single or averaged effect, produced a higher mean effect size than averaging all effect sizes together, although the difference did not reach statistical significance. The sampling distribution of effect size means approached that of the population of 60 studies for subsets consisting of 40 studies, but not for subsets of 20 studies. Results of this study indicated that the researcher may choose any of the methods for effect size calculation or cumulation without fear of biasing the outcome of the metaanalysis. If weighted effect sizes are to be used, care must be taken to avoid giving undue influence to studies which may have large sample sizes, but not necessarily be the most meaningful, theoretically representative, or elegantly designed. It is important for the researcher to locate all relevant studies on the topic under investigation, since selective or even random sampling may bias the results of small meta-analyses.