Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 123-129).

Almost twenty years ago Texas implemented a functions-based approach (FBA) to teaching algebra. This approach emphasized the use of nearly all multiple representations, use of a graphing calculator to explore graphs, and modeling of linear and quadratic functions. This interpretation of FBA in conjunction with curriculum placing the teaching of simplifying expressions and solving equations close in sequence may contribute to student confounding of the rules for simplifying and solving. The purpose of this exploratory qualitative study was to explore student rating of the usefulness of teacher-provided and function-based approach (FBA) strategies for simplifying expressions and solving equations in Algebra. The subjects of this study were two algebra teachers and their respective algebra students. The teachers, who taught both Algebra 1 and Algebra 2, were at a high school campus located in an urban district. A researcher created survey based on teacher-provided strategies used by participating teachers was administered to 100 students and 22 teachers. The teacher survey results were used as a professional basis for comparing students' results. Descriptive statistics were used to create graphical representations of students by course groups and identify students who confounded rules. Student FBA preferences and course groups were used to identify 18 student interviewees. Student and teacher interviews were used to corroborate survey results. Participating teachers identified and commented on areas of concern from the survey results. Both teachers approved of the low percentages of students rating FBA strategies as useful but were concerned about higher percentages of students (30% or greater) confounding rules or not realizing the usefulness of relevant sub-strategies. Neither teachers nor students were aware of benefits of graphing calculator use in simplifying. Students, regardless of course group or FBA preference, justified the use of teacher-provided strategies with symbolic manipulation and changed FBA ratings to less likely. There were few student references to equivalence and equality that were supported by FBA. These results are important for algebraic instruction in Texas. Texas has mandated use of graphing calculator on 8th grade Mathematics STAAR exam. Recognizing the benefits of a complete FBA along with effective use of graphing technology may prevent this type of confounding. / text

abstract: During the initial stages of experimentation, there are usually a large number of factors to be investigated. Fractional factorial (2^(k-p)) designs are particularly useful during this initial phase of experimental work. These experiments often referred to as screening experiments help reduce the large number of factors to a smaller set. The 16 run regular fractional factorial designs for six, seven and eight factors are in common usage. These designs allow clear estimation of all main effects when the three-factor and higher order interactions are negligible, but all two-factor interactions are aliased with each other making estimation of these effects problematic without additional runs. Alternatively, certain nonregular designs called no-confounding (NC) designs by Jones and Montgomery (Jones & Montgomery, Alternatives to resolution IV screening designs in 16 runs, 2010) partially confound the main effects with the two-factor interactions but do not completely confound any two-factor interactions with each other. The NC designs are useful for independently estimating main effects and two-factor interactions without additional runs. While several methods have been suggested for the analysis of data from nonregular designs, stepwise regression is familiar to practitioners, available in commercial software, and is widely used in practice. Given that an NC design has been run, the performance of stepwise regression for model selection is unknown. In this dissertation I present a comprehensive simulation study evaluating stepwise regression for analyzing both regular fractional factorial and NC designs. Next, the projection properties of the six, seven and eight factor NC designs are studied. Studying the projection properties of these designs allows the development of analysis methods to analyze these designs. Lastly the designs and projection properties of 9 to 14 factor NC designs onto three and four factors are presented. Certain recommendations are made on analysis methods for these designs as well. / Dissertation/Thesis / Ph.D. Industrial Engineering 2012

Ståndort är ett område där ett bestånd av en viss växt finns, ofta avses träd inom skogsproduktion. Förutsättningarna för detta, ståndortsfaktorer, återfinns i markens egenskaper (edafiska faktorer) och klimatet. Dessa påverkar därigenom växtens produktion, något som särskilt är av intresse inom skogsbruket och de skogliga vetenskaperna. Till detta kommer att växter samspelar med andra växter och organismer såsom svampar, bakterier och djur, och även den antropogena påverkan med faktorer såsom husdjursbete, atmosfäriskt nedfall och skogsproduktion har en stark inverkan på vegetationen. Utifrån att studera några av de mer kända teorierna om växtsamhällen och -strategier samt olika vinklar av ståndortsfaktorer var hypotesen att det går att få fram en problematiserande bild och hitta störfaktorer (confoundingvariabler), som kan ge felaktiga tolkningar av resultat. Ett antal kända verk inom vegetationsklassificering gicks igenom, kompletterat med stödjande litteratur. En artikelsökning genomfördes också, med kombinationer av specifika sökord med anknytning till ståndort. För att begränsa urvalet och ge en mer regional prägel på arbetet ställdes sökfiltren i artikelsökningen in på att enbart visa resultat från Skandinavien och Finland. Artiklarna delades in efter teman och behandlades efter dessa. Även om få huvudsakliga faktorer styr vegetationen finns flera variabler som lokalt har en stor betydelse, såsom snö, genetiska egenskaper och symbios med andra organismer. Dessa variabler kan vara svåra att mäta och det finns mycket på detaljnivå som är dåligt undersökt. Markanvändningar påverkar de edafiska faktorerna långt efter att brukandet ändrats eller upphört, men detta har olika stor lokal påverkan. Kvävets och kolets halter och cykler är återkommande osäkerhetsfaktorer i artiklarna, där det atmosfäriska kvävenedfallet spelar en viktig men ojämn roll, och jämförbara mätningar försvåras av skillnader i väder och klimat. Till detta kommer påverkan av markorganismer, vilka har en mycket viktig del i växternas näringsupptag, men är svår att mäta. Även om alla aspekter av en växtplats inte kan tas med bör fler felkällor tas i beaktande och modeller ha möjlighet att kalibreras mot olika teorier om växtsamhällen och -strategier. Flera faktorer som traditionellt inte räknas som ståndortsfaktorer, såsom snödjup, symbios med markorganismer och markanvändning, kan vara betydelsefulla att ta med i exempelvis modellering. / A site is an area where a population of a specific plant species has its habitat, often the connotation is forestry. The prerequisites for this, the site indices (also site variables or stand variables), can be found in the characteristics of the ground (edaphic factors) as well as the climatic impact. These elements affect the growth and production, which is of interest in forestry and forest sciences. Upon this the plants interact with each other as well as with other organisms, i.e. fungi, bacteria and animals, and there is also an anthropogenic impact where factors such as livestock grazing, atmospheric deposition and forest production strongly affects the vegetation. By studying some of the more prominent theories on vegetation societies/sociologies and plant strategies, as well as different aspects of the site concept, the hypothesis was that a problematizing picture of site indices can be found and some confounding variables that can give erroneous interpretation of results. A number of major works in vegetation classification was gone through, supplemented by supporting literature. An article search was conducted to find journal articles, using combinations of specific search terms related to site indices. To narrow down the results and give a more regional touch to the thesis, the filter was set only to show results from Scandinavia and Finland. The articles were grouped into themes and handled theme-wise. Even though there are few principal factors controlling the vegetation there are a number of variables which locally can have a large impact, such as snow, genetic traits and symbiosis. These variables can be hard to measure, and a lot of things at a detailed level are poorly investigated. Land use modifies the edaphic properties long after the usage have changed or been discontinued. The amounts and cycles of nitrogen and carbon are recurrent uncertainties in the articles, where deposits of nitrogen from the atmosphere plays an important but uneven role and measurements can be hard to compare due to differences in weather and climate. Added to this, organisms in the ground have a major role in the plants’ nutrient uptake, but the effects can be hard to study. A concluding remark is that even though all aspects of a site cannot always be included more confounding variables could be taken in account and models should be able to be calibrated to different theories on vegetation societies/sociologies and plant strategies. Many factors normally not counted as site indices, i.e. snow depth, soil biota symbiosis, and land use, could be valuable to include in e.g. modelling.

Thesis (Ph. D.)--University of Oklahoma. / Includes bibliographical references.

Abstract To date, most epidemiological studies have shown a weak or moderate association between dental diseases such as periodontal infections, dental caries and tooth loss, and atherosclerotic vascular diseases. However, the nature of this association is not known; it may be due to the biological effect of oral infections on initiation or progress of atherosclerosis or it may be non-causal due to determinants in common, either biological or behavioural. Methodological shortcomings, inconsistent results and a lack of definite proof from intervention studies have led to the conclusion that causality between dental diseases and atherosclerotic vascular diseases has not been established. The aim of this study was to produce evidence on the nature of the association between dental diseases and atherosclerotic vascular diseases. The study uses data from the 1966 Birth Cohort of Northern Finland (N = 11,637). The data were collected in 1997–1998, when the cohort members had reached 31 years of age. The respondents were asked through a postal questionnaire about their oral health. In addition, respondents were asked about their general health and oral and general health habits. The response rate was 75.3%. Those who lived in Northern Finland or the capital city region were invited to clinical health examination (N = 8,463). Altogether 5,696 subjects supplied the data, representing 67.3% of those who were invited to the clinical examination. While the study showed an association of self-reported gingivitis, dental caries and tooth loss with the prevalent angina pectoris, it also showed that these self-reported dental diseases were not important determinants for elevated C-reactive protein levels. This suggests that the associations that were found between dental conditions and prevalent angina pectoris are mainly caused by factors other than biological mechanisms related to infection or inflammation. The lack of a biological explanation related to infections or inflammatory processes suggests that other biological mechanisms or biases, including confounding, should be considered as an alternative explanation. However, it must be noted that the possibility that oral infections also contribute to the development of atherosclerosis should not be rejected either.

Evaluating the effectiveness of an intervention can pose challenges if there is not an adequate control group. The effects of the intervention can be distorted by observable differences in the characteristics of the control and treatment groups. Propensity score matching can be used to confirm the outcomes of an intervention are due to the treatment and not other characteristics that may also explain the intervention effects. Propensity score matching is an advanced statistical technique that uses background information on the characteristics of the study population to establish matched pairs of treated participants and controls. This technique improves the quality of control groups and allowing for a better evaluation of the true effects of an intervention. The purpose of this study was to implement this technique to derive county-level matches across the southeastern United States for existing counties within a single state where future statewide initiatives are planned. Statistical analysis was performed using SAS 9.4 (Cary, NC, USA). A select set of key county-level socio-demographic measures theoretically relevant for deriving appropriate matches was examined. These include the proportion of African Americans in population, population density, and proportion of the female population below poverty level. To derive the propensity-matched counties, a logistic regression model with the state of primary interest as the outcome was conducted. The baseline covariates of interest were included in the model and used to predict the probability of a county being in the state of primary interest; this acts as the propensity score used to derive matched controls. A caliper of 0.2 was used to ensure the ratio of the variance of the linear propensity score in the control group to the variance of the linear propensity score in the treatment group is close to 1. The balance of covariates before and after the propensity score matching were assessed to determine if significant differences in each respective covariate persisted after the propensity score matching. Before matching, a significant difference was found in the proportion of African Americans in control group (21.08%, n=3,450) and treatment group (36.95%, n=230) using the t-test (P<0.0001). The percent of females below poverty level showed significant difference between control and treatment group (P=0.0264). The t-test of population density also showed significant differences between the groups (P=0.0424). After matching, the mean differences for the treated-control groups were all zero for these three covariates and the characteristics were no longer showing any significant differences between the two groups. This study found that the use of propensity score matching methods improved the accuracy of matched controls. Ensuring that the control and treatment counties have statistically similar characteristics is important for improving the rigor of future studies examining county-level outcomes. Propensity score matching does not account for unobserved differences between the treatment and control groups that may affect the observed outcomes; however, it does ensure that the observable characteristics between the groups are statistically similar.This method reduces the threat to internal validity that observable characteristics pose on interventions by matching for these potentially confounding characteristics.

No description available.

Prognostic scores, and more specifically comorbidity scores, are important and widely used measures in the health care field and in health services research. A comorbidity is an existing disease an individual has in addition to a primary condition of interest, such as cancer. A comorbidity score is a summary score that can be created from these individual comorbidities for prognostic purposes, as well as for confounding adjustment. Despite their widespread use, the properties of and conditions under which comorbidity scores are valid dimension reduction tools in statistical models is largely unknown. This dissertation explores the use of summary comorbidity measures in statistical models. Three particular aspects are examined. First, it is shown that, under standard conditions, the predictive ability of these summary comorbidity measures remains as accurate as the individual comorbidities in regression models, which can include factors such as treatment variables and additional covariates. However, these results are only true when no interaction exists between the individual comorbidities and any additional covariate. The use of summary comorbidity measures in the presence of such interactions leads to biased results. Second, it is shown that these measures are also valid in the causal inference framework through confounding adjustment in estimating treatment effects. Lastly, we introduce a time dependent extension of summary comorbidity scores. This time dependent score can account for changes in patients' health over time and is shown to be a more accurate predictor of patient outcomes. A data example using breast cancer data from the SEER Medicare Database is used throughout this dissertation to illustrate the application of these results to the health care field. / Statistics

No description available.