Each year thousands of students enrol in introductory statistics courses at universities throughout Australia, bringing with them formal and informal statistical knowledge and reasoning, as well as a wide range of basic numeracy skills, mathematical inclinations and attitudes towards statistics, which have the potential to impact on their ability to develop statistically. This research develops and investigates measures of each of these components for students at the interface of secondary and tertiary education, and investigates the relationships that exist between them, and a range of background variables. The focus of the research is on measuring and analysing levels and abilities in statistical reasoning for a range of students at the tertiary interface, with particular interest also in investigating their basic numeracy skills and how these may or may not link with statistical reasoning allowing for other variables and factors. Information from three cohorts in an introductory data analysis course, whose focus is real data investigations, provides basis for the research. This course is compulsory for all students in degree programs associated with all sciences or mathematics. The research discusses and reports on the development of questionnaires to measure numeracy and statistical reasoning and the students' attitudes and reflections on their prior school experiences with statistics. Students' attitudes are found to be generally positive, particularly with regard to their self-efficacy. They are also in no doubt as to the links that exist between mathematics and statistics. The Numeracy Questionnaire, developed to measure pre-calculus skills relevant to an introductory data analysis course which emphasises real data investigations, demonstrates that many students who have completed a basic algebra and calculus senior school subject struggle with skills which are in the pre-senior curricula. Direct examination of the responses helps to understand where and why difficulties tend to occur. Rasch analysis is used to validate the questionnaire and assist in the description of levels of skill. General linear models demonstrate that a student's numeracy score depends on the result obtained in senior mathematics, whether or not the student is a mathematics student, gender, whether or not higher level mathematics has been studied, self-efficacy and year. The research indicates that either the pre-senior curricula need strengthening or that exposure to mathematics beyond the core senior course is required to establish confidence with basic skills particularly when applied to new contexts and multi- step situations. The Statistical Reasoning Questionnaire (SRQ) is developed for use in the Australian context at the secondary/tertiary interface. As with the Numeracy Questionnaire, detailed examination of the responses provides much insight into the range and features of statistical reasoning at this level. Rasch analyses, both dichotomous and polychotomous, are used to establish the appropriateness of this instrument as a measuring tool at this level. The polychotomous, Rasch partial credit model is also used to define a new approach to scoring a statistical reasoning instrument and enables development and application of a hierarchical model and measures levels of statistical reasoning appropriate at the school/tertiary interface. General linear models indicate that numeracy is a highly significant predictor of statistical reasoning allowing for all other variables including tertiary entrance score and students' backgrounds and self-efficacy. Further investigation demonstrates that this relationship is not limited to more difficult or overtly mathematical items on the SRQ. Performance on the end of semester component of assessment in the course is shown to depend on statistical reasoning at the beginning of semester as measured by the partial credit model, allowing for all other variables. Because of the dominance of the relationship between statistical reasoning (as measured by the SRQ) and numeracy on entry, some further analysis of the end of semester assessment is carried out. This includes noting the higher attrition rates for students with less mathematical backgrounds and lower numeracy.

Made available in DSpace on 2016-06-02T19:50:28Z (GMT). No. of bitstreams: 1 TeseABS.pdf: 2232752 bytes, checksum: a1757428e1651e0e6c2121d798b0d831 (MD5) Previous issue date: 2006-02-09 / With the growth of customer demand level, at last two decades it appeared quality improvement approach focusing customer satisfaction as the way to the organizations improve the efficiency and effectiveness of their processes. Though this, to get their aim, it was necessary broke some paradigms; to stimulate creativity; to innovate; to intensify the effort to reduce processes variation; and above all to assume customer satisfaction in all operations as a priority. Six Sigma approach has been solidifying as an efficient alternative to organizational growth on the strength of quality levels elevation. But, how can we define Six Sigma? Making a theoretical and conceptual research several definitions founded in literature were rescued and examined with purpose to compose a broader definition which translates better Six Sigma meaning. About structure of Six Sigma Quality Program (PQSS), this thesis became as a link between theory and practice when it aided others theories to Six Sigma context and when it used empirical subsidies to identify and evaluate the essential components to structure the PQSS. The empirical subsidies were obtained from qualitative research (case studies) involving four Brazilian subsidiaries of American multinational companies. After to analyze the empirical evidences, it was possible to formalize a set of arguments to purpose a Reference Model to structure the PQSS. This model is sustained by the followings components: strategic orientation; statistical thinking; performance measurement; Six Sigma methodology; and people graduation and qualification. To evaluate the Reference Model it was developed a quantitative research based in Green belts, Black belts and Master Black belts information. Statistical results showed that each one of these components has a meaningful relevance to compose the minimal structure to the PQSS. As principal conclusions this thesis highlights: (1) the PQSS as an integrator program of strategic and operational objectives; (2) strategic orientation and alignment are fundamental to define Six Sigma projects; (3) the use of performance measures increases the potential of Six Sigma projects; (4) its not clear for many specialists that statistical thinking is a background to PQSS; (5) Six Sigma projects are catalysts of a system which uses these projects to reflect it strategic orientation and customer focus importance to get measurable results; and (6) the Reference Model can be valid and can be utilized to structure or re-structure the PQSS implementation. / Com o aumento do nível de exigências dos clientes, as iniciativas de melhoria da qualidade que surgiram nas últimas duas décadas focaram fortemente a satisfação do cliente como o caminho para as organizações aumentarem a eficiência e a eficácia de seus processos produtivos. Todavia, para trilharem este caminho, foi necessário quebrar paradigmas; estimular a criatividade; inovar; intensificar o esforço em reduzir a variação dos processos; e, sobretudo, priorizar a satisfação dos clientes em todas as operações. O Seis Sigma é uma abordagem que vêm se consolidando como uma forma eficiente de crescimento organizacional, decorrente da elevação dos níveis de qualidade. Mas, afinal, como Seis Sigma é definido? Por meio de uma pesquisa teórico-conceitual, diversas definições encontradas na literatura foram resgatadas e analisadas visando compor uma definição mais ampla, e que traduza melhor a abrangência do Seis Sigma. No tocante ao Programa de Qualidade Seis Sigma (PQSS), esta tese trouxe um enlace de teoria e prática ao incorporar outras teorias ao contexto do Seis Sigma, e ao agregar subsídios empíricos para identificar e avaliar componentes que são essenciais para estruturar o PQSS. Estes subsídios decorreram de uma pesquisa com abordagem qualitativa realizada com quatro subsidiárias brasileiras de empresas multinacionais americanas (estudo de casos). Após análise das evidências empíricas foi possível formalizar um conjunto de argumentos que levaram a proposição de um Modelo de Referência para estruturar o PQSS, o qual é sustentado basicamente pelos seguintes componentes essenciais: orientação estratégica; pensamento estatístico; medição de desempenho; metodologia Seis Sigma; e capacitação/especialização das pessoas. Uma avaliação preliminar do Modelo de Referência é apresentada logo após o modelo ter sido proposto e detalhado. Esta avaliação foi realizada com base em uma pesquisa empírica com abordagem quantitativa que envolveu Green belts, Black belts e Master black belts. Realizada a análise estatística, os resultados obtidos revela ram, entre outros pontos, que cada um dos componentes considerados no Modelo de Referência possui uma relevância significativa para estruturar o PQSS. Como conclusões a tese destaca que: (1) o PQSS é um programa integrador dos objetivos estratégicos e operacionais que facilita o direcionamento e a implementação dos projetos Seis Sigma; (2) a orientação estratégica e o alinhamento são priorizados na definição dos projetos Seis Sigma; (3) o uso de indicadores de desempenho aumenta o potencial dos projetos Seis Sigma; (4) ainda não há uma compreensão de que o pensamento estatístico consiste num pano de fundo para o PQSS; (5) os projetos Seis Sigma são catalisadores de um sistema que reflete, por meio destes, a visão estratégica e a importância do foco no cliente para se conseguir resultados mensuráveis que impactam em uma ou mais dimensões do sistema de medição do desempenho organizacional; e (6) há evidências de que o Modelo de Referência pode ser válido, o que permite que ele seja utilizado para estruturar ou re-estruturar o PQSS.