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Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 66-70).

Thesis (M. Phil.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 107-113).

No description available.

This thesis is composed of six papers, all dealing with the issue of sampling from a finite population. We consider two different topics: real time sampling and distributions in sampling. The main focus is on Papers A–C, where a somewhat special sampling situation referred to as real time sampling is studied. Here a finite population passes or is passed by the sampler. There is no list of the population units available and for every unit the sampler should decide whether or not to sample it when he/she meets the unit. We focus on the problem of finding suitable sampling methods for the described situation and some new methods are proposed. In all, we try not to sample units close to each other so often, i.e. we sample with negative dependencies. Here the correlations between the inclusion indicators, called sampling correlations, play an important role. Some evaluation of the new methods are made by using a simulation study and asymptotic calculations. We study new methods mainly in comparison to standard Bernoulli sampling while having the sample mean as an estimator for the population mean. Assuming a stationary population model with decreasing autocorrelations, we have found the form for the nearly optimal sampling correlations by using asymptotic calculations. Here some restrictions on the sampling correlations are used. We gain most in efficiency using methods that give negatively correlated indicator variables, such that the correlation sum is small and the sampling correlations are equal for units up to lag m apart and zero afterwards. Since the proposed methods are based on sequences of dependent Bernoulli variables, an important part of the study is devoted to the problem of how to generate such sequences. The correlation structure of these sequences is also studied. The remainder of the thesis consists of three diverse papers, Papers D–F, where distributional properties in survey sampling are considered. In Paper D the concern is with unified statistical inference. Here both the model for the population and the sampling design are taken into account when considering the properties of an estimator. In this paper the framework of the sampling design as a multivariate distribution is used to outline two-phase sampling. In Paper E, we give probability functions for different sampling designs such as conditional Poisson, Sampford and Pareto designs. Methods to sample by using the probability function of a sampling design are discussed. Paper F focuses on the design-based distributional characteristics of the π-estimator and its variance estimator. We give formulae for the higher-order moments and cumulants of the π-estimator. Formulae of the design-based variance of the variance estimator, and covariance of the π-estimator and its variance estimator are presented.

Traditional tests for large-scale assessment of mathematics learning have been criticized for several reasons, such as their mismatch between the vision of mathematical competence and the content covered by the test, and their failure to provide relevant information for guiding further learning and instruction. To achieve that large-scale assessments can function as tools for monitoring and improving learning and teaching, one has to move away from the rationale, the constraints, and the practices of traditional tests. As an illustration this paper presents an alternative approach to largescale assessment of elementary school mathematics developed in Flanders, Belgium Using models of item response theory, 14 measurement scales were constructed, each representing a cluster of curriculum standards and covering as a whole the mathematics curriculum relating to numbers, measurement and geometry. A representative sample of 5,763 sixth-graders (12-year-olds) belonging to 184 schools participated in the study. Based on expert judgments a cut-off score was set that determines the minimum level that students must achieve on each scale to master the standards. Overall, the more innovative curriculum standards were mastered less well than the more traditional ones. Few gender differences in performance were observed. The advantages of this approach and its further development are discussed.

Traditional tests for large-scale assessment of mathematics learning have been criticized for several reasons, such as their mismatch between the vision of mathematical competence and the content covered by the test, and their failure to provide relevant information for guiding further learning and instruction. To achieve that large-scale assessments can function as tools for monitoring and improving learning and teaching, one has to move away from the rationale, the constraints, and the practices of traditional tests. As an illustration this paper presents an alternative approach to largescale assessment of elementary school mathematics developed in Flanders, Belgium Using models of item response theory, 14 measurement scales were constructed, each representing a cluster of curriculum standards and covering as a whole the mathematics curriculum relating to numbers, measurement and geometry. A representative sample of 5,763 sixth-graders (12-year-olds) belonging to 184 schools participated in the study. Based on expert judgments a cut-off score was set that determines the minimum level that students must achieve on each scale to master the standards. Overall, the more innovative curriculum standards were mastered less well than the more traditional ones. Few gender differences in performance were observed. The advantages of this approach and its further development are discussed.