• Journal of the Korean Statistical Society
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• v.17 no.2
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• pp.93-100
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• 1988

Two properties of ancillary statistics are considered. One is to find a role of ancillary statistics in the statistical inference by showing that the ancillary statistic can recover the lost information and to give a criteria for comparing the conditional inference with unconditional inference. The other is to find an ancillary statistic of translation model and its relationship with observed Fisher information.

• Research in Mathematical Education
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• v.17 no.4
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• pp.243-266
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• 2013

Accompanied with ongoing calls for reform in statistics curriculum, mathematics and statistics teachers purposefully have been reconsidering the curriculum and the content taught in statistics classes. Changes made are centered around statistical inference since teachers recognize that students struggle with understanding the ideas and concepts used in statistical reasoning. Despite the efforts to change the curriculum, studies are sparse on the topic of characterizing student learning and understanding of statistical inference. Moreover, there are no tools to evaluate students' statistical reasoning in a coherent way. In response to the need for a research instrument, in a series of research study, the researcher developed a reliable and valid measure to assess students' inferential reasoning in statistics (IRS). This paper describes processes of test blueprint development that has been conducted from review of the literature and expert reviews.

• Education of Primary School Mathematics
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• v.22 no.3
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• pp.149-166
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• 2019

The purpose of this study is to analyze the statistical literacy in elementary school students when they beginning inference. Picto-graphs provide statistical information and often data-related arguments they certainly qualify as objects for interpretation, for critical evaluation, and for discussion or communication of the conclusions presented. For research, the inference from pictograph task was designed and statistical literacy standards for evaluating the student's level was presented based on prior studies. Evaluating student's statistical literacy is meaningful in that it can check their current level. To know the student's current level can help them achieve a higher level of performance. The outcomes of this research indicate that pictograph can provide a basis for rich tasks displaying not only student's counting skills but also their appreciation of variation and uncertainty in prediction. Raising statistical thinking by students is an important goal in statistical education, and the experience of informal statistical reasoning can help with formal statistical reasoning that will be learned later. Therefore, the task about the inference from a pictograph, discussions on statistical learning of elementary school children are expected to present meaningful implications for statistical education.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.109-114
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• 2003

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter, which is peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose nonparametric maximum likelihood estimator of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Proceedings of the Korean Information Science Society Conference
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• 2007.06c
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• pp.263-266
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• 2007

This paper discusses the Bayesian statistical inference. This paper discusses the Bayesian inference, MCMC (Markov Chain Monte Carlo) integration, MCMC method, Metropolis-Hastings algorithm, Gibbs sampling, Maximum likelihood estimation, Expectation Maximization algorithm, missing data processing, and BMA (Bayesian Model Averaging). The Bayesian statistical inference is used to process a large amount of data in the areas of biology, medicine, bioengineering, science and engineering, and general data analysis and processing, and provides the important method to draw the optimal inference result. Lastly, this paper discusses the method of principal component analysis. The PCA method is also used for data analysis and inference.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• School Mathematics
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• v.19 no.3
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• pp.533-551
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• 2017

The statistical education researchers advise instructors to educate informal statistical inference and they are paying close attention to the progress of the statistical inference in general. This study was conducted by analyzing the levels and the traits of each levels of the informal statistical inference of the middle and high school students for comparing the samples of data and estimating the graph of a population. Research has shown that five levels of the informal statistical inference were identified for comparing the samples of data: responses that are distracted or misled by an irrelevant aspect, responses that focus on frequencies of individual data points and hold a local view of the sample data sets, responses that the student's view of the data is transitioning from local to global, responses that hold a global view but do not clearly integrate multiple aspects of the distribution, and responses that integrate multiple aspects of the distribution. Another five levels of the informal statistical inference were identified for estimating the graph of a population: responses that are distracted or misled by an irrelevant aspect, responses that focus only on representativeness, responses that consider both representativeness and variability and focus on one particular aspect of the distribution, responses that focus on multiple aspects of distribution but do not clearly integrate them, and responses that integrate multiple aspects of the distribution.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.115-120
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• 2003

Inference for probability P(Y

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.913-926
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• 2000

An electronic statistics text on the web is implemented. The introduced text provide interactive instructions on the statistical estimation and inference. As a by-product, we also provide a calculation of quantiles and p-value of t-distribution and standard normal distribution. This program was written in JAVA programming language.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.313-313
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• 2000