• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.417-427
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• 2015

Measures in response rate used to measure the representativeness of the sample (the more high response rate) better explain the representativeness of the sample. However, we cannot often explain the representativeness of the sample because there is nonresponse even in the high response rate. Therefore, Schouten et al. (2009) presented a new R-indicator measure that can be described as a representative of the sample. We research the new estimator of the R-indicator in this paper because there are parameters that require estimations. We describe the meanings as representative of the R-indicator; consequently, the bias and efficiency of the proposed estimator for R-indicator are compared to the existing estimator under various simulations. The representativeness of the sample is also explained by applying the proposed estimators in the actual data.

• School Mathematics
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• v.17 no.3
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• pp.515-530
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• 2015

The concepts of sample and sampling are central to make a statistically correct decision, so we need to be emphasized their importance in the statistics education. Nevertheless, there were not enough studies which discuss how to teach the concepts of sample and sampling. In this study, teaching sample and sampling is addressed by foreign curricula and cases of instruction in order to obtain suggestions for teaching sample and sampling. In particular, the curricular of Australia, New Zealand, England and the United States are analyzed, considering the sample representativeness and the sampling variability; the two elements in the concept of sample. Also foreign textbooks and cases of instruction when it comes to teach sample are analyzed. The results say that with respect to teach sample can be divided into four suggestions: first, sample was taught in the process of statistical inquiry such as data collection, analysis, and results. Second, sample was introduced earlier than Korea curriculum. Third, when it comes to teach sample, sample variability, as well as sample representativeness was considered. Fourth, technological tools were used to enhance understanding sample.

• School Mathematics
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• v.16 no.4
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• pp.727-743
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• 2014

The concepts of sample and sampling are central to the statistical thinking and foundations of the statistical literacy, so we need to be emphasized their importance in the statistics education. However, many researches which dealt with samples only analyze textbooks or students' responses. In this study, the concept of sample is addressed by a historical consideration which is one aspect of the didactical analysis. Moreover, developing concept of sample is analyzed from the preceding studies about the statistical literacy, considering the sample representativeness and the sampling variability. The results say that the historical process of developing the concept of sample can be divided into three step: understanding the sample representativeness; appearing the sample variance; recognizing the sampling variability. Above all, it is important to aware and control the sampling variability, but many related researches might not consider sample variability. Therefore, it implies that the awareness and control of sampling variability are needed to reflect to the teaching-learing of sample for developing the students' statistical literacy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.10
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• pp.2650-2662
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• 2012

Due to the semantic gap issue, the performance of automatic image annotation is still far from satisfactory. Active learning approaches provide a possible solution to cope with this problem by selecting most effective samples to ask users to label for training. One of the key research points in active learning is how to select the most effective samples. In this paper, we propose a novel active learning approach based on sparse graph. Comparing with the existing active learning approaches, the proposed method selects the samples based on two criteria: uncertainty and representativeness. The representativeness indicates the contribution of a sample's label propagating to the other samples, while the existing approaches did not take the representativeness into consideration. Extensive experiments show that bringing the representativeness criterion into the sample selection process can significantly improve the active learning effectiveness.

• The Mathematical Education
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• v.56 no.1
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• pp.19-39
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• 2017

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don't appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers' understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson's statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.69-82
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• 2017

R-indicator (representativeness indicator) is used to check the representativeness of samples when non-responses occur. The representativeness is related with the accuracy of parameter estimator and the accuracy is related with bias of the estimator. Hence, unbiased estimator generates high accuracy. Therefore, high value of R-indicator guarantees the accuracy of parameter estimation with a small bias. R-indicator is calculated through propensity scores obtained by logit or probit modeling. In this paper we investigate the degree of relation between R-indicator and different non-response rates in strata using simulation studies. We also analyze a modified Korea Economic Census data for real data analysis.

• Journal of Environmental Impact Assessment
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• v.24 no.6
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• pp.607-618
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• 2015

Five years have passed since the first set of environmental samples was taken in 2011 to represent various ecosystems which would help future generations lead back to the past environment. Those samples have been preserved cryogenically in the National Environmental Specimen Bank(NESB) at the National Institute of Environmental Research. Even though there is a strict regulation (SOP, standard operating procedure) that rules over the whole sampling procedure to ensure each sample to represent the sampling area, it has not been put to the test for the validation. The question needs to be answered to clear any doubts on the representativeness and the quality of the samples. In order to address the question and ensure the sampling practice set in the SOP, many steps to the measurement of the sample, that is, from sampling in the field and the chemical analysis in the lab are broken down to evaluate the uncertainty at each level. Of the 8 species currently taken for the cryogenic preservation in the NESB, pine tree samples from two different sites were selected for this study. Duplicate samples were taken from each site according to the sampling protocol followed by the duplicate analyses which were carried out for each discrete sample. The uncertainties were evaluated by Robust ANOVA; two levels of uncertainty, one is the uncertainty from the sampling practice, and the other from the analytical process, were then compiled to give the measurement uncertainty on a measured concentration of the measurand. As a result, it was confirmed that it is the sampling practice not the analytical process that accounts for the most of the measurement uncertainty. Based on the top-down approach for the measurement uncertainty, the efficient way to ensure the representativeness of the sample was to increase the quantity of each discrete sample for the making of a composite sample, than to increase the number of the discrete samples across the site. Furthermore, the cost-effective approach to enhance the confidence level on the measurement can be expected from the efforts to lower the sampling uncertainty, not the analytical uncertainty. To test the representativeness of a composite sample of a sampling area, the variance within the site should be less than the difference from duplicate sampling. For that, a criterion, ${i.e.s^2}_{geochem}$(across the site variance) <${s^2}_{samp}$(variance at the sampling location) was proposed. In light of the criterion, the two representative samples for the two study areas passed the requirement. In contrast, whenever the variance of among the sampling locations (i.e. across the site) is larger than the sampling variance, more sampling increments need to be added within the sampling area until the requirement for the representativeness is achieved.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2005.06a
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• pp.151-157
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• 2005

For the treatment of regulatory clearance of the soils, a procedure for the radionuclides and radioactivity concentration analysis is under development. A strategy for soil sampling including random sampling after homogenization and standardization was set up. Statistical representativeness is considered for not only sampling strategy but also sample size. In this study, designed sample size was designed with confidence interval and error bound of soil using the pilot samples which were taken following the sampling strategy.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.91-97
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• 2016

This study is concerned about the process capability index in single process. Previous process capability indices have been developed for the consistency with the nonconforming rate due to the process target value and skewness. These indices calculate the process capability by measuring one spot in an item. But the only one datum in an item reduces the representativeness of the item. In addition to the lack of representativeness, there are many cases that the uniformity of the item such as flatness of panel is absolutely important. In these cases, we have to measure several spots in an item. Also the nonconforming judgment to an item is mainly due to the range not due to the standard variation or the shift from the specifications. To imply the uniformity concept to the process capability index, we should consider only the variation in an item. It is the within subgroup variation. When the universe is composed of several subgroups, the sample standard deviation is the sum of the within subgroup variation and the between subgroup variation. So the range R which represents only the within subgroup variation is the much better measure than that of the sample standard deviation. In general, a subgroup contains a couple of individual items. But in our cases, a subgroup is an item and R is the difference between the maximum and the minimum among the measured data in an item. Even though our object is a single process index, causing by the subgroups, its analytic structure looks like a system process capability index. In this paper we propose a new process capability index considering the representativeness and uniformity.

• The Mathematical Education
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• v.57 no.4
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• pp.413-431
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• 2018

In this study, I developed an activity oriented lesson to support the understanding of probabilistic and quantitative estimating population ratios according to the standard statistical principles and discussed its implications in didactical respects. The developed activity lesson, as an efficient physical simulation activity by sampling with replacement, simulates unknown populations and real problem situations through completely closed 'Closed Box' in which we can not see nor take out the inside balls, and provides teaching and learning devices which highlight the representativeness of sample ratios and the sampling variability. I applied this activity lesson to the gifted students who did not learn estimating population ratios and collected the research data such as the activity sheets and recording and transcribing data of students' presenting, and analyzed them by Qualitative Content Analysis. As a result of an application, this activity lesson was effective in recognizing and reflecting on the representativeness of sample ratios and recognizing the random sampling variability. On the other hand, in order to show the sampling variability clearer, I discussed appropriately increasing the total number of the inside balls put in 'Closed Box' and the active involvement of the teachers to make students pay attention to controlling possible selection bias in sampling processes.