표본 지도에 대한 고찰: 국외 교육과정 분석을 중심으로

구나영,이경화,강현영,탁병주 대한수학교육학회 2015 학교수학 Vol.17 No.3

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 representativeness, as well as sample variability were considered. Fourth, technological tools were used to enhance understanding sample. 통계 교육에서 표본(sample)과 표집(sampling)은 통계적으로 올바르고 합리적인 의사결정을 하기 위해 강조되어야하는 개념이다. 그럼에도 불구하고 표본과 표집 개념을 어떻게 지도하는지에 관해서는 충분히 연구되지 않은 상황이다. 이에 본고에서는 표본과 관련된 지도 방법에 대한 시사점을 얻기 위하여 국외 교육과정 및 지도 사례를 중심으로 표본이 어떻게 지도되는지 살펴보았다. 특히, 표본 개념의 두 요소인 표본대표성(sample representativeness)과 표집변이성(sampling variability)을 중심으로, 호주, 뉴질랜드, 영국, 미국의 교육과정을 분석했다. 또한 외국 교과서와 선행 연구의 표본 지도 사례를 분석하였다. 이를 토대로, 표본 지도에 관하여 첫째, 자료수집, 분석, 결과 해석이라는 통계적 탐구과정의 경험과 함께 지도하고, 둘째, 현재 지도시기보다 빨리 지도하고, 셋째, 표본대표성 뿐만 아니라 표집변이성을 고려하여 지도하고, 넷째, 효과적인 지도를 위해 공학 도구를 활용해야 한다는 시사점을 도출하였다.

중등수학 예비교사들의 통계적 소양 : 표본 개념에 대한 이해를 중심으로

탁병주 ( Tak Byungjoo ),구나영 ( Ku Na-young ),강현영 ( Kang Hyun-young ),이경화 ( Lee Kyeong-hwa ) 한국수학교육학회 2017 수학교육 Vol.56 No.1

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.

Concept Designs of a Sampler Device for Taking Representative Samples From Waste Packages of High Integrity Containers (HICs)

Hang-Rae Cho,Sang-June Park,Young-Hwan Hwang,Su-Il Bang 한국방사성폐기물학회 2022 한국방사성폐기물학회 학술논문요약집 Vol.20 No.2

Radioactive spent resin and concentrate waste powder generated from the primary system of nuclear power plants (NPPs) should be treated and disposed of in the form of solidified products or high integrity container (HIC) packages. We are preparing for the application of polymer concrete high integrity containers (PC-HICs) that has been approved for disposal and field application after going through the disposal suitability review of the repository operator and the license review process of the regulatory body. A reliable assessment of nuclide inventory in waste drum is required for the disposal of the radioactive waste drums, and the representative samples should be collected for both the indirect (non-destructive assessment based on the scaling factor, average radioactivity concentration, etc.) and direct (destructive analysis) evaluation of the difficult-to-measure (DTM) nuclides. It is important to secure the representativeness of samples for reliable and accurate evaluation of radionuclide inventory and approval of methodologies for highly radioactive waste such as spent resin and concentrate waste poser, and in order to secure the radiation safety of the sampling workers and representativeness of the samples, a remote sampling method is required with excellent convenience and safety and sufficient representativeness of the sample. The simple sampling device used in the past to collect samples for the scaling factor does not have a remote control function, so high-radiation samples must be collected within a very short time and it is difficult to obtain sufficiently representative samples due to structural characteristics that cannot collect the entire sample in the axial direction of the package. Therefore we developed concept designs for a remote sampling device that can satisfy both sample representativeness, operator convenience and safety.

국가환경시료은행 생태계 대표시료의 채취 및분석 표준운영절차에 대한 단계별 측정불확도 평가 연구

이종천 ( Jongchun Lee ),이장호 ( Jangho Lee ),박종혁 ( Jong Hyouk Park ),이유진 ( Eugene Lee ),심규영 ( Kyuyoung Shim ),김태규 ( Taekyu Kim ),한아름 ( Areum Han ),김명진 ( Myungjin Kim ) 한국환경영향평가학회 2015 환경영향평가 Vol.24 No.6

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. s2 geochem(across the site variance) 〈s2 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.

Review on the Methodology for Evaluating the Radioactivity in the High Integrity Container Packages of Dried Spent Resin and Concentrate Radwaste

Hang-Rae Cho,Seong-Jin Maeng,Ji-Soo Yoon,Kyung-Rok Park,Jung-Kwon Son 한국방사성폐기물학회 2023 한국방사성폐기물학회 학술논문요약집 Vol.21 No.2

To safely dispose of highly radioactive spent resin and concentrate waste generated through nuclear power plant operations, it is essential to meet the physicochemical properties requirements of the packages and ensure the accuracy and reliability of radiological characteristics determination. Both spent resin and concentrate are packaged in high-integrity containers (HICs) after drying and are homogeneous waste products generated in the primary system and liquid radioactive waste treatment system. Meeting the physicochemical properties requirements does not appear to be difficult. However, to achieve reliable radiological characterization of high-integrity container packages, it is necessary to take a representative sample and perform accurate radiological analysis. Therefore, this paper discusses the methodology for evaluating the radionuclide inventory of high radioactive resin and concentrate packages, as well as the essential element technology and considerations. For relatively high radioactive resin and concentrate packages, the radionuclide inventory for each package should be evaluated with high reliability through direct radiological analysis of the representative samples collected for each package. This can contribute to the efficient operation of radioactive waste disposal facilities. Radionuclide-specific concentrations directly analyzed for each package will be managed in a database. As analytical data accumulates and direct measurements of high-integrity container package such as the radwaste drum assay system (RAS) become feasible, statistical techniques such as correlation analysis between easy-tomeasure (ETM) nuclides and difficult-to-measure (DTM) nuclides can lead to the development of efficient and reasonable indirect evaluation methods, such as scaling factor and the mean activity concentration method. As for the element technology, a remote representative sampling technique should be developed to safely and effectively take representative samples of highly radioactive materials, including granulated or hardened concentrate waste. Considerations should also be given to determining the sample quantity representing each package, as well as establishing radiation calibration and measurement methods appropriate to the radiation levels of the representative samples.

예비교사들의 통계적 표집에 대한 이해

고은성,이경화 대한수학교육학회 2011 수학교육학연구 Vol.21 No.1

본 연구에서는 예비교사들의 통계적 표집에 대한 이해를 조사하였다. 먼저 선행연구를 바탕으로 표집의 이해와 관련된 주요 주제를 표본의 대표성, 표집 변이성, 표집분포로 구분하고, 각각의 주요 주제에 대한 세부 개념 요소들을 선정하였다. 이에 대한 예비교사들의 이해를 조사한 결과 대부분의 예비교사들이 편의를 일으키지 않는 무작위 추출이 표집방법으로 적절함을 이해하고 있었으나 약 64%의 예비교사들만이 표본을 모집단의 준비례적 축소버전으로 인식하고 있었다. 표집에서 표본이 모집단에서 차지하는 비율보다 표본의 크기 자체가 중요함을 인식하는 예비교사는 극소수에 불과했으며, 조사 대상의 절반에 해당하는 예비교사들만이 신뢰할 수 있는 결과를 도출하기 위해 전체 표본의 크기가 아니라 표집 횟수가 중요함을 인식하였다. 그리고 표집분포는 모집단 분포의 형태와 무관하게 모집단의 평균을 중심으로 대칭적인 형태를 나타낸다는 것을 이해하는 예비교사는 매우 적었다. This study investigated pre-service teachers' understanding of statistical sampling. The researchers categorized major topics related to sampling into representativeness of samples, sampling variability, and sampling distribution, and selected concepts connected to each topic. Findings on this study are as follows: Even though most of the pre-service teachers considered the random sampling bringing unbiased outcomes as a proper sampling method, only 64% of them recognized that sample is a quasi-proportional, small-scale version of population; Few pre-service teachers understood that more important is the size of sample, not the portion of sample to population, and half of them appreciated that the number of sampling has a powerful effect on drawing of reliable results than the size of sample; Few pre-service teachers understood that sampling distribute is irrelevant to the shape of population and has a symmetrical bell-shape.

植物考古學에 適用되는 土壤試料 크기의 標準化 및 種子 遺體 密度의 相對 比較法 : 南江댐 水沒地區 靑銅器時代 遺蹟 出土種子遺體를 중심으로

이경아 한국청동기학회 2012 한국청동기학보 Vol.10 No.-

본고는 각 표본집단(토양시료)이 모집단에 대하여 동일한 대표성을 갖게 산출하고 식물유체의 수량 비교시 통계적 유의성을 갖춘 계측치를 제시하고자 한다. 먼저 본고는 상대오차와 확률에 기초하여 여러 유적에서 채취된 토양시료 표본의 크기를 표준화하는 통계법을 제시하였다. 표본 크기의 표준화는 여러 유적에서 출토된 식물유체 간 수량의 차이가 단지 표본의 크기 차이에서 비롯됨이 아니라 문화적 원인 즉 식물 자원 이용상의 차이를 반영한다고 추정할 수 있는 근거를 마련한다. 통계적 대표성과 토양시료 채취는 기본적으로 군집표집의 일환이므로 토양시료의 수를 표본의 크기로 각 토양시료에서 추출된 종자의 밀도를 변수로 간주하였다. 이러한 표본 크기 표준화 방법을 남강댐 수몰지구 어은 및 옥방 유적 청동기시대 유구에서 출토된 식물유체에 적용하여 그 실효성을 타진하고자 한다. 또한 여러 표본(예, 유적, 유구)의 변수(종자 밀도)를 비교할 때 상이한 보존율과 복원율이 미치는 영향을 최소화할 수 있는 표본간 종별 중복비율을 모식도를 통해 제시하였다. One of the main questions in paleoethnobotany is how large the sample size should be andthen how to achieve the compatibility among samples with different sizes. A sample inpaleoetnobtany is in fact a feature, a three-dimensional context, but what is wanted is acertain quantity of plant remains from it. That is paleoethnobotanical sampling is in the realmof cluster sampling, not a random sampling of seeds themselves. The relation between thetwo (i.e, seed density) is only apparent after the sample has been taken and the analysis hasbeen done. The difficulty herein is to predict the sample size that will be needed to yield therequired degree of precision. This paper aims to devise a formula to estimate sample sizeswith the same amount of relative error at a fixed confidence level across all samples. Theformula is applied to estimating the required sample sizes for the Early and Middle Bronze-period features in the Nam River valley, South Korea. The next step is to design thequantitative methods which are less sensitive to differences in preservation and retrieval ratesamong samples. The suggested ratios of the ratios between seed taxa across the samplesreflect the comparisons between the two original (target) populations, that is the buriedassemblages.

법정대리인의 동의에 의한 음주운전자 채혈의 법적 문제 - 대법원 2014.11.13. 선고 2013도1228 판결 [공2014하,2390]

문성도 한국경찰법학회 2023 경찰법연구 Vol.21 No.2

Korean Criminal Procedure Act provides, in a case involving a criminal offense to which the provisions of Articles 9 through 11 of the Criminal Act do not apply and in a case the defendant or the suspect is devoid of mental capacity, he shall be represented by his legal representative in regard of acts of litigation. In the 2013Do1228 Judgment sentenced by the Korean Supreme Court on November 13, 2014, the question was whether a legal representative could consent to blood collection on behalf of a suspect who is devoid of mental capacity if it was necessary to collect blood from a minor suspect. This issue had to be discussed in two stages. The first question was whether Article 26 of the Criminal Procedure Act could be a legal basis for legal representatives' consent to blood collection. In other words, the question was whether Article 26 of the Criminal Procedure Act explicitly recognized proxy for litigation activities such as consent to blood collection. The Supreme Court did not approve of this. It interpreted "a criminal case not subject to Articles 9 to 11 of the Criminal Code" as a criminal case that can be punished in the same way as mentally mature even if a person is mentally deficient or incapable. It saw that this was a criminal case that had to invoke the state's right to punish a person in order to achieve the legislative purpose, even if he was not responsible. The next step was whether litigation activity could be represented without the basis of explicit regulations if Article 26 was not a clear basis for representation of litigation activity called consent to blood collection. In this case, the Supreme Court did not allow representation of litigation activities unless there were explicit provisions. This attitude of the Supreme Court may be considered appropriate. Where it is necessary to protect the rights of suspects and defendants, it shall be deemed that there are specific provisions in place. For example, regarding the evidence preservation procedure under Article 184 of the Criminal Procedure Act, Korean Criminal Procedure Act recognizes prosecutors, suspects, defendants and lawyers as claimants and does not recognize representation. However, defendants and suspects can request the preservation of evidence by appointing lawyers and prepare for defense using the assistant system Article 29 of the Korean Criminal Procedure Act. In order to use the assistant system as a legal basis for the litigation activity of consenting to drunk blood collection, it will be necessary to legally guarantee a reduction in punishment equivalent to surrender or release of hostages. It is questionable why there cannot be a clause on reducing punishment for cooperation in drinking tests while punishing drunk driving and criminalizing non-compliance with drinking tests. It is necessary to distinguish it from the self-denunciation of general criminals by making it a necessary reduction rather than an arbitrary reduction. 우리 형사소송법은 형법 제9조 내지 제11조의 규정의 적용을 받지 아니하는 범죄사건에 관하여 피고인 또는 피의자가 의사능력이 없는 때에는 그 법정대리인이 소송행위를 대리하도록 하고 있다(제26조). 대법원 2014.11.13. 선고 2013도1228 판결에서는 음주운전과 관련한 도로교통법 위반죄의 범죄수사를 위하여 미성년자인 피의자의혈액채취가 필요한 경우, 법정대리인이 의사능력 없는 피의자를 대리하여 채혈에 관한동의를 할 수 있는지 여부가 문제되었다. 이 문제에 대해서는 두 단계로 나누어 논의할 필요가 있었다. 먼저 형사소송법 제26조가 법정대리인의 채혈동의에 대한 법적 근거가 될 수 있는가 하는 점이었다. 말하자면 채혈 동의라는 소송행위에 대한 대리를 형사소송법 제26조가 명문으로 인정한것이라고 할 수 있는가 하는 점이다. 이에 대해 대법원은 인정하지 않았다. ‘형법 제9조 내지 제11조의 규정의 적용을 받지 아니하는 범죄사건’이란 책임무능력 혹은 한정책임능력의 경우에도 완전한 책임능력을 가진 경우와 동일하게 처벌할 수 있는 범죄사건이라고 본 것이다. 입법 목적의 달성을 위하여 책임능력이 없는 경우에도 국가형벌권을 발동하여야 하는 범죄사건이 여기에 해당한다고 보았다. 다음 단계로는 만일 제26조가 채혈동의라는 소송행위의 대리에 대한 명문 근거가되지 않는다면, 명문 규정의 근거 없이 소송행위의 대리를 인정할 수 있는가 여부이었다. 이 사건에서 대법원은 명문의 규정이 없는 경우 소송행위의 대리를 인정하지 않았다. 생각건대 이러한 대법원의 태도는 타당하다 할 것이다. 피의자 및 피고인의 권리보호를 위해 필요한 경우에는 명문규정을 특별히 두고 있다고 보아야 할 것이다. 가령형사소송법 제184조의 증거보전절차와 관련하여 우리 형사소송법은 청구권자로 검사, 피의자, 피고인, 변호인을 인정하 면서 이에 대한 대리를 인정하지 않고 있다. 하지만, 피고인·피의자는 변호인을 선임하여 증거보전청구를 할 수 있고, 보조인 제도를 활용하여 방어준비를 할 수 있다. 음주채혈 동의라는 소송행위에 대한 대리의 법적 근거로서 보조인제도를 활용하기 위해서는 자수 내지 인질석방에 준하는 형벌 감면을 법적으로 보장하여야 할 것이다. 보조인에 의한 소송행위 대리(제29조)는 의사무능력자의 법정대리인에 의한 소송행위의 대리(제26조)와는 달리 임의적인 것으로 피의자 측의 의사에 맡겨져 있기 때문이다. 음주운전행위를 처벌하고 나아가 음주측정불응행위를 형사처벌하면서 음주측정협조행위에 대해서는 왜 형벌 감면조항을 두지 않는 것인지 의문이다. 임의적 감면보다는 필요적 감면으로 하여 일반적인 범죄자의 자수와 구별할 필요가 있다.

단기간 소음도의 대표성 확보를 위한 소음도 추출기법 연구

류훈재(Ryu, Hun Jae),고준희(Ko, Joon Hee),장서일(Chang, Seo Il),이병찬(Lee, Byung Chan) 한국소음진동공학회 2012 한국소음진동공학회 논문집 Vol.22 No.12

The purpose of this study is to present a guideline to design a short-term manual measurement of environmental noise level, which is more economical and flexible, but less representative than long-term automatic measurement. The proposed guideline can provide the number of measurement times and the length of measurement term required to secure the extent of the representativeness. The data was collected at 4 sites located in Seoul and at 4 sites located outside of Seoul. The probabilities for five-minute equivalent noise levels, Leq, 5min, to stay in an error range from the quarterly representative noise level were used to evaluate sampling techniques. The probability analysis of the daytime period showed that the noise levels measured between 10 am and 2 pm and between 9 pm and 10 pm have the probabilities higher than 60 %. On the other hand, even for the same length of total measurement time, increasing the number of random samplings results in higher probabilities than increasing the length of measurement term.

표본 개념에 대한 고찰: 역사적 분석을 중심으로

탁병주,구나영,강현영,이경화 대한수학교육학회 2014 학교수학 Vol.16 No.4

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. 표본(sample)과 표집(sampling)은 통계적 사고의 핵심이며 통계적 소양의 기초로서 통계교육에서 매우 강조되어야 하는 개념이다. 그러나 표본에 관한 선행연구에서는 대개 교과서 분석과 학생의 반응 분석 등에 그치고 있다. 이에 본고에서는 표본 개념에 대한 교수학적 분석의 한 측면으로서 역사적 분석을 시행하였다. 특히, 통계적 소양의 관점에서 이루어진 선행연구를 토대로, 표본 개념을 이해하기 위한 두 핵심요소인 표본대표성과 표집변이성에 기반을 두고 표본 개념의 역사적 발달을 분석하였다. 연구 결과, 표본 개념의 역사적 발달 과정은 표본대표성(sample representativeness)의 이해, 표본 변이(sample variance)의 등장, 표집변이성(sampling variability)의 인식으로 분류할 수 있으며, 특히 표집변이성을 인식하고 이를 제어하는 과정의 중요성을 확인할 수 있었다. 그러나 표본 개념의 이해 수준에 대한 기존의 선행연구에는 표집변이성 개념이 잘 반영되지 않고 있다. 이를 토대로, 표본 개념의 교수학습에서 표집변이성을 강조해야 하며, 통계적 소양의 함양을 위해 표집변이성의 인식과 해결의 과정을 포함해야 한다는 시사점을 도출하였다.