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Objective: The current research was conducted with the aim of studying the scaffolding strategy and providing a new approach for teaching random variables in probability courses of science and engineering students. Methods: In this article, firstly, some issues are raised about active learning and factors such as group work, corrective feedback, and the use of computers that help students learn courses related to statistics and probability. Then the demonstration programs that can replace the classical educational methods were introduced. Results: In the following, some common misconceptions of students about events, random variables and continuous random variables will be mentioned and these concepts will be analyzed by citing a number of examples. In the last part, the concept of scaffolding and its application in random variable education and a teaching approach in statistics and probability courses are described. Conclusion: According to the items stated in the article, it is suggested to teach the basic topics of random variables, instead of teaching discrete and continuous random variables separately, random variables should be taught in general. [ABSTRACT FROM AUTHOR]

Misconceptions often pose significant barriers to effective mathematics learning. This study aimed to investigate the misconceptions prevalent in general mathematics and statistics and probability among senior high school students taught during the modular learning modality. Through a mixed-methods approach, involving quantitative surveys and qualitative interviews, mathematical misconceptions such as procedural knowledge, misapplication of formulas, internal barriers, misleading assumptions, and limited question understanding were identified. The study highlights the implications of these findings for curriculum design, teacher professional development, student-centered instruction, and the development of supplementary resources. Moreover, the study underscores the need for tailored interventions to rectify misconceptions, cultivate a deeper understanding of mathematical concepts, and foster accurate probabilistic reasoning among senior high school students during the new normal mode of instruction. [ABSTRACT FROM AUTHOR]

Copyright of Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education is the property of Balikesir University, Necatibey Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Actas de Diseño is the property of Facultad de Diseno y Comunicacion, Fundacion Universidad de Palermo and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Learning is weak not because learning is weak. Learning becomes weak because the modules were not prepared to become self-directed. The goal of this design and development project was to create a self-directed statistics and probability instructional module. Data were gathered from teachers, learners, and experts. The data-gathering instruments were Competency Checklist, Students' and Experts' Evaluation Checklist, and Reflection Guide. According on teacher perceptions, a survey of the learners' five least-mastered competencies served as the foundation for the development of the module. This module was pilot tested on a group of Grade 11 learners. Learners utilized the module at home and were asked to answer the exercises. Learners took pictures and short videos while they were answering the module. Afterward, learners evaluated the module. In order to assess the module's level of acceptability, experts were requested to complete the Expert's Evaluation Checklist. Thematic analysis, rank, the mean, and standard deviation were all used as data analysis tools. The results show that the following were the five least-mastered competencies: solving problems involving confidence interval of the population mean, solving problems involving regression analysis, solving problems involving sample size determination, solving problems that require population proportion test of hypothesis, and solving problems involving correlation analysis. Additionally, the experts rated the produced module's acceptability as "highly acceptable." While the learners gave the module a "highly acceptable" rating. As a result, the developed module is appropriate for assisting learners in performing the competencies in the area of Statistics and Probability. It is recommended that teachers should use the Self-directed instructional module for whatever mode of learning their school will have. [ABSTRACT FROM AUTHOR]

Aim/Purpose: The study examined how the developed mobile courseware can be used as instructional material to improve senior high school statistics and probability learning, particularly during distance learning caused by the COVID-19 pandemic. The study also aims to assess the gamified mobile courseware's engagement, functionality, aesthetics, and information quality using the Mobile App Rating Scale (MARS) and a researcher-made Gamified Mobile Courseware Assessment Tool (GMCET). Background: The need to investigate the effectiveness of incorporating game-based elements into mathematics courses through innovative instructional materials inspired the study. The COVID-19 pandemic has made distance learning a necessity, and gamified mobile courseware is a potential solution to improve learning outcomes and engagement in mathematics courses. Methodology: The study employed a descriptive-evaluative method with quantitative and qualitative data to achieve its objectives. Five IT practitioners assessed the developed courseware using the MARS regarding engagement, functionality, aesthetics, and information. A researcher-made GMCET was also used to evaluate the app's content quality, learning objectives, content presentation, learning assessment, and usability. Five math experts and 12 math teachers rated the app using the GMCET. The study used weighted mean to analyze the quantitative data and content analysis for the qualitative data. Contribution: The study provides insights into the strengths and weaknesses of gamified mobile courseware from the perspective of IT practitioners, math experts, and math teachers. The study's findings can inform improvements in future iterations of courseware, and the study provides a valuable guide for practitioners looking to develop gamified mobile courseware for mathematics courses. Findings: The quantitative results based on the weighted mean indicate that the IT practitioners had a moderately positive perception of the developed courseware across all categories. At the same time, the math teachers and math experts showed highly positive perceptions of the gamified mobile courseware in Statistics and Probability, rating it highly across all categories. The qualitative data analysis through content analysis highlights the need for improving the user interface, usability, user experience design, user control, flexibility in interaction, data quality, reliability, and user privacy of the developed app. Recommendations for Practitioners: Practitioners can use the study's findings to improve the design of gamified mobile courseware for mathematics courses and other content areas. The study recommends that practitioners focus on improving the user interface, usability, user experience design, user control, flexibility in interaction, data quality, reliability, and user privacy of gamified mobile courseware. Recommendations for Researchers: Future research can build on this study's findings by exploring the use of gamified mobile courseware in other mathematical courses and other subject areas. Further research can also examine how gamified mobile courseware can improve learning outcomes for students with different learning needs. Impact on Society: The study's findings could improve the effectiveness of gamified mobile courseware in enhancing student learning outcomes in mathematics courses. This can lead to better student performance, improved engagement, and increased interest in mathematics courses, positively impacting society. Future Research: Future research can explore using gamified mobile courseware in other mathematics courses and other subject areas. Additionally, future studies can examine how gamified mobile courseware can improve learning outcomes for students with different learning needs. Further research can also investigate the impact of gamified mobile courseware on student motivation, interest, and performance in mathematics courses. [ABSTRACT FROM AUTHOR]

The continuous changes in education require reflection on new practices in Statistics and Probability teaching. The teacher's role facing globalization's emerged changes requires behavioral and methodological changes. In this context, this article presents the application of an alternative methodology to the traditional axis of transmission-assimilation, to demonstrate new possibilities for statistics and probability teaching in management courses at Estácio University in Curitiba. This article objective is to present the results obtained with the Collective Systematization of Knowledge methodology application in the class of Statistics and Probability in the Business Administration and Accounting courses of Estácio University in two different contexts: face-to-face teaching and remote teaching. To this end, at two different times, in 2019 and 2020, the methodology (MARTINS, 2009) was applied with undergraduate students of the management courses, according to the particularities of the remote and face-to-face modalities, through survey-teaching (SEVERINO, 2017), observations, discussion group and questionnaires. The results showed very similar indications for both remote and face-to-face teaching regarding the collective systematization of knowledge (MARTINS, 2009) as a methodological alternative for statistics and probability classes in management courses in the institution involved in the study. [ABSTRACT FROM AUTHOR]

Recently, OT (operational technology) networks of industrial control systems have been combined with IT networks. Therefore, OT networks have inherited the vulnerabilities and attack paths existing in IT networks. Consequently, attacks on industrial control systems are increasing, and research on technologies combined with artificial intelligence for detecting attacks is active. Current research focuses on detecting attacks and improving the detection accuracy. Few studies exist on metrics that interpret anomaly detection results. Different analysis metrics are required depending on the characteristics of the industrial control system data used for anomaly detection and the type of attack they contain. We focused on the fact that industrial control system data are time series data. The accuracy and F1-score are used as metrics for interpreting anomaly detection results. However, these metrics are not suitable for evaluating anomaly detection in time series data. Because it is not possible to accurately determine the start and end of an attack, range-based performance metrics must be used. Therefore, in this study, when evaluating anomaly detection performed on time series data, we propose a range-based performance metric with an improved algorithm. The previously studied range-based performance metric time-series aware precision and recall (TaPR) evaluated all attacks equally. In this study, improved performance metrics were studied by deriving ambiguous instances according to the characteristics of each attack and redefining the algorithm of the TaPR metric. This study provides accurate assessments when performing anomaly detection on time series data and allows predictions to be evaluated based on the characteristics of the attack. [ABSTRACT FROM AUTHOR]

A model forecasting ionospheric disturbances and its impact on GNSS positioning is proposed, called HAPEE (High lAtitude disturbances Positioning Error Estimator). It allows predicting ROTI index and corresponding Precise Point Positioning (PPP) error in Arctic region (i.e. latitudes > 50°). The model is forecasting for the next hour a probability of a disturbance index or PPP error to exceed a given threshold, from solar wind conditions measured at L1 Lagrange point. Or alternatively, it is forecasting a disturbance index level that is exceeded during the next hour for a given percentage of the time. The ROTI model has been derived from NMA network measurements, considering a database covering the years 2007 up to 2019. It is demonstrated that the statistical variability of the ROTI index is mainly following a lognormal distribution. The proposed model has been tested favorably on measurements performed using measurements from stations of the NMA network that were not used for the model derivation. It is also shown that the statistics of PPP error conditioned by ROTI is following a Laplace distribution. Then a new compound model has been proposed, based on a conditional probability combining ROTI distribution conditioned by solar wind conditions and error distributions conditioned by ROTI index level. [ABSTRACT FROM AUTHOR]

The field of 'Statistics and Probability' has expanded its scope over the last few decades and have become an integral part of many fields with continuously increasing demand. This manuscript aimed for at a bibliometric analysis and comparison of all published documents during 2015 - 2019, from journals in the study topic category of 'Statistics and Probability' for Q4 Impact Factor (IF) journals and Emerging Source Citation Index (ESCI) of Web of Science (WoS). Sources with incomplete data for study timeframe were excluded and 31 sources from Q4 IF and 32 from ESCI journals were selected yielding 12808 and 4294 documents respectively. After data extraction from WoS, the bibliometric analysis at; source, author and document levels, were performed using "Bibliometrix" R-package. Q4-IF sources produced around 3 times more documents than ESCI sources. Articles were the main document type for both categories. China and USA were leading countries for Q4-IF while India, USA and Korea were dominant among ESCI documents. Two authors, namely, 'Cordeiro GM' and 'Alizadeh M' were among the 10 most productive authors in both categories. Sources "Communications in Statistics-Theory and Methods" and "Korean Journal of Applied Statistics" were leading contributors for Q4-IF and ESCI category respectively. For both categories, mainly similar trends were observed for keywords and topic coverage. In both Q4-IF and ESCI journals 'Maximum likelihood' and 'Ordered statistics' were observed to be most predominant keywords. A consistent publication trend with few similarities was observed in terms of documents production over the years for these two categories. [ABSTRACT FROM AUTHOR]

Quantitative researchers often discuss research ethics as if specific ethical problems can be reduced to abstract normative logics (e.g., virtue ethics, utilitarianism, deontology). Such approaches overlook how values are embedded in every aspect of quantitative methods, including 'observations,' 'facts,' and notions of 'objectivity.' We describe how quantitative research practices, concepts, discourses, and their objects/subjects of study have always been value-laden, from the invention of statistics and probability in the 1600s to their subsequent adoption as a logic made to appear as if it exists prior to, and separate from, ethics and values. This logic, which was embraced in the Academy of Management from the 1960s, casts management researchers as ethical agents who ought to know about a reality conceptualized as naturally existing in the image of statistics and probability (replete with 'constructs'), while overlooking that S&P logic and practices, which researchers made for themselves, have an appreciable role in making the world appear this way. We introduce a different way to conceptualize reality and ethics, wherein the process of scientific inquiry itself requires an examination of its own practices and commitments. Instead of resorting to decontextualized notions of 'rigor' and its 'best practices,' quantitative researchers can adopt more purposeful ways to reason about the ethics and relevance of their methods and their science. We end by considering implications for addressing 'post truth' and 'alternative facts' problems as collective concerns, wherein it is actually the pluralistic nature of description that makes defending a collectively valuable version of reality so important and urgent. [ABSTRACT FROM AUTHOR]

This work is the result of the studies of a research group that works with Didactic Engineering as a research methodology; it comes from two researches and aims to expose in defense of this methodology in works that focus, above all, on events that occur in the classroom. This relevance of "how" to conduct a research is justified, on the one hand, by the fact of systematizing the researcher's task, maintaining focus and discipline. On the other hand, because it allows internalizing the effects of observation, from the way in which students carry out the proposed activities to any apparatus that is in the physical and cognitive environment in question, also served as a methodological procedure. Therefore, the question that guides this article is: What are the potentials and limitations that Didactic Engineering as a methodological procedure offered during the research? To answer this question, it was decided to analyze the results obtained by a student who participated in all phases of Didactic Engineering, as a methodological procedure, during the approach of ideas that surround the first contacts with the concept of probability. In view of this, we have found that the potentialities can be described as the possibility of checking the students' previous knowledge; valuing the context in which the student is inserted; the student's active participation in the process; the moments of discussion and the student's voice, full of beliefs, while the limitations have led us to see the students' dependence on the figure of the teacher, as the holder of knowledge. [ABSTRACT FROM AUTHOR]

This study investigates preservice middle school mathematics teachers' understanding of statistics and probability and provides a cognitive diagnostic assessment of their strengths and weaknesses on these subjects. A statistical reasoning test that included 15 multiple-choice and 5 open-ended items was developed from the perspective of the log-linear cognitive diagnosis model, which is a general form of the cognitive diagnosis models. The statistical reasoning test was applied to 456 preservice teachers from 4 universities in 3 different regions of Turkey. The collected data were analyzed using the Mplus 6.12 software, and diagnostic feedback on the preservice teachers' responses was provided based on the findings. The analysis suggested that although many preservice teachers were able to represent and interpret the given data, most experienced difficulty in drawing inferences about populations based on samples, selecting and using appropriate statistical methods, and understanding and applying the basic concepts of probability. In addition, preservice teachers had difficulty answering open-ended items. Implications for teaching are also discussed. [ABSTRACT FROM AUTHOR]

This study investigated the effects of two different accountability scoring mechanisms (ASMs), which were used during the peer instruction (PI) process, on preservice middle school mathematics teachers’ (PSTs) achievements in statistics and probability. In the spring semester of 2016-2017 academic year, 46 third-year PSTs, who had been attending a statistics and probability course, participated in the study. Based on their pre-test scores, the PSTs were randomly divided into two equally achieving groups (Group 1 and Group 2). The data of this study were collected using an academic achievement test and PI and course evaluation forms. A learning management system (LMS), which was a web-based application designed by the first author, was used in collecting the PSTs’ responses to the given conceptual questions. Two different ASMs were used in calculating the PSTs’ PI scores. The findings showed that the PSTs in Group 1 obtained significantly higher overall academic, PI, and post-test scores than the PSTs in Group 2. Therefore, the PSTs’ PI and overall academic achievement scores differed based on the ASM used. Thus, using an ASM during a PI process found to be effective in increasing the PSTs’ engagement in the peer discussion. Finally, the analysis of the PSTs’ opinions regarding to the PI, learning process, and learning environment indicated their overall satisfaction. [ABSTRACT FROM AUTHOR]

The Solar Accumulated and Peak Proton and Heavy Ion Radiation Environment (SAPPHIRE) model provides environment specification outputs for all aspects of the Solar Energetic Particle (SEP) environment. The model is based upon a thoroughly cleaned and carefully processed data set. Herein the evolution of the solar proton model is discussed with comparisons to other models and data. This paper discusses the construction of the underlying data set, the modelling methodology, optimisation of fitted flux distributions and extrapolation of model outputs to cover a range of proton energies from 0.1 MeV to 1 GeV. The model provides outputs in terms of mission cumulative fluence, maximum event fluence and peak flux for both solar maximum and solar minimum periods. A new method for describing maximum event fluence and peak flux outputs in terms of 1-in-x-year SPEs is also described. SAPPHIRE proton model outputs are compared with previous models including CREME96, ESP-PSYCHIC and the JPL model. Low energy outputs are compared to SEP data from ACE/EPAM whilst high energy outputs are compared to a new model based on GLEs detected by Neutron Monitors (NMs).

Context. Changes in the spectral solar irradiance (SSI) are a key driver of the variability of the Earth’s environment, strongly affecting the upper atmosphere, but also impacting climate. However, its measurements have been sparse and of different quality. The “First European Comprehensive Solar Irradiance Data Exploitation project” (SOLID) aims at merging the complete set of European irradiance data, complemented by archive data that include data from non-European missions. Aims. As part of SOLID, we present all available space-based SSI measurements, reference spectra, and relevant proxies in a unified format with regular temporal re-gridding, interpolation, gap-filling as well as associated uncertainty estimations. Methods. We apply a coherent methodology to all available SSI datasets. Our pipeline approach consists of the pre-processing of the data, the interpolation of missing data by utilizing the spectral coherency of SSI, the temporal re-gridding of the data, an instrumental outlier detection routine, and a proxy-based interpolation for missing and flagged values. In particular, to detect instrumental outliers, we combine an autoregressive model with proxy data. We independently estimate the precision and stability of each individual dataset and flag all changes due to processing in an accompanying quality mask. Results. We present a unified database of solar activity records with accompanying meta-data and uncertainties. Conclusions. This dataset can be used for further investigations of the long-term trend of solar activity and the construction of a homogeneous SSI record.

The massive repository of images of the Sun captured by the Solar Dynamics Observatory (SDO) mission has ushered in the era of Big Data for Solar Physics. In this work, we investigate the entire public collection of events reported to the Heliophysics Event Knowledgebase (HEK) from automated solar feature recognition modules operated by the SDO Feature Finding Team (FFT). With the SDO mission recently surpassing five years of operations, and over 280,000 event reports for seven types of solar phenomena, we present the broadest and most comprehensive large-scale dataset of the SDO FFT modules to date. We also present numerous statistics on these modules, providing valuable contextual information for better understanding and validating of the individual event reports and the entire dataset as a whole. After extensive data cleaning through exploratory data analysis, we highlight several opportunities for knowledge discovery from data (KDD). Through these important prerequisite analyses presented here, the results of KDD from Solar Big Data will be overall more reliable and better understood. As the SDO mission remains operational over the coming years, these datasets will continue to grow in size and value. Future versions of this dataset will be analyzed in the general framework established in this work and maintained publicly online for easy access by the community.

Context: The Sun as seen by Extreme Ultraviolet (EUV) telescopes exhibits a variety of large-scale structures. Of particular interest for space-weather applications is the extraction of active regions (AR) and coronal holes (CH). The next generation of GOES-R satellites will provide continuous monitoring of the solar corona in six EUV bandpasses that are similar to the ones provided by the SDO-AIA EUV telescope since May 2010. Supervised segmentations of EUV images that are consistent with manual segmentations by for example space-weather forecasters help in extracting useful information from the raw data. Aims: We present a supervised segmentation method that is based on the Maximum A Posteriori rule. Our method allows integrating both manually segmented images as well as other type of information. It is applied on SDO-AIA images to segment them into AR, CH, and the remaining Quiet Sun (QS) part. Methods: A Bayesian classifier is applied on training masks provided by the user. The noise structure in EUV images is non-trivial, and this suggests the use of a non-parametric kernel density estimator to fit the intensity distribution within each class. Under the Naive Bayes assumption we can add information such as latitude distribution and total coverage of each class in a consistent manner. Those information can be prescribed by an expert or estimated with an Expectation-Maximization algorithm. Results: The segmentation masks are in line with the training masks given as input and show consistency over time. Introduction of additional information besides pixel intensity improves upon the quality of the final segmentation. Conclusions: Such a tool can aid in building automated segmentations that are consistent with some ground truth’ defined by the users.

The Rate Of TEC Index (ROTI) is a commonly used measure of ionospheric activity. ROTI values have been computed every 5 min for the year 2012, for 10 receivers at latitudes from 59° to 79° North. We present the results in geomagnetic coordinates, showing that elevated ROTI values occur mainly in the cusp and nightside auroral oval regions. Elevated ROTI values are more common in the cusp, but in the nightside auroral oval they are stronger. To investigate the relation to positioning errors, receiver coordinates were computed using the GIPSY software, for the same receivers and time resolution. We found that there is a strong positive correlation between Precise Point Positioning (PPP) error and ROTI for receivers that are affected by space weather. The 3D position error increases exponentially with increasing ROTI. A statistical analysis presents also the risk of having several satellites observing enhanced ROTI values simultaneously, showing that this risk is greater at high latitudes.

We describe how the use of a games environment combined with technology supports upper primary children in engaging with a concept traditionally considered too advanced for the primary classes: The Law of Large Numbers. [ABSTRACT FROM AUTHOR]

Copyright of Journal of International Social Research is the property of Journal of International Social Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The composite (superposed epoch) analysis technique has been frequently employed to examine a hypothesized link between solar activity and the Earth’s atmosphere, often through an investigation of Forbush decrease (Fd) events (sudden high-magnitude decreases in the flux cosmic rays impinging on the upper-atmosphere lasting up to several days). This technique is useful for isolating low-amplitude signals within data where background variability would otherwise obscure detection. The application of composite analyses to investigate the possible impacts of Fd events involves a statistical examination of time-dependent atmospheric responses to Fds often from aerosol and/or cloud datasets. Despite the publication of numerous results within this field, clear conclusions have yet to be drawn and much ambiguity and disagreement still remain. In this paper, we argue that the conflicting findings of composite studies within this field relate to methodological differences in the manner in which the composites have been constructed and analyzed. Working from an example, we show how a composite may be objectively constructed to maximize signal detection, robustly identify statistical significance, and quantify the lower-limit uncertainty related to hypothesis testing. Additionally, we also demonstrate how a seemingly significant false positive may be obtained from non-significant data by minor alterations to methodological approaches.

The Zubrzycki method is utilized to find all sunspot groups which are close to each other during each Carrington rotation. The sunspot group areas and their positions for the years 1874–2008 are used. The descending, the ascending and the maximum phases of solar cycles for each solar hemisphere are considered separately. To establish the size of the region D where the clusters are searched, the correlation function dependent on the distance between two groups is applied. The method estimates the weighted area of each cluster. The weights dependent on the correlation function of distances between sunspot groups created each cluster. For each cluster the weighted position is also evaluated. The weights dependent on the areas of sunspot groups created a given cluster. The number distribution of the sunspot groups created each cluster and the cluster statistics within different phases of the 11-year cycle and within all considered solar cycles are also presented.

This brief communications aims at sharing the list of impact factor journals of 'Statistics & Probability' as per the Journal Citation Report 2011 released by Institute of Scientific Information. This would update the academia and practitioner on their information about the ranking of the journals. The study makes country and regions wise comparisons of the changes in no of journals and their mean impact factors reported in the previous and current reports. [ABSTRACT FROM AUTHOR]

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions. [ABSTRACT FROM AUTHOR]

In this paper we present two simple mathematical models to describe human behavior in reaction to deadlines. When a real commitment (e.g. money) is involved, as in the case of a payment deadline, the expected reaction is to postpone it as close as possible to the deadline to minimize the risk of loosing the value. For low risk commitments this tendency is still present but expected to be looser. In order to test these predictions in a quantitative way, we performed data analysis for the total number of registrations and fee payments vs. time for the recent scientific conference “Statphys 23”, comparing it with the data of another conference in order to recover universal features. Two related models respectively for registrations (weak engagement) and fee payment (strong engagement) are then introduced which are able to explain in a simple way both behaviors, and which show an excellent agreement with real data. [ABSTRACT FROM AUTHOR]

When mining a large database, the number of patterns discovered can easily exceed the capabilities of a human user to identify interesting results. To address this problem, various techniques have been suggested to reduce and/or order the patterns prior to presenting them to the user. In this paper, our focus is on ranking summaries generated from a single dataset, where attributes can be generalized in many different ways and to many levels of granularity according to taxonomic hierarchies. We theoretically and empirically evaluate twelve diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases. The twelve diversity measures have previously been utilized in various disciplines, such as information theory, statistics, ecology, and economics. We describe five principles that any measure must satisfy to be considered useful for ranking summaries. Theoretical results show that the proposed principles define a partial order on the ranked summaries in most cases, and in some cases, define a total order. Theoretical results also show that seven of the twelve diversity measures satisfy all of the five principles. We empirically analyze the rank order of the summaries as determined by each of the twelve measures. These empirical results show that the measures tend to rank the less complex summaries as most interesting. Finally, we analyze the distribution of the index values generated by each of the twelve diversity measures. Empirical results, obtained using synthetic data, show that the distribution of index values generated tend to be highly skewed about the mean, median, and middle index values. Finally, we demonstrate a technique, based upon our principles, for visualizing the relative interestingness of summaries. The objective of this work is to gain some insight into the behaviour that can be expected from our principled approach in practice. [ABSTRACT FROM AUTHOR]