Statistics Online Computational Resource

Rapid technological advances, our insatiable appetite for instantaneous rewards, and the massive information overflow are impacting our everyday lives. The long term effects of the social informatification, people’s overreliance on massive amounts of dynamic digital information, remain enigmatic and poorly understood. Our ability to anticipate, prepare, react and adopt to potential negative consequences of the minute-by-minute existence in the new infoctratic world, complete virtual immersion into a digital information where most time, energy and resources are dedicated to rapid acquisition, processing and inference using large amounts of information, may have a significant long term impact on mankind. This opinion outlines the scope of our virtualized abilities to manage and interpret Exabytes of information and suggests that timely prediction and appropriate response to the information avalanche will be critical to managing the unavoidable social and cultural changes ahead.

The web-based, Java-written SOCR (Statistical Online Computational Resource) tools have been utilized in many undergraduate and graduate level statistics courses for seven years now. It has been proven that these resources can successfully improve students' learning. Being �first published online in 2005, SOCR Analyses is a somewhat new component and it concentrate on data modeling for both parametric and non-parametric data analyses with graphical model diagnostics. One of the main purposes of SOCR Analyses is to facilitate statistical learning for high school and undergraduate students. As we have already implemented SOCR Distributions and Experiments, SOCR Analyses and Charts ful�ll the rest of a standard statistics curricula. Currently, there are four core components of SOCR Analyses. Linear models included in SOCR Analyses are simple linear regression, multiple linear regression, one-way and two-way ANOVA. Tests for sample comparisons include t-test in the parametric category. Some examples of SOCR Analyses' in the non-parametric category are Wilcoxon rank sum test, Kruskal-Wallis test, Friedman's test, Kolmogorov-Smirno� test and Fligner-Killeen test. Hypothesis testing models include contingency table, Friedman's test and Fisher's exact test. The last component of Analyses is a utility for computing sample sizes for normal distribution. In this article, we present the design framework, computational implementation and the utilization of SOCR Analyses.

Modern approaches for technology-based blended education utilize a variety of recently developed novel pedagogical, computational and network resources. Such attempts employ technology to deliver integrated, dynamically-linked, interactive-content and heterogeneous learning environments, which may improve student comprehension and information retention. In this paper, we describe one such innovative effort of using technological tools to expose students in probability and statistics courses to the theory, practice and usability of the Law of Large Numbers (LLN). We base our approach on integrating pedagogical instruments with the computational libraries developed by the Statistics Online Computational Resource (www.SOCR.ucla.edu). To achieve this merger we designed a new interactive Java applet and a corresponding demonstration activity that illustrate the concept and the applications of the LLN. The LLN applet and activity have common goals – to provide graphical representation of the LLN principle, build lasting student intuition and present the common misconceptions about the law of large numbers. Both the SOCR LLN applet and activity are freely available online to the community to test, validate and extend (Applet: http://socr.ucla.edu/htmls/exp/Coin_Toss_LLN_Experiment.html, and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_LLN).

This technical report describes the statistical method of expectation maximization (EM) for parameter estimation. Several of 1D, 2D, 3D and n-D examples are presented in this document. Applications of the EM method are also demonstrated in the case of mixture modeling using interactive Java applets in 1D (e.g., curve fitting), 2D (e.g., point clustering and classification) and 3D (e.g., brain tissue classification).

Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (www.SOCR.ucla.edu) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem).

Contemporary science education at all levels presents several critical pedagogical and social challenges to educators and learners alike. Among these challenges are the widening Intergenerational Information Technology (IIT) divide and the need for a comprehensive and balanced multidisciplinary training. In the past few years, it has become clear that one significant hurdle impedes the efforts to integrate information technology in the classroom – the Intergenerational IT divide. The IIT gap eflects a different growing misalignment between providers and recipients of the science and technology educational content in terms of the expected vs. supplied, needed vs. perceived and contextual vs. abstract specialized learning. The common K12 teacher or college instructor is much less familiar with, and slower to adapt to, the new ether of communication and novel IT resources. The transfer and blending of data, research challenges and methodologies between diverse areas of science is also critical in motivating wider spectra of students, demonstrating crossdisciplinary methodological concepts and synergies, as well as for engaging students in research projects. This article discusses the problems faced by modern science educators and suggests some methods and vision for coping with the increasing IIT divide and the social need to train “complete” and broadly educated citizens.

Technology-based instruction represents a new recent pedagogical paradigm that is rooted in the realization that new generations are much more comfortable with, and excited about, new technologies. The free and Internetbased NSF-funded Statistics Online Computational Resource (www.SOCR.ucla.edu) provides a number of educational materials and interactive tools for enhancing instruction in various undergraduate and graduate courses in probability and statistics using observed or computer generated data. SOCR includes class notes, practice activities, statistical calculators, interactive graphical user interfaces, computational and simulation applets, tools for data analysis and visualization. Based on the promising results from our pilot study in 2005-2006, where we saw a consistent trend of improvement in the SOCR treatment group compared to the control group, in terms of quantitative examination measures, our 2006-2007 study involves over 300 UCLA students. We use a cross-over design for one course, (introduction to probability) taught by one instructor, and a randomized controlled study for two different courses (an introductory statistics course for the life sciences and an introductory course in probability). For the cross-over design course, SOCR-based and non SOCR-based activities or homework are assigned and analyzed relative to their performance. In the controlled study, one class uses SOCR the other does not. Several components of the SOCR-based materials are heavily dependent on simulated data to enhance the understanding on distributions, which is a major topic for the classes tested. Little is known about how interactive simulation based applets can enhance students’ learning, understanding and interest in statistics. As a result, separate questionnaires (Felder-Soloman Learning Style inventory, ATS survey, and entry and exit assessment of student knowledge questionnaire) are also collected separately to explore how SOCR affects the performance of students in relation to their learning style, attitudes towards statistics, prior knowledge and demographic characteristics, and reaction to these applets. The first goal of this study is to try to associate the effects of SOCR with students’ individual learning style based on the Felder-Silverman-Soloman index. How these applets assist students with different learning styles is yet to be observed. Our second goal is to assess students’ achievement with a closer look based on homework and activities directly related to SOCR. The students’ feedback and performances from this study tell us how to best optimize the SOCR resources based on their needs. Moreover, its result gives us a more accurate assessment of SOCR specifically and an assessment of internet-based resources in introductory and more advanced courses of statistics and probability.