Volume 6, Issue 1, 2012
An Exploration of the Exact Distribution and Probabilities for Sample Means for Small Random Samples
The computer algebra system, MathematicaTM, is used to determine the exact distributions for sums and means of small random samples taken from a specific probability density function. The method used is the Inverse Laplace Transform for real-valued functions. These distributions are used to compare exact probabilities for probability interval statements for sums and means with normal approximations for these probabilities using the Central Limit Theorem. The maximum normal approximation errors are determined for probability intervals for various sample sizes.
Website and software products that have the potential to raise the profile of statistics in society are described. The website has links to case study videos describing contexts, study designs, data files and lessons using the new software for data exploration and analysis. Case study videos dealing with current research applying statistics have been selected to motivate discussion in class, and further “hands on” learning can be achieved through use of the software. During the development phase in New Zealand in 2010 the software was trialed and student and teacher experiences are reported. A full day professional development workshop for teachers involving lessons using the software was recorded and these are on the website to assist teachers and students. The software is free for teachers and students at education institutes, and the procedure for obtaining a license is outlined.
Online instructional modules that combine an applet, audio-visual tutorials, and guided discovery questions were created to teach the concept of sampling variability. The modules did contribute to an increase in understanding. However, they are a supplement to, not a replacement for, traditional instruction. The researchers found, using pretests and posttests, that student understanding of sampling distributions increased. There is room for futher improvement, which could be accomplished in two ways. A focus on designing for the introductory, rather than advanced, statistics student could be helpful. Also, giving students more feedback could help their performance in later modules.
Simulations can make complex ideas easier for students to visualize and understand. It has been shown that guidance in the use of these simulations enhances students’ learning. This paper describes the implementation and evaluation of the Independent Interactive Inquiry-based (I3) Learning Modules, which use existing open-source Java applets, combined with audio-visual instruction. Students are guided to discover and visualize important concepts in post-calculus and algebra-based courses in probability and statistics. Topics include the binomial distribution, confidence intervals, significance testing, and randomization. We show that this format can be used independently by students at the introductory and advanced levels. The percentage of students answering correctly on posttests was larger than that for pretests for three of the four modules described.
This paper reports on the use, in 2011, of some recent data visualizations to both motivate students and assist them to understanding underlying official statistics concepts. Examples of visualisations used in a Masters course in public policy and an applied statistics honours course are presented. These visualizations are free, either on-line or open-source and easy to access. Although they are of aggregates of very large official data sets and so may mask some of the underlying variation they provide students with fun tools to explore the patterns and relationships between variables in the data set, discuss its implications and sometimes lead to new questions and analyses. Geo-visualisations help demonstrate the inter-disciplinary nature of official statistics in the real world. Initial feedback from students in these courses was enthusiastic. The on-going challenge for the teacher is to keep up-to-date in a world of rapidly evolving technology and to see the learning opportunities that it may provide. This paper suggests data visualisation is a valuable teaching resource now and, in the longer term, may have implications not only on how we teach but also on what we teach in statistics.
Online Homework vs. Traditional Homework: Statistics Anxiety and Self-Efficacy in an Educational Statistics Course
The purpose of the study was to investigate whether online homework benefits students over traditional homework in the areas of statistics self-efficacy, statistics anxiety, and grades. Using a nonequivalent control-group design, one section of students was assigned traditional homework while the other section was assigned online homework. The two groups were then compared on measures of self-efficacy, statistics anxiety, and homework, test, and final grades. Results indicated that homework delivery method affected only student homework grades, but did not affect their other grades, self-efficacy, or anxiety.
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