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# Literature Index

Displaying 141 - 150 of 3326
• ### A Novel Method of Proof With an Application to Regression

Author(s):
Shaffer, J. P., &amp; Chen, Y.
Year:
1999
Abstract:
A useful way of approaching a statistical problem is to consider whether the addition of some missing information would transform the problem into a standard form with a known solution. The EM algorithm (Dempster, Laird, and Rubin 1977), for example, makes use of this approach to simplify computation. Occasionally it turns out that knowledge of the missing values is not necessary to apply the standard approach. In such cases the following simple logical argument shows that any optimality properties of the standard approach in the full-information situation generalize immediately to the approach in the original limited-information situation: If any better estimate were available in the limited-information situation, it would also be available in the full-information situation, which would contradict the optimality of the original estimator. This approach then provides a simple proof of optimality, and often leads directly to a simple derivation of other properties of the solution. The approach can be taught to graduate students and theoretically-inclined undergraduates. Its application to the elementary proof of a result in linear regression, and some extensions, are described in this paper. The resulting derivations provide more insight into some equivalences among models as well as proofs simpler than the standard ones.
• ### A Personal Journey Toward A Virtual Introductory Statistics Course: Not (Quite) Ready For Prime Time

Author(s):
Wisenbaker, J. M.
Editors:
Phillips, B.
Year:
2002
Abstract:
Drawing from web-based materials previously developed to supplement on-campus sections of an introductory statistics course for graduate students in education, the author started offering an on-line virtual class in the fall of 2001. The course, designed for doctoral students already participating in a program making extensive use of web-based materials, relied on students working independently with the on-line material (that included course lectures and notes) supported by access to the instructor using e-mail and the telephone. End of course performance was lower and much more variable than had been expected. Many students expressed the need for much more organization and contact with the instructor. Comparisons are made with reports of more successful virtual courses suggesting the need for a much greater degree of instructor supplied organization and direction.
• ### A Photographic View of Cumulative Distribution<br>Functions

Author(s):
Robert W. Jernigan
Year:
2008
Abstract:
This article shows a concrete and easy recognizable view of a cumulative distribution function(cdf).<br>Photograph views of the search tabs on dictionaries are used to increase students' understanding and<br>facility with the concept of a cumulative distribution function. Projects for student investigations are<br>also given. This motivation and view helps the cdf become a bit more tangible and understandable
• ### A Pilot Study of Short Computing Video Tutorials in a Graduate Public Health Biostatistics Course

Author(s):
Lauren Hund and Christina Getrich
Year:
2015
Abstract:
Traditional lecture-centered classrooms are being challenged by active learning hybrid curricula. In small graduate programs with limited resources and primarily non-traditional students, exploring how to use online technology to optimize the role of the professor in the classroom is imperative. However, very little research exists in this area. In this study, the use of short statistical computing video tutorials was explored using a pilot study in a small Public Health Program at the University of New Mexico. The videos were implemented in two Master’s-level biostatistics courses and student perception of the videos was assessed using quantitative surveys and qualitative focus groups. The results from 16 survey respondents and 12 focus group participants are presented across the two courses. Viewing rates for the videos were high, with 15 out of 16 respondents reporting usually or always viewing the videos. Overall perception of the videos as a learning tool was positive, with 14 out of 16 respondents agreeing that the videos offer advantages to them. Two prominent themes emerged in our analysis: (1) the usability and convenience of the videos and (2) the deeper learning facilitated by having the videos available. We conclude that the short video tutorials were a useful learning tool in our study population.
• ### A Pilot Study Teaching Metrology in an Introductory Statistics Course

Author(s):
Emily Casleton, Amy Beyler, Ulrike Genschel, and Alyson Wilson
Year:
2014
Abstract:
Undergraduate students who have just completed an introductory statistics course often lack deep understanding of variability and enthusiasm for the field of statistics. This paper argues that by introducing the commonly underemphasized concept of measurement error, students will have a better chance of attaining both. We further present lecture materials and activities that introduce metrology, the science of measurement, which were developed and tested in a pilot study at Iowa State University. These materials explain how to characterize sources of variability in a dataset, in a way that is natural and accessible because the sources of variability are observable. Everyday examples of measurements, such as the amount of gasoline pumped into a car, are presented, and the consequences of variability within those measurements are discussed. To gauge the success of the material, students’ initial and subsequent understanding of variability and their attitude toward the usefulness of statistics were analyzed in a comparative study. Questions from the CAOS and ARTIST assessments that pertain to using variability to make comparisons, understanding the standard deviation, and using graphical representations of variability were included in the assessment. The results of the comparative study indicate that most students who were exposed to the material improved their understanding of variability and had a greater appreciation of the value of statistics.
• ### A post-calculus introduction to statistics for future secondary teachers.

Author(s):
Rossman, A., Medina, E., &amp; Chance, B.
Editors:
Rossman, A., &amp; Chance, B.
Year:
2006
Abstract:
We describe our experiences with developing and teaching a new introductory statistics course for prospective teachers of secondary mathematics. The course emphasizes statistical concepts through their applications in the context of recent scientific studies, and it uses an interactive technology-enhanced pedagogical approach that models recommended practice for teachers. A concurrent seminar course introduces students to seminal articles and research findings in statistics education, and encourages them to reflect on their learning experiences in the course as a way to prepare for their own teaching of statistics. Feedback and evaluation from students will be discussed.
• ### A potential for learning probability in young children

Author(s):
Falk, R., Falk, R., &amp; Levin, I.
Year:
1980
Abstract:
Sixty-one children, from 4 to 11 years old, were presented with two sets, each containing blue and yellow elements. Each time, one colour was pointed out as the payoff colour (POC). The child had to choose the set from which he or she would draw at random a POC element in order to be rewarded. The sets were of varying sizes with different proportions of the two colours. The problem was to select the higher of the two probabilities. Three kinds of materials were used; Pairs of urns with blue and yellow beads, pairs of roulettes divided into blue and yellow sectors, and pairs of spinning tops, likewise divided into two colours. Roughly around the age of six, children started to select the greater of the two probabilities systematically. The dominant error was selecting the set with the greater number of POC elements. Verbal concepts of probability and chance were explored and some 'egocentric' thought processes were described. The study indicates that probability concepts could be introduced into school teaching even in the first grades. The deterministic orientation in the instruction for young ages should be attenuated, permitting concepts of uncertainty right from the beginning.
• ### A PRACTICAL APPROACH TO PROBABILITY<br>IN THE CONTEXT OF A SCIENCE FAIR

Author(s):
Hugo M. Hern&aacute;ndez Trevethan, Ver&ocirc;nica Y. Kataoka,<br>&amp; Marcelo da Silva Oliveira
Year:
2009
Abstract:
In a society that generates information rapidly, schools have to fulfil their programmes<br>imaginatively. Thus, extra-curricular activities may be helpful for the students to acquire wider knowledge<br>than that they may get within the classrooms. On the other hand, randomness is present in almost all everyday<br>decisions, mainly based on prior information so it is important to have at least a rough idea on how specific<br>events may affect the chances of other events. We explore both ideas here in the context of a science fair, in<br>which two high-school senior students conducted an investigation about conditional probability using a game<br>called "Shut the box". We also want to pose, as a research question, if, after their participation in the science<br>fair, these students have reached higher levels in probabilistic reasoning compared to their classmates or have<br>acquired knowledge about concepts far beyond the official curriculum.
• ### A practical approach to statistics

Author(s):
Kapadia, R.
Editors:
Grey, D. R., Holmes, P., Barnett, V., &amp; Constable, G. M.
Year:
1983
Abstract:
The first part provides a perspective showing how the influence of the subject has grown. From this the main aims are advocated and a specimen syllabus linked to applications is outlined. Suitable teaching strategies are described, illustrated by a specific example. References to suitable teaching materials are also given. Throughout, the international context is borne in mind, for statistics is an essential part in any education system.
• ### A practical approach to the central limit theorem

Author(s):
Glencross, M. J.
Editors:
Davidson, R., &amp; Swift, J.
Year:
1986
Abstract:
The most important aspect of the Central Limit Theorem is that no stipulation is made concerning the population from which one is sampling. From a pedagogical point of view, a student needs to draw a random sample from a population with a known distribution and then to compare the sample mean with the population mean to see "how close", he or she comes. Any student who does this will know the difference between the two. Students will also be led to understand the difference between the population mean and the mean of the sample means. It is not enough for a teacher to talk about these ideas - concrete experience with sampling is necessary for success. It is hoped that these experiments go some way towards enabling students to observe the central limit phenomenon operating, as well as providing empirical evidence of the truth of the theorem.