Confidence intervals are pedagogically important but often misinterpreted. This article describes Java applets designed to help students understand two interpretations of confidence intervals.
Confidence intervals are pedagogically important but often misinterpreted. This article describes Java applets designed to help students understand two interpretations of confidence intervals.
This article describes 'The World of Chance', an unconventional statistics course taught at the University of Canberra since 1998, modeled on the Chance courses devised at Dartmouth College. Statistical concepts are introduced via a mixture of lectures, class distributions of news stories, and activities.
Infants are too young to engage in real, useful statistical work. This activity allowed comparisons between distributions of two species of flowers in three different habitats.<br>How old must children be before they can learn about statistics? I had agreed to lead a group of six-year-old around a woodland nature reserve. The prime aim of the visit was for it to be used as a stimulus for written work in connection with the Key Stage 1 writing test (England, age 6-7) where children are expected to recount sequences of events. I wished to ensure that the visit was used to give them some understanding of at least some aspects of the ecology of the wood - clearly an opportunity for statistical work. I was assured by their teacher that they could record using the 5-bar-gate tallying system. This is a basic statistical skill but is sufficient to be able to examine differences in habitat preferences between plant species.
Rolling dice and tossing coins can still be used to teach probability even if students know (or think they know) what happens in these experiments. This article considers many simple variations of these experiments which are interesting, potentially enjoyable and challenging. Using these variations can cause students (and teachers) to think again about the statistical issues involved - and learn in the process.
In a recent paper in Teaching Statistics, Croucher (2004) discussed an upper bound on the standard deviation of a set of sample data in terms of the range of the data. He derived the result that for any three numbers the standard deviation can never exceed 1/sqrt(3) or 58% of the range. He also conjectured that the maximum value of standard deviation divided by range was a decreasing function of sample size. This conjecture can easily be shown to be incorrect since, for example, the maximum value of standard deviation divided by range in equal for samples of size 3 and 4. We prove a modified version of Croucher's conjecture, that the maximum value of standard deviation divided by range is a non-increasing function of sample size. Our derivation uses a simplified approach and analogous ideas of the physical meaning of standard deviation.<br><br>This article disproves a conjecture that the ratio of the maximum standard deviation to the range of a set of data decreases as the number of data points increases. It also provides an alternative and more general approach for examining the standard deviation as a function of the range.
The use of so-called 'drill and practice' exercises is almost universal in elementary statistics courses. Even in higher education, where there is easy access to statistical computer packages, many teachers still consider that there is an educational benefit in students using hand calculation to work through simple examples on topics such as the Normal distribution or linear regression. Such exercises are particularly attractive for teachers to set as home work assignments since they tend to have unique numerical answers, making them much quicker to mark than more open-ended tasks where students engage in discussion of their results. Regrettably the exercises are equally attractive to minority of lazy students who can happily copy the solutions of a more diligent but weak-willed colleague. The purpose of this article is not to debate the relative merits of such assignments, but merely to facilitate the setting of individualized tasks to combat the increasing problem of plagiarism. Simonite et al. (1998) describe a similar approach, but their method involves Visual Basic macros, which require a substantially higher technical capability than the method described here.<br>This article describes how the mail merge facility within Microsoft Word can be used in conjunction with Microsoft Excel to generate personalized assignments for students at all levels.
This article discusses the theory and practice of constructivism and suggests a way to move from the theory into the practice of it.
This article shows how the use of factorial moments provides a simple, consistent yet elegant approach to finding the mean dn variance of standard discrete probability distributions.
The tremendously popular movie Titanic has rejuvenated interest in the Titanic and its passengers. Students are particularly captivated by the story and by the people involved. Consequently, when I was preparing to explore categorical data and the chi square distribution with my class, I decided to use the available data about the Titanic's passengers to interest students in these topics. This article describes the activities that I incorporated into my statistics class and gives additional resources for collecting information about the Titanic.
In this paper we describe an interactive activity that illustrates simple linear regression. Students collect data and analyze it using simple linear regression techniques taught in an introductory applied statistics course. The activity is extended to illustrate checks for regression assumptions and regression diagnostics taught in an intermediate applied statistics course.