Teaching

  • There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean (mu) and variance (sigma) , the expected value of the sample variance is sigma squared . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps "demystify" the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.

  • Testing statistical hypotheses introduces new vocabulary, concepts and a way of thinking that some students might initially find difficult. We provide a simple case that can be used in class as a gentle introduction to the ideas and procedures of hypothesis testing.

  • Typically, external assessment of school statistics concentrates on lower--level skills. This article discusses how use of the real data of CensusAtSchool makes it possible to devise questions and activities that assess deeper levels of understanding, as described in BloomÅfs Taxonomy of Cognitive Learning.

  • This article gives a flavour of the CHIME materials on data handling in Microsoft Excel. It demonstrates the facilities for data validation within Excel.

  • We derive a model, using trigonometry and the Normal distribution, for the probability that a golf putt is successful. We describe a class activity in which we lead the students through the steps of examining the data, considering possible models, constructing a probability model and checking the fit. The model is,of necessity, oversimplified, a point which the class discusses at the end of the demonstration.

  • The discussion of problems associated with the use of language, specifically vocabulary and symbolism, is extended from the teaching and learning of mathematics to the particular area of statistics.

  •  This article considers the composition of juries, asking whether this is representative of the general populations from which the juries were drawn. The binomial and hypergeometric distributions are used for probability calculations. Several example applications of both of these distributions are given, addressing racial, sex and age distributions in various cases.

  • This article shows how the birthday problem can be used to introduce the exponential distribution.

  • Consulting in statistics is usually deferred until at least near the end of a first degree, but this article shows how some aspects can be effectively taught to students in upper secondary or early tertiary courses in a way which reinforces their learning of standard basic concepts. We suggest that the existence of a real client adds a degree of realism not available in other ways, and emphasizes to students the importance of blending statistical calculations with meaningful communication.

  • This article illustrates the use of spreadsheets as a simulation tool for solving a collection of probability problems.

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