The ?<sup>2</sup> goodness-of-fit test is often one of the first tests of hypotheses encountered by students. When some of the expected frequencies are small, classes need to be combined. A real-life example is given that illustrates a surprising sensitivity of the results of the test to the way in which such combinations are chosen.
This article defines the generalized mean and shows how it relates to such statistics as the arithmetic, geometric and harmonic means.
Summary This article describes situations in which regression through the origin is appropriate, derives the normal equation for such a regression and explains the controversy regarding its evaluative statistics. Differences between three popular software packages that allow regression through the origin are illustrated using examples from previous issues of Teaching Statistics .
Summary This article discusses three probabilistic scenarios based on the television game show 'Who Wants to be a Millionaire?'. These situations provide motivational opportunities for high-school students to explore the concepts of expected value, permutations and independent events.
Summary The notion of independence between two nominal variables is typically introduced through the use of chi-square analysis of contingency tables, while the topic of prediction of one nominal variable from a second nominal variable using optimal prediction to the mode is often omitted. Through the use of a questionnaire, this article indicates that there is considerable confusion among students on the difference between the concepts of independence and prediction, and remedies are suggested.
Summary The issue of whether football teams have good or bad patches during the course of a season is of concern to many supporters. This interest can be harnessed to make the classroom teaching of probability more relevant. In this article, the unfamiliar runs test for multiple outcomes is used to test for possible clustering in wins, draws and defeats in a short series of consecutive matches.
Summary In this article we derive the distribution, mean and variance of the number of cycles in a randomly selected permutation of the first n integers.
This article describes an example which is useful when teaching hypothesis testing in order to highlight the interrelationships that exist among the level of significance, the sample size and the statistical power of a test. The example also allows students to see how what they learn in the classroom directly affects the content of some of the commercials that they watch on television.
In this note, a coin tossing experiment which leads to three discrete distributions is discussed.
Summary This article suggests how to move from the primary school notion of the average being 'fair shares for all' to the secondary school idea of the mean being a 'balancing point'.