When two sealed envelopes contain money, one twice as much as the other, a player should be indifferent between them. But when one envelope is opened, one's decision should vary as a function of the observed value and one's subjective probabilities.

Very little explanatory power is required in order for regressions to exhibit statistical significance. This article discusses some of the causes and implications. (Contains 2 tables.)

We find the correlation of two jointly distributed random variables connected with a coin tossing experiment. The marginal distributions are binomial and negative binomial.

The Statistics Online Computational Resource (http://www.SOCR.ucla.edu) provides one of the largest collections of free Internet-based resources for probability and statistics education. SOCR develops, validates and disseminates two core types of materials--instructional resources and computational libraries. (Contains 2 figures.)

This article suggests how to explain a problem of small sample size when considering correlation between two Normal variables. Two techniques are shown: one based on graphs and the other on simulation. (Contains 3 figures and 1 table.)

This article demonstrates that the variance of three or four observations can be expressed in terms of the range and the first order differences of the observations. A more general result, which holds for any number of observations, is also stated.

This article reflects on whether probability statements can usefully be made about one-off exceptional events.

A classroom practical exercise exploring the reliability of a basic capture-mark-recapture method of population estimation is described using great whale conservation as a starting point. Various teaching resources are made available.

This article describes a model for an interactive, introductory secondary- or tertiary-level statistics course that is designed to develop students' statistical reasoning. This model is called a "Statistical Reasoning Learning Environment" and is built on the constructivist theory of learning.

In this short note, the difference between improbable and unexpected outcomes is demonstrated via an example that uses the hypergeometric distribution.

A simple way is given to create residual plots that are words or pictures. Three illustrative examples are presented.

The binomial distribution is used to predict the winner of the 49th International Shooting Sport Federation World Championship in double trap shooting held in 2006 in Zagreb, Croatia. The outcome of the competition was definitely unexpected.

Interpretation of correlation is often based on rules of thumb in which some boundary values are given to help decide whether correlation is non-important, weak, strong or very strong. This article shows that such rules of thumb may do more harm than good, and instead of supporting interpretation of correlation--which is their aim--they teach a…

The older one gets, the more one's life expectancy exceeds the population's given expectancy (at birth). Yet longevity is finite. This apparent paradox is analysed probabilistically with reference to empirical demographic data.

We explain how to simulate both univariate and bivariate raw data sets having specified values for common summary statistics. The first example illustrates how to "construct" a data set having prescribed values for the mean and the standard deviation--for a one-sample t test with a specified outcome. The second shows how to create a bivariate data…