The times of arrivals of passengers and departures of buses have been observed at ten bus stops in suburban London. The different bus stops were observed at different times of the day, but the observations at each were repeated at the same time on each of eight different days. Due to the predictability of the bus services, passengers' waiting times were observed to be about 30 per cent less than they would have been had the passengers arrived at random times. An explanation of this involves considering passengers to be of three types: a proportion q whose arrival time is causally coincidental with the bus, a proportion p(1 − q) who arrive at the optimal time (the time at which the expected waiting time is smallest), and a proportion (1 − p)(1 − q) who arrive at random. It was found that p is positively correlated with the expected gain from arriving at the optimal time as opposed to arriving at random. Furthermore, p was found to be larger at those bus stops observed in the peak than at those observed in the off-peak. A number of other results relating various parameters of the bus services are also given.

When assessing agreement between experts, it is important to distinguish between disagreements that can and cannot be explained by different placing of the boundaries between categories. Cohen's kappa statistic is affected by both types of disagreement, tetrachoric correlation only by the second.

Theories are put forward that attempt to answer the practical question of 'How should we correct for guessing in multiple choice tests?' and the theoretical question of 'How can we mathematically describe partial knowledge so as to predict behaviour in tasks which enable it to be shown?'. Empirical findings relating to performance on variants of the multiple choice task are reviewed, and compared to the predictions of the theories.

Abstract. The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient p. If the pair (X, Y)has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population correlation coefficient p. The bivariate lognormal is chosen as our case study for this robustness study. Two approaches are used: (i) by simulation and (ii) numerical computations.Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating p can be very large if p s0, and it can be substantially reduced only after a large number (three to four million) of observations. This phenomenon, though unexpected at first, was found to be consistent to our findings by our numerical analysis.

No abstract