In a recent Monte Carlo study, a most unsatisfactory sampling distribution was obtained when supposedly standard techniques were employed to simulate a simple random sample from the standard normal distribution. A selection of observed and expected frequencies (the latter rounded to the nearest integer) in the tails of the distribution for a sample of size 1,000,000 is given in Table 1. It hardly needs a chi‐square test to indicate that the observed frequencies are not following the expected pattern! Note particularly that all the 1,000,000 observations are restricted to the range (–3·3 : 3·6), and that the sampling distribution has marked local maxima approximately at the points –3·3, 30 and 3·6.

This paper investigates such phenomena.