RELAXING ASSUMPTIONS IN THE ONE SAMPLE t‐TEST

Summary This paper reviews what is currently known about the behaviour of the t‐statistic when one is no longer sampling from a normal distribution. Suppose Y is a batch of data on which the t‐test is performed. Briefly then, heavy‐tailed components of Y give a light‐tailed t , positive correlation among Y gives a heavy‐tailed t, and positively skewed components of Y give a negatively skewed t. The emphasis is on understanding why one gets this type of behaviour, although some numerical tables are presented to illustrate the conclusions.