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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.
Noel Cressie (Sun,) studied this question.
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