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RELAXING ASSUMPTIONS IN THE ONE SAMPLE t ‐TEST
Author(s) -
Cressie Noel
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01161.x
Subject(s) - statistic , mathematics , statistics , sample (material) , test (biology) , sampling (signal processing) , distribution (mathematics) , test statistic , sampling distribution , econometrics , computer science , statistical hypothesis testing , mathematical analysis , physics , thermodynamics , geology , paleontology , filter (signal processing) , computer vision
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.