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Four improved statistics for contrasting means by correcting skewness and kurtosis
Author(s) -
Yanagihara Hirokazu,
Yuan KeHai
Publication year - 2005
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711005x64060
Subject(s) - kurtosis , skewness , statistic , normality , statistics , mathematics , econometrics , order statistic , independent and identically distributed random variables , contrast (vision) , normality test , sufficient statistic , statistical hypothesis testing , random variable , computer science , artificial intelligence
This paper is concerned with removing the influence of non‐normality in the classical t ‐statistic for contrasting means. Using higher‐order expansion to quantify the effect of non‐normality, four corrected statistics are provided. Two aim to correct the mean bias and two to correct the overall distribution. The classical t ‐statistic is also robust against non‐normality when the observed variables satisfy certain structures. A special case is when the marginal distributions of the contrast are independent and identically distributed.