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Transformation works for non‐normality? On one‐sample transformation trimmed t methods
Author(s) -
Luh WeiMing,
Guo JiinHuarng
Publication year - 2001
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 - 10.1348/000711001159537
Subject(s) - normality , type i and type ii errors , transformation (genetics) , mathematics , truncated mean , sample (material) , statistics , sample size determination , simple (philosophy) , statistical hypothesis testing , estimator , biochemistry , chemistry , chromatography , gene , philosophy , epistemology
If the assumption of normality is not satisfied, there is no simple solution to this problem for the one‐sample t test. The present study proposes Hall's or Johnson's transformation in conjunction with the trimmed mean to deal with the problem. Computer simulation is carried out to evaluate the small‐sample behaviour of the proposed methods in terms of Type I error rate and statistical power. The proposed methods are compared with the conventional Student t , Yuen's trimmed t , Johnson's transformation untrimmed t , and Hall's transformation untrimmed t statistics for one‐sided and two‐sided tests. The simulation results indicate that the proposed methods can control Type I error well in very extreme conditions and are more powerful than the conventional methods.