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Implications of statistical power for confidence intervals
Author(s) -
Liu Xiaofeng Steven
Publication year - 2012
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 - 10.1111/j.2044-8317.2011.02035.x
Subject(s) - statistics , confidence interval , mathematics , statistical power , sample size determination , coverage probability , tolerance interval , multiplicative function , cdf based nonparametric confidence interval , statistical hypothesis testing , null hypothesis , robust confidence intervals , p value , power (physics) , power function , mathematical analysis , physics , quantum mechanics
The statistical power of a hypothesis test is closely related to the precision of the accompanying confidence interval. In the case of a z ‐test, the width of the confidence interval is a function of statistical power for the planned study. If minimum effect size is used in power analysis, the width of the confidence interval is the minimum effect size times a multiplicative factor φ . The index φ , or the precision‐to‐effect ratio, is a function of the computed statistical power. In the case of a t‐ test, statistical power affects the probability of achieving a certain width of confidence interval, which is equivalent to the probability of obtaining a certain value of φ . To consider estimate precision in conjunction with statistical power, we can choose a sample size to obtain a desired probability of achieving a short width conditional on the rejection of the null hypothesis.