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The effect of covariate mean differences on the standard error and confidence interval for the comparison of treatment means
Author(s) -
Liu Xiaofeng Steven
Publication year - 2011
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 - 10.1348/000711010x526575
Subject(s) - covariate , statistics , standard error , confidence interval , mathematics , standard deviation , statistic , sample size determination , mean difference
The use of covariates is commonly believed to reduce the unexplained error variance and the standard error for the comparison of treatment means, but the reduction in the standard error is neither guaranteed nor uniform over different sample sizes. The covariate mean differences between the treatment conditions can inflate the standard error of the covariate‐adjusted mean difference and can actually produce a larger standard error for the adjusted mean difference than that for the unadjusted mean difference. When the covariate observations are conceived of as randomly varying from one study to another, the covariate mean differences can be related to a Hotelling's T 2 . Using this Hotelling's T 2 statistic, one can always find a minimum sample size to achieve a high probability of reducing the standard error and confidence interval width for the adjusted mean difference.