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Non‐parametric analysis of covariance based on predicted medians
Author(s) -
Wilcox Rand R.
Publication year - 1991
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.2044-8317.1991.tb00957.x
Subject(s) - mathematics , statistics , jackknife resampling , covariate , covariance , standard error , parametric statistics , contrast (vision) , analysis of covariance , econometrics , computer science , artificial intelligence , estimator
A common problem is comparing two independent treatment groups in terms of some random variable Y when there is some covariate X . Typically the comparison is made in terms of E(Y|X ). However, highly skewed distributions occur in psychology (Micceri, 1989), and so a better method might be to compare the two groups in terms of the median of Y given X , say M ( Y | X ). For the j th group, assume that M(Y|X) = β j X + α j . The βs and αs can be estimated with the Brown‐Mood procedure, but there are no results on how one might test H 0 :β 1 = β 2 or H 0 :α 1 = α 2 . Let and be the estimates of α and β, respectively. One of the more obvious approaches is to use a jackknife estimate of the variance of and then assume that the resulting test statistics have a standard normal distribution. This approach was found to be unsatisfactory. Some alternative procedures were considered, some of which gave good results when testing H 0 :α 1 = α 2 , but they were too conservative, in terms of Type I errors, when testing H 0 :β 1 = β 2 . Still another procedure was considered and found to be substantially better than all others. The new procedure is based on a modification of the Brown‐Mood procedure and a bootstrap estimate of the standard errors. Some limitations of the new method are noted.