| mercuryfish {coin} | R Documentation |
The mercury level in the blood, the proportion of cells with abnormalities and the proportion of cells with chromosome aberrations for a group of consuments of mercury contaminated fish and a control group.
data("mercuryfish")
A data frame with 39 observations on the following 4 variables.
control and exposed.
Subjects who ate contaminated fish for more than three years in the
exposed group and subjects of a control group are to be compared.
Instead of a multivariate comparison, Rosenbaum (1994)
applied a coherence criterion. The observations are partially ordered: an
observation is smaller than another when all three variables (mercury,
abnormal and ccells) are smaller and a score reflecting the
`ranking' is attached to each observation. The distribution of the scores
in both groups is to be compared and the corresponding test is called
`POSET-test' (partially ordered sets).
S. Skerfving, K. Hansson, C. Mangs, J. Lindsten, N. Ryman (1974), Methylmercury-induced chromosome damage in men. Environmental Research 7, 83–98.
P. R. Rosenbaum (1994). Coherence in Observational Studies. Biometrics 50, 368–374.
Torsten Hothorn, Kurt Hornik, Mark A. van de Wiel & Achim Zeileis (2006). A Lego system for conditional inference, The American Statistician, 60(3), 257–263.
### coherence criterion
coherence <- function(data) {
x <- as.matrix(data)
matrix(apply(x, 1, function(y)
sum(colSums(t(x) < y) == ncol(x)) -
sum(colSums(t(x) > y) == ncol(x))), ncol = 1)
}
### POSET-test
poset <- independence_test(mercury + abnormal + ccells ~ group, data =
mercuryfish, ytrafo = coherence)
### linear statistic (T in Rosenbaum's, 1994, notation)
statistic(poset, "linear")
### expectation
expectation(poset)
### variance (there is a typo in Rosenbaum, 1994, page 371,
### last paragraph Section 2)
covariance(poset)
### the standardized statistic
statistic(poset)
### and asymptotic p-value
pvalue(poset)
### exact p-value
independence_test(mercury + abnormal + ccells ~ group, data =
mercuryfish, ytrafo = coherence, distribution = "exact")
### multivariate analysis
mvtest <- independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish)
### global p-value
pvalue(mvtest)
### adjusted univariate p-value
pvalue(mvtest, method = "single-step")