# mercuryfish

##### Chromosomal Effects of Mercury-Contaminated Fish Consumption

The mercury level in blood, the proportion of cells with abnormalities, and the proportion of cells with chromosome aberrations in consumers of mercury-contaminated fish and a control group.

- Keywords
- datasets

##### Usage

`mercuryfish`

##### Details

Control subjects (`"control"`

) and subjects who ate contaminated fish for
more than three years (`"exposed"`

) are under study.

Rosenbaum (1994) proposed a coherence criterion defining a partial ordering, i.e., an observation is smaller than another when all responses are smaller, and a score reflecting the “ranking” is attached to each observation. The corresponding partially ordered set (POSET) test can be used to test if the distribution of the scores differ between the groups. Alternatively, a multivariate test can be applied.

##### Format

A data frame with 39 observations on 4 variables.

`group`

a factor with levels

`"control"`

and`"exposed"`

.`mercury`

mercury level in blood.

`abnormal`

the proportion of cells with structural abnormalities.

`ccells`

the proportion of \(C_u\) cells, i.e., cells with asymmetrical or incomplete-symmetrical chromosome aberrations.

##### References

Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego
system for conditional inference. *The American Statistician*
**60**(3), 257--263. 10.1198/000313006X118430

Rosenbaum, P. R. (1994). Coherence in observational studies.
*Biometrics* **50**(2), 368--374. 10.2307/2533380

##### Examples

```
# NOT RUN {
## 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)
}
## Asymptotic POSET test
poset <- independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish, ytrafo = coherence)
## Linear statistic (T in the notation of Rosenbaum, 1994)
statistic(poset, type = "linear")
## Expectation
expectation(poset)
## Variance
## Note: typo in Rosenbaum (1994, p. 371, Sec. 2, last paragraph)
variance(poset)
## Standardized statistic
statistic(poset)
## P-value
pvalue(poset)
## Exact POSET test
independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish, ytrafo = coherence,
distribution = "exact")
## Asymptotic multivariate test
mvtest <- independence_test(mercury + abnormal + ccells ~ group,
data = mercuryfish)
## Global p-value
pvalue(mvtest)
## Single-step adjusted p-values
pvalue(mvtest, method = "single-step")
## Step-down adjusted p-values
pvalue(mvtest, method = "step-down")
# }
```

*Documentation reproduced from package coin, version 1.3-1, License: GPL-2*