adManyOneTest() R function from [PMCMRplus]

Anderson-Darling Many-To-One Comparison Test

Performs Anderson-Darling many-to-one comparison test.


adManyOneTest(x, ...)

## Default S3 method:
adManyOneTest(x, g, p.adjust.method = p.adjust.methods, ...)

## S3 method for class 'formula'
adManyOneTest(
  formula,
  data,
  subset,
  na.action,
  p.adjust.method = p.adjust.methods,
  ...
)

Arguments

x: a numeric vector of data values, or a list of numeric data vectors.
...: further arguments to be passed to or from methods.
g: a vector or factor object giving the group for the corresponding elements of "x". Ignored with a warning if "x" is a list.
p.adjust.method: method for adjusting p values (see p.adjust).
formula: a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.
data: an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
subset: an optional vector specifying a subset of observations to be used.
na.action: a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

Returns

A list with class "PMCMR" containing the following components:

method: a character string indicating what type of test was performed.
data.name: a character string giving the name(s) of the data.
statistic: lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
p.value: lower-triangle matrix of the p-values for the pairwise tests.
alternative: a character string describing the alternative hypothesis.
p.adjust.method: a character string describing the method for p-value adjustment.
model: a data frame of the input data.
dist: a string that denotes the test distribution.

Details

For many-to-one comparisons (pairwise comparisons with one control) in an one-factorial layout with non-normally distributed residuals Anderson-Darling's non-parametric test can be performed. Let there be $k$ groups including the control, then the number of treatment levels is $m = k - 1$ . Then $m$ pairwise comparisons can be performed between the $i$ -th treatment level and the control. H $_i: F_0 = F_i$ is tested in the two-tailed case against A $_i: F_0 \ne F_i, ~~ (1 \le i \le m)$ .

This function is a wrapper function that sequentially calls adKSampleTest for each pair. The calculated p-values for Pr(>|T2N|)

can be adjusted to account for Type I error inflation using any method as implemented in p.adjust.

Note

Factor labels for g must be assigned in such a way, that they can be increasingly ordered from zero-dose control to the highest dose level, e.g. integers {0, 1, 2, ..., k} or letters {a, b, c, ...}. Otherwise the function may not select the correct values for intended zero-dose control.

It is safer, to i) label the factor levels as given above, and to ii) sort the data according to increasing dose-levels prior to call the function (see order, factor).

Examples


## Data set PlantGrowth
## Global test
adKSampleTest(weight ~ group, data = PlantGrowth)

##
ans <- adManyOneTest(weight ~ group,
                             data = PlantGrowth,
                             p.adjust.method = "holm")
summary(ans)

References

Scholz, F.W., Stephens, M.A. (1987) K-Sample Anderson-Darling Tests. Journal of the American Statistical Association 82 , 918--924.

adManyOneTest function