chenJanTest {PMCMRplus} | R Documentation |
Chen and Jan Many-to-One Comparisons Test
Description
Performs Chen and Jan nonparametric test for contrasting increasing (decreasing) dose levels of a treatment in a randomized block design.
Usage
chenJanTest(y, ...)
## Default S3 method:
chenJanTest(
y,
groups,
blocks,
alternative = c("greater", "less"),
p.adjust.method = c("single-step", "SD1", p.adjust.methods),
...
)
Arguments
y |
a numeric vector of data values, or a list of numeric data vectors. |
groups |
a vector or factor object giving the group for the
corresponding elements of |
blocks |
a vector or factor object giving the block for the
corresponding elements of |
alternative |
the alternative hypothesis. Defaults to |
p.adjust.method |
method for adjusting p values
(see |
... |
further arguments to be passed to or from methods. |
Details
Chen's test is a non-parametric step-down trend test for
testing several treatment levels with a zero control. Let
there be groups including the control and let
the zero dose level be indicated with
and the highest
dose level with
, then the following
m = k - 1
hypotheses are tested:
Let
be
a i.i.d. random variable of at least ordinal scale. Further,the zero dose
control is indicated with
.
The Mann-Whittney statistic is
where where the indicator function returns
otherwise
.
Let
and
The mean and variance of are
with the number of ties in the
th block and
the size of the tied group
.
The test statistic is asymptotically multivariate normal
distributed.
If p.adjust.method = "single-step"
than the p-values
are calculated with the probability function of the multivariate
normal distribution with . Otherwise
the standard normal distribution is used to calculate
p-values and any method as available
by
p.adjust
or by the step-down procedure as proposed
by Chen (1999), if p.adjust.method = "SD1"
can be used
to account for -error inflation.
Value
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.
References
Chen, Y.I., Jan, S.L., 2002. Nonparametric Identification of the Minimum Effective Dose for Randomized Block Designs. Commun Stat-Simul Comput 31, 301–312.
See Also
Examples
## Example from Chen and Jan (2002, p. 306)
## MED is at dose level 2 (0.5 ppm SO2)
y <- c(0.2, 6.2, 0.3, 0.3, 4.9, 1.8, 3.9, 2, 0.3, 2.5, 5.4, 2.3, 12.7,
-0.2, 2.1, 6, 1.8, 3.9, 1.1, 3.8, 2.5, 1.3, -0.8, 13.1, 1.1,
12.8, 18.2, 3.4, 13.5, 4.4, 6.1, 2.8, 4, 10.6, 9, 4.2, 6.7, 35,
9, 12.9, 2, 7.1, 1.5, 10.6)
groups <- gl(4,11, labels = c("0", "0.25", "0.5", "1.0"))
blocks <- structure(rep(1:11, 4), class = "factor",
levels = c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11"))
summary(chenJanTest(y, groups, blocks, alternative = "greater"))
summary(chenJanTest(y, groups, blocks, alternative = "greater", p.adjust = "SD1"))