normalScoresManyOneTest {PMCMRplus}

Lu-Smith Many-One Comparisons Normal Scores Test

Description

Performs Lu-Smith multiple comparison normal scores test with one control.

Usage

normalScoresManyOneTest(x, ...)

## Default S3 method:
normalScoresManyOneTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)

## S3 method for class 'formula'
normalScoresManyOneTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", 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.

alternative

the alternative hypothesis. Defaults to two.sided.

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").

Details

For many-to-one comparisons in an one-factorial layout with non-normally distributed residuals Lu and Smith's normal scores transformation can be used prior to a many-to-one comparison test. A total of m = k-1 hypotheses can be tested. The null hypothesis H_{i}: F_0(x) = F_i(x) is tested in the two-tailed test against the alternative A_{i}: F_0(x) \ne F_i(x), ~~ 1 \le i \le k-1. For p.adjust.method = "single-step" the multivariate t distribution is used to calculate p-values (see pmvt). Otherwise, the t-distribution is used for the calculation of p-values with a latter p-value adjustment as performed by p.adjust.

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.

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).

References

Lu, H., Smith, P. (1979) Distribution of normal scores statistic for nonparametric one-way analysis of variance. Journal of the American Statistical Association 74, 715–722.

See Also

normalScoresTest, normalScoresAllPairsTest, normOrder, pmvt.

Examples

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

## Lu-Smith's many-one comparison test
ans <- normalScoresManyOneTest(weight ~ group, data = PlantGrowth, p.adjust.method = "holm")
summary(ans)