normalScoresManyOneTest() R function from [PMCMRplus]

Lu-Smith Many-One Comparisons Normal Scores Test

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


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").

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 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.

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
normalScoresTest(weight ~ group, data = PlantGrowth)

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

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.

normalScoresManyOneTest function