PMCMRplus (version 1.9.12)

frdManyOneDemsarTest: Demsar's Many-to-One Test for Unreplicated Blocked Data

Description

Performs Demsar's non-parametric many-to-one comparison test for Friedman-type ranked data.

Usage

frdManyOneDemsarTest(y, ...)
# S3 method for default
frdManyOneDemsarTest(
  y,
  groups,
  blocks,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = p.adjust.methods,
  ...
)

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.

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 "x". Ignored with a warning if "x" is a list.

blocks

a vector or factor object giving the block 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).

...

further arguments to be passed to or from methods.

Details

For many-to-one comparisons (pairwise comparisons with one control) in a two factorial unreplicated complete block design with non-normally distributed residuals, Demsar's test can be performed on Friedman-type ranked data.

Let there be \(k\) groups including the control, then the number of treatment levels is \(m = k - 1\). A total of \(m\) pairwise comparisons can be performed between the \(i\)-th treatment level and the control. H\(_i: \theta_0 = \theta_i\) is tested in the two-tailed case against A\(_i: \theta_0 \ne \theta_i, ~~ (1 \le i \le m)\).

The \(p\)-values are computed from the standard normal distribution. Any of the \(p\)-adjustment methods as included in p.adjust can be used for the adjustment of \(p\)-values.

References

Demsar, J. (2006) Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research 7, 1--30.

See Also

friedmanTest, friedman.test, frdManyOneExactTest, frdManyOneNemenyiTest.

Examples

 ## Sachs, 1997, p. 675
 ## Six persons (block) received six different diuretics
 ## (A to F, treatment).
 ## The responses are the Na-concentration (mval)
 ## in the urine measured 2 hours after each treatment.
 ## Assume A is the control.

 y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))

 ## Global Friedman test
 friedmanTest(y)

 ## Demsar's many-one test
 summary(frdManyOneDemsarTest(y=y, p.adjust = "bonferroni",
                      alternative = "greater"))

 ## Exact many-one test
 summary(frdManyOneExactTest(y=y, p.adjust = "bonferroni",
                     alternative = "greater"))

 ## Nemenyi's many-one test
 summary(frdManyOneNemenyiTest(y=y, alternative = "greater"))

 ## House test
 frdHouseTest(y, alternative = "greater")