frdManyOneDemsarTest {PMCMRplus}

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, ...)

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

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

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")