frdManyOneNemenyiTest {PMCMRplus}

Nemenyi's Many-to-One Test for Unreplicated Blocked Data

Description

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

Usage

frdManyOneNemenyiTest(y, ...)

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

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.

...

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, Nemenyi'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 multivariate normal distribution. As pmvnorm applies a numerical method, the estimated p-values are seet depended.

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

Hollander, M., Wolfe, D. A., Chicken, E. (2014), Nonparametric Statistical Methods. 3rd ed. New York: Wiley. 2014.

Miller Jr., R. G. (1996), Simultaneous Statistical Inference. New York: McGraw-Hill.

Nemenyi, P. (1963), Distribution-free Multiple Comparisons. Ph.D. thesis, Princeton University.

Siegel, S., Castellan Jr., N. J. (1988), Nonparametric Statistics for the Behavioral Sciences. 2nd ed. New York: McGraw-Hill.

Zarr, J. H. (1999), Biostatistical Analysis. 4th ed. Upper Saddle River: Prentice-Hall.

See Also

friedmanTest, friedman.test, frdManyOneExactTest, frdManyOneDemsarTest pmvnorm, set.seed

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")