Nemenyi's Many-to-One Test for Unreplicated Blocked Data
Nemenyi's Many-to-One Test for Unreplicated Blocked Data
Performs Nemenyi's non-parametric many-to-one comparison test for Friedman-type ranked data.
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.
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 (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. Hi:θ0=θi is tested in the two-tailed case against Ai:θ0=θi,(1≤i≤m).
The p-values are computed from the multivariate normal distribution. As pmvnorm applies a numerical method, the estimated p-values are seet depended.
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")
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.