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"),
...
)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 |
blocks |
a vector or factor object giving the block for the
corresponding elements of |
alternative |
the alternative hypothesis. Defaults to |
... |
further arguments to be passed to or from methods. |
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: θ_0 = θ_i is tested in the two-tailed case against A_i: θ_0 \ne θ_i, ~~ (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.
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
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.
## 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 frdManyOneDemsarTest(y=y, p.adjust = "bonferroni") ## Exact many-one test frdManyOneExactTest(y=y, p.adjust = "bonferroni") ## Nemenyi's many-one test frdManyOneNemenyiTest(y=y)
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