frdManyOneExactTest() R function from [PMCMRplus]

Exact Many-to-One Test for Unreplicated Blocked Data

Performs an exact non-parametric many-to-one comparison test for Friedman-type ranked data according to Eisinga et al. (2017).


frdManyOneExactTest(y, ...)

## Default S3 method:
frdManyOneExactTest(y, groups, blocks, 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.
p.adjust.method: method for adjusting p values (see p.adjust).
``: 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, an exact 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 exact $p$ -values are computed using the code of "pexactfrsd.R"

that was a supplement to the publication of Eisinga et al. (2017). Additionally, any of the $p$ -adjustment methods as included in p.adjust can be selected, for $p$ -value adjustment.

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

Eisinga, R., Heskes, T., Pelzer, B., Te Grotenhuis, M. (2017) Exact p-values for Pairwise Comparison of Friedman Rank Sums, with Application to Comparing Classifiers, BMC Bioinformatics, 18:68.

frdManyOneExactTest function