PMCMR (version 4.3)

# posthoc.friedman.nemenyi.test: Pairwise post-hoc Test for Multiple Comparisons of Mean Rank Sums for Unreplicated Blocked Data (Nemenyi-Test)

## Description

Calculate pairwise comparisons using Nemenyi post-hoc test for unreplicated blocked data. This test is usually conducted post-hoc after significant results of the friedman.test. The statistics refer to upper quantiles of the studentized range distribution (Tukey).

## Usage

posthoc.friedman.nemenyi.test(y, …)# S3 method for default
posthoc.friedman.nemenyi.test (y, groups, blocks,
…)# S3 method for formula
posthoc.friedman.nemenyi.test (formula, data, subset,
na.action, …)

## Arguments

y

either a numeric vector of data values, or a data matrix.

groups

a vector giving the group for the corresponding elements of y if this is a vector; ignored if y is a matrix. If not a factor object, it is coerced to one.

blocks

a vector giving the block for the corresponding elements of y if this is a vector; ignored if y is a matrix. If not a factor object, it is coerced to one.

formula

a formula of the form a ~ b | c, where a, b and c give the data values and corresponding groups and blocks, respectively.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

further arguments to be passed to or from methods.

## Value

A list with class "PMCMR"

method

The applied method.

data.name

The name of the data.

p.value

The p-value according to the studentized range distribution.

statistic

The estimated upper quantile of the studentized range distribution.

Defaults to "none"

%% ...

## Details

A one-way ANOVA with repeated measures that is also referred to as ANOVA with unreplicated block design can also be conducted via the friedman.test. The consequent post-hoc pairwise multiple comparison test according to Nemenyi is conducted with this function.

If y is a matrix, than the columns refer to the treatment and the rows indicate the block.

See vignette("PMCMR") for details.

Let $$R_j$$ and $$n_j$$ denote the sum of Friedman-ranks and the sample size of the $$j$$-th group, respectively, then a difference between two groups is significant on the level of $$\alpha$$, if the following inequality is met:

$$\left| \frac{R_i}{n_i} - \frac{R_j}{n_j} \right| > \frac{q_{\infty;k;\alpha}}{\sqrt{2}} \sqrt{\frac{k \left( k + 1 \right)}{6 n}}$$

with $$k$$ the number of groups (or treatments) and $$n$$ the total number of data.

## References

Janez Demsar (2006), Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research, 7, 1-30.

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

Lothar Sachs (1997), Angewandte Statistik. Berlin: Springer. Pages: 668-675.

friedman.test, kruskal.test, posthoc.kruskal.nemenyi.test, Tukey

## Examples

Run this code
# NOT RUN {
##
## 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.
##
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,c("A","B","C","D","E","F")))
print(y)
friedman.test(y)
posthoc.friedman.nemenyi.test(y)
# }


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