0
$\begingroup$

After a successful Friedman test, I would like to perform post-hoc analysis using the all pairs comparisons Nemenyi's test. Specifically, as I am interested in finding out if the values of some of my samples are greater than the others, I'm trying to apply a one-tailed Nemenyi's test using the PMCMRplus R package with the alternative="greater" parameter. However, it seems to to me that the alternative parameter is always ignored. Example below.

Using the example from the PMCMRplus documentation:


## 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, LETTERS[1:6]))

friedmanTest(y)

I obtain a p-value less than 0.05

Friedman rank sum test

data:  y
Friedman chi-squared = 23.333, df = 5, p-value = 0.0002915

So my understanding is that I can apply post-hoc analysis. I would like to use the Nemenyi's test to perform all possible pairwise comparisons:

## Nemenyi's test
frdAllPairsNemenyiTest(y) 

Results:

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox all-pairs test for a two-way balanced complete block design

data: y

  A      B      C      D      E     
B 0.1880 -      -      -      -     
C 0.0917 0.9996 -      -      -     
D 0.9996 0.3388 0.1880 -      -     
E 0.0395 0.9898 0.9996 0.0917 -     
F 0.0016 0.6363 0.8200 0.0052 0.9400

P value adjustment method: single-step

However, in my case I have to perform a one-tailed test as I want to compare if some samples have greater values than others. Hence:

## Nemenyi's test
frdAllPairsNemenyiTest(y, alternative="greater")

But I get the exact same results as before:

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox all-pairs test for a two-way balanced complete block design

data: y

  A      B      C      D      E     
B 0.1880 -      -      -      -     
C 0.0917 0.9996 -      -      -     
D 0.9996 0.3388 0.1880 -      -     
E 0.0395 0.9898 0.9996 0.0917 -     
F 0.0016 0.6363 0.8200 0.0052 0.9400

P value adjustment method: single-step

And the same happens if I try :

frdAllPairsNemenyiTest(y, alternative="less")

Results:

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox all-pairs test for a two-way balanced complete block design

data: y

  A      B      C      D      E     
B 0.1880 -      -      -      -     
C 0.0917 0.9996 -      -      -     
D 0.9996 0.3388 0.1880 -      -     
E 0.0395 0.9898 0.9996 0.0917 -     
F 0.0016 0.6363 0.8200 0.0052 0.9400

P value adjustment method: single-step

This leads me to believe that the alternative parameter does not work as intended. Am I misinterpreting the results? or am I missing something about the test?

EDIT: the same package offers a frdManyOneNemenyiTest function for many-to-one comparisons using the same test. When using that function the alternative parameter is taken into consideration:

frdManyOneNemenyiTest(y, alternative='greater')
frdManyOneNemenyiTest(y, alternative='less')
frdManyOneNemenyiTest(y)

Results:

> frdManyOneNemenyiTest(y, alternative='greater')

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox-Miller many-to-one test for a two-way balanced complete block design

data: y

  A      
B 0.04119
C 0.01845
D 0.72552
E 0.00747
F 0.00027

P value adjustment method: single-step
alternative hypothesis: greater
> frdManyOneNemenyiTest(y, alternative='less')

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox-Miller many-to-one test for a two-way balanced complete block design

data: y

  A   
B 1.00
C 1.00
D 0.91
E 1.00
F 1.00

P value adjustment method: single-step
alternative hypothesis: less
> frdManyOneNemenyiTest(y)

    Pairwise comparisons using Nemenyi-Wilcoxon-Wilcox-Miller many-to-one test for a two-way balanced complete block design

data: y

  A      
B 0.08243
C 0.03711
D 0.99817
E 0.01475
F 0.00052

P value adjustment method: single-step
alternative hypothesis: two.sided
```
$\endgroup$
2
  • $\begingroup$ Looking at the documentation of the function it doesn't look like alternative is an argument of the function (rather the value of alternative is returned along with other values): rdocumentation.org/packages/PMCMRplus/versions/1.7.1/topics/… I'm not familiar with this test but if the sampling distribution is symmetrical you can just divide the p-value by 2 to get the one-tailed test (provided the sample effect is in the hypothesized direction) $\endgroup$ Commented Dec 19, 2020 at 21:20
  • $\begingroup$ Not too familiar with the test either, but the same package offers a function frdManyOneNemenyiTest for many to one comparisons that does take into account the alternative parameter (frdManyOneNemenyiTest(y, alternative='greater') and frdManyOneNemenyiTest(y, alternative='less') do give me opposite results as expected) Perhaps I can just use this function in a round-robin fashion to compare all my samples? $\endgroup$ Commented Dec 20, 2020 at 8:43

1 Answer 1

1
$\begingroup$

The function frdAllPairsNemenyiTest has no argument alternative. It is only intended to do non-directional pairwise hypotheses tests (i.e. two-sided per default). See also help(frdAllPairsNemenyiTest).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.