Kruskal-Wallis test with details on pairwise comparisons

Question

The standard stats::kruskal.test module allows to calculate the kruskal-wallis test on a dataset: ``` >>> data(diamonds) >>> kruskal.test(price~carat, data=diamonds) Kruskal-Wallis rank sum test data: price by carat by color Kruskal-Wallis chi-squared = 50570.15, df = 272, p-value < 2.2e-16 ``` This is correct, it is giving me a probability that all the groups in the data have the same mean. However, I would like to have the details for each pair comparison, like if diamonds of colors D and E have the same mean price, as some other softwares do (SPSS) when you ask for a Kruskal test. I have found kruskalmc from the package pgirmess which allows me to do what I want to do: ``` > kruskalmc(diamonds$price, diamonds$color) Multiple comparison test after Kruskal-Wallis p.value: 0.05 Comparisons obs.dif critical.dif difference D-E 571.7459 747.4962 FALSE D-F 2237.4309 751.5684 TRUE D-G 2643.1778 726.9854 TRUE D-H 4539.4392 774.4809 TRUE D-I 6002.6286 862.0150 TRUE D-J 8077.2871 1061.7451 TR…

Accepted Answer

One other approach besides kruskal::agricolae mentioned by Marek, is the Nemenyi-Damico-Wolfe-Dunn test implemented in the help page for oneway_test in the coin package that uses multcomp. Using hadley's setup and reducing the B= value for the approximate() function so it finishes in finite time:

```
#updated translation of help page implementation of NDWD
NDWD <- 
    independence_test(dv ~ iv, data = sum_codings1, distribution = approximate(B = 10000), 
                          ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), 
                          xtrafo = mcp_trafo(iv = "Tukey"))

### global p-value
    print(pvalue(NDWD))

### sites (I = II) != (III = IV) at alpha = 0.01 (page 244)
    print(pvalue(NDWD, method = "single-step"))
```

More stable results on that larger dataset may require increasing the B value and increasing the user's patience.

Jan: 2012: There was recently a posting on R-help claiming unexpected results from this method so I forwarded that email to the maintainer. Mark Difford said he had confirmed the problems and offered an alternate tests with the nparcomp package: https://stat.ethz.ch/pipermail/r-help/2012-January/300100.html

There were also in the same week a couple of other suggestions on rhelp for post-hoc contrasts to KW tests: kruskalmc suggested by Mario Garrido Escudero and `rms::polr` followed by `rms::contrasts` suggested by Frank Harrell https://stat.ethz.ch/pipermail/r-help/2012-January/300329.html

Nov 2015: Agree with toto_tico that help page code of coin package has been changed in the intervening years. The `?independence_test` help page now offers a multivariate-KW test and the `?oneway_test` help page has replace its earlier implementation with the code above usng the `independence_test` function.

Kruskal-Wallis test with details on pairwise comparisons

Solution

Problem