[R] kruskal.test followed by kruskalmc
peter dalgaard
pdalgd at gmail.com
Fri Jul 5 20:07:54 CEST 2013
On Jul 5, 2013, at 16:34 , Humber Andrade wrote:
> Thank you Dr. Dalgaard. I understood. I know that this list is not to discuss statistics but I would be very glad if you or someone else can give me some opinion on how to proceed. The kruskal.test says there are differences but the multiple comparisons do not point out what are the differences. Can you suggest a suitable way (maybe paired wilcoxon) to infer what are the differences? I am asking for the hint because I am sure the journal editor/reviewer will ask me to point out which groups differ from each other.
>
I'm afraid it can't be done. You really can be in a situation where you reject the global null hypothesis that all groups are the same, yet cannot point out any two groups that differ from eachother.
-pd
> Regards, Humber
>
>
> On Fri, Jul 5, 2013 at 11:04 AM, peter dalgaard <pdalgd at gmail.com> wrote:
>
> On Jul 5, 2013, at 15:00 , Humber Andrade wrote:
>
> > Thank you Prof. José Iparraguirre. Maybe I am wrong but I think the issues
> > are not the same. His data doesn't showed significant differences after
> > kruskal.test(), that was not my case. Anyway follow below my the results
> > I've got and the database.
> >
>
> This can happen. It is a matter of probability theory, not of R. The following is a simplified paraphrase of what is going on:
>
> # 15 random normals, compare range test to variance test
> # Simulate everything for simplicity
>
>
> # Null distribution
> M0 <- replicate(10000, rnorm(15))
> vv <- apply(M0,2,var)
> rg <- apply(M0,2,range)
> rr <- apply(rg,2,diff)
> r.95 <- quantile(rr, .95)
> v.95 <- quantile(vv, .95)
> v.995 <- quantile(vv, .995)
>
> # Distribution at quadrupled variance
> M <- replicate(10000, rnorm(15,sd=2))
> vv <- apply(M,2,var)
> rg <- apply(M,2,range)
> rr <- apply(rg,2,diff)
> plot(rr,vv)
> abline(h=c(v.95,v.995),v=r.95, col="red")
>
> Notice that the two statistics are correlated, but not equivalent. There are cases where one value is beyond the .95 level and the other is not. Since it is theoretically optimal to use the variance as the test statistic in this model, there are quite a few more cases where rr is below the cutoff and vv is above than the other way around. There are even a sizable number of cases where vv is beyond v.995 and rr does not reach r.95.
>
> (The theoretical optimality applies only because I use an increased variance alternative. For specific alternatives, the picture can change. Try it, for instance with a single mean substantially different from the others:
>
> M <- replicate(10000, rnorm(15,mean=rep(c(4,0),c(1,14))))
>
> )
>
>
> > Thank you,
> >
> > #################
> >> kruskal.test(data$resp,data$group)
> >
> > Kruskal-Wallis rank sum test
> >
> > data: data$resp and data$group
> > Kruskal-Wallis chi-squared = 32.3546, df = 14, p-value = 0.003566
> > ################
> >> kruskalmc(data$resp,data$group)
> > Multiple comparison test after Kruskal-Wallis
> > p.value: 0.05
> > Comparisons
> > obs.dif critical.dif difference
> > A-B 4.8303571 62.37688 FALSE
> > A-C 3.8928571 62.37688 FALSE
> > A-D 0.4821429 62.37688 FALSE
> > .............................................................
> > .............................................................
> > .............................................................
> > M-P 14.2500000 60.26179 FALSE
> > N-O 1.3750000 60.26179 FALSE
> > N-P 6.1250000 60.26179 FALSE
> > O-P 4.7500000 60.26179 FALSE
> >
> > ############# database
> > group resp A 0.1 A 581.8 A 90.5 A 70.1 A 820.1 A 1159.2 A 2478.1
> > A 2475.3 B 351.8 B 370.1 B 326.1 B 751.9 B 931 B 588.2 B 70.1 B
> > 1754.9 C 289.8 C 254.1 C 370.3 C 459.8 C 412.5 C 591.5 C 986.9 C 890
> > D 425.6 D 397.4 D 464 D 370.9 D 417.3 D 455 D 568.2 D 599.4 E 405.1
> > E 626.2 E 299 E 493.8 E 362.6 E 309.8 E 522.7 E 433.3 F 698.6 F 42.5
> > F 7.4 F 10.6 F 95.8 F 497.5 F 987.9 F 925.1 G 492.9 G 376 G 413 G
> > 278.3 G 344.2 G 292.2 G 429.4 G 368 H 241.6 H 230.5 H 310.4 H 372.5
> > H 366.1 H 307.9 H 480 H 529.8 I 296 I 288.8 I 302.1 I 300.8 I 150.1
> > I 381.9 I 583.1 I 489.4 J 1.2 J 18.6 J 7.7 J 11.6 J 48.1 J 121.8 J
> > 1284.1 J 944.7 L 0.5 L 44.4 L 80.9 L 15.3 L 80 L 379.9 L 940.6 L
> > 829.3 M 323.6 M 401.5 M 162.1 M 136.5 M 139.4 M 363.3 M 280.7 M
> > 356.5 N 197.6 N 245.9 N 221.5 N 224.3 N 185.4 N 265.3 N 304.8 N
> > 351.9 O 189.9 O 237.3 O 247.1 O 230.4 O 272.2 O 155.1 O 270.7 O
> > 315.2 P 48.4 P 15.5 P 53.1 P 72.8 P 74.8 P 132.3 P 550 P 478.7
> >
> >
> > On Fri, Jul 5, 2013 at 8:06 AM, Jose Iparraguirre <
> > Jose.Iparraguirre at ageuk.org.uk> wrote:
> >
> >> Humber,
> >> Have a look at this:
> >> http://r.789695.n4.nabble.com/Multiple-Comparisons-Kruskal-Wallis-Test-kruskal-agricolae-and-kruskalmc-pgirmess-don-t-yield-the-sa-td4639004.html
> >> Hope it helps.
> >> Kind regards,
> >>
> >> José
> >>
> >> Prof. José Iparraguirre
> >> Chief Economist
> >> Age UK
> >>
> >>
> >>
> >> -----Original Message-----
> >> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> >> On Behalf Of Humber Andrade
> >> Sent: 05 July 2013 11:38
> >> To: r-help at r-project.org
> >> Subject: [R] kruskal.test followed by kruskalmc
> >>
> >> Hi all,
> >>
> >> After running kruskal.test I have got results (p<0,005) pointing to reject
> >> the hypothesis that the samples were draw from the same population.
> >> Howerver when I run the kruskalmc there are no significant differences in
> >> any of the multiple comparisons. Is that possible? Some clarification?
> >>
> >> Thanks, Humber
> >>
> >>
> >> <https://sites.google.com/site/humberandrade>
> >>
> >> [[alternative HTML version deleted]]
> >>
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> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
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> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Peter Dalgaard, Professor
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
>
>
>
--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
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