[R] Interpreting the results of Friedman test

Fri Apr 24 15:42:46 CEST 2009

Hello,

Peter Dalgaard wrote:
> Not necessarily, but the first suspicion one gets is that what you're
> doing with Friedman is not equivalent to what you're doing with ANOVA,
> could you show us the code and data (or an outline of it)?

Please find attached the R script and the data input files.
The values in dataForFriedmanTest.dat represent the geometric mean of
the values of three repetitions for one observer and one condition.

Am I doing something wrong there?

Thanks in advance

Doerte

PS: I'm not sure if it is possible to send the dat-files by mail.
Therefore I renamed them to *.txt. Please rename back to *.dat.

-------- Original-Nachricht --------
> Datum: Fri, 24 Apr 2009 14:52:44 +0200
> Von: Peter Dalgaard <P.Dalgaard at biostat.ku.dk>
> An: Doerte <doerte.apelt at gmx.de>
> Betreff: Re: [R] Interpreting the results of Friedman test

> Doerte wrote:
> > Hello,
> > 
> > I have problems interpreting the results of a Friedman test. It seems
> > to me that the p-value resulting from a Friedman test and with it the
> > "significance" has to be interpreted in another way than the p-value
> > resulting from e.g. ANOVA?
> > 
> > Let me describe the problem with some detail: I'm testing a lot of
> > different hypotheses in my observer study and only for some the
> > premises for performing an ANOVA are fulfilled (tested with Shapiro
> > Wilk and Bartlett). For the others I perform a Friedman test.
> > 
> > To my surprise, the p-value of the Friedman test is < 0.05 for all my
> > tested hypotheses. Thus, I tried to "compare" the results with the
> > results of an ANOVA by performing both test methods (Friedman, ANOVA)
> > to a given set of data.
> > While ANOVA results in p = 0.34445 (--> no significant difference
> > between the groups), the Friedman test results in p = 1.913e-06 (-->
> > significant difference between the groups?).
> > 
> > How can this be?
> > 
> > Or am I doing something wrong? I have three measured values for each
> > condition. For ANOVA I use them all, for the Friedman test I
> > calculated the geometric mean of the three values, since this test
> > does not work with replicated values. Is this a crude mistake?
> 
> Not necessarily, but the first suspicion one gets is that what you're
> doing with Friedman is not equivalent to what you're doing with ANOVA,
> could you show us the code and data (or an outline of it)?
> 
> -- 
>    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

-- 

-------------- next part --------------
Observer | Condition | Repetition | AUC 
2 | 1 | 2 |  11.6698729267
2 | 1 | 3 |  11.3614841831
2 | 1 | 1 |  11.6320875675
3 | 1 | 3 |  11.3813182648
3 | 1 | 2 |  11.9791654383
3 | 1 | 1 |  11.3193295274
4 | 1 | 3 |  11.6271912743
4 | 1 | 1 |  11.7277539642
4 | 1 | 2 |  11.3073525275
6 | 1 | 2 |  11.5356087785
6 | 1 | 3 |  11.8625252416
6 | 1 | 1 |  11.1631417327
7 | 1 | 1 |  12.0811987417
7 | 1 | 2 |  11.4253889199
7 | 1 | 3 |  11.1438163937
8 | 1 | 2 |  12.3351513361
8 | 1 | 1 |  11.0075952969
8 | 1 | 3 |  11.2701354076
1 | 1 | 2 |  11.9582160341
1 | 1 | 3 |  11.3128071894
1 | 1 | 1 |  11.4041971251
2 | 2 | 2 |  11.1937509173
2 | 2 | 1 |  11.6252278612
2 | 2 | 3 |  11.7113976885
3 | 2 | 3 |  11.1192253767
3 | 2 | 1 |  11.3755159053
3 | 2 | 2 |  12.0029900345
4 | 2 | 3 |  11.6105418939
4 | 2 | 2 |  11.4205387926
4 | 2 | 1 |  11.5200504433
6 | 2 | 2 |  11.3150843227
6 | 2 | 3 |  11.087942451
6 | 2 | 1 |  12.0640315424
7 | 2 | 1 |  11.6605537521
7 | 2 | 3 |  11.6189671844
7 | 2 | 2 |  11.2636316548
8 | 2 | 3 |  11.3865060588
8 | 2 | 2 |  12.1672455368
8 | 2 | 1 |  10.9692943665
1 | 2 | 3 |  11.4617141335
1 | 2 | 1 |  11.5455368466
1 | 2 | 2 |  11.5463396473
2 | 3 | 2 |  11.3473263733
2 | 3 | 1 |  11.7839556008
2 | 3 | 3 |  11.1316960504
3 | 3 | 3 |  11.8686526315
3 | 3 | 2 |  11.0739149317
3 | 3 | 1 |  11.403959013
4 | 3 | 1 |  11.5870552325
4 | 3 | 2 |  11.3401354648
4 | 3 | 3 |  11.3424292954
6 | 3 | 3 |  11.3615420894
6 | 3 | 1 |  11.4887245966
6 | 3 | 2 |  11.3741010608
7 | 3 | 2 |  11.3180993919
7 | 3 | 1 |  11.4960941843
7 | 3 | 3 |  11.454173957
8 | 3 | 3 |  11.2121329748
8 | 3 | 1 |  11.5712149501
8 | 3 | 2 |  11.4525667984
1 | 3 | 3 |  11.1470495671
1 | 3 | 1 |  11.3843720685
1 | 3 | 2 |  11.7803942389
2 | 4 | 1 |  11.7049906947
2 | 4 | 2 |  11.3104231298
2 | 4 | 3 |  11.6789580111
3 | 4 | 2 |  11.9600062087
3 | 4 | 3 |  11.2497720322
3 | 4 | 1 |  11.5070118114
4 | 4 | 3 |  11.6880141384
4 | 4 | 2 |  11.6823046979
4 | 4 | 1 |  11.3789895286
6 | 4 | 1 |  11.2340767853
6 | 4 | 3 |  12.0463303433
6 | 4 | 2 |  11.4281136904
7 | 4 | 2 |  11.9397313286
7 | 4 | 1 |  11.5816813225
7 | 4 | 3 |  11.2157780218
8 | 4 | 3 |  11.3649382115
8 | 4 | 1 |  11.7537482956
8 | 4 | 2 |  11.6151737679
1 | 4 | 2 |  11.8833021895
1 | 4 | 1 |  11.6774568059
1 | 4 | 3 |  11.218661679
-------------- next part --------------
1 | 11.5549259143 | 11.5177949943 | 11.4343007933 | 11.5897878773
2 | 11.5536609678 | 11.5078788328 | 11.4177885112 | 11.5633767055
3 | 11.5561528638 | 11.4933075157 | 11.4442169793 | 11.5685580088
4 | 11.5527009607 | 11.516782224 | 11.4226218647 | 11.5821980029
5 | 11.5527009607 | 11.516782224 | 11.4226218647 | 11.5821980029
6 | 11.516876305 | 11.4815469835 | 11.4079793857 | 11.564376866
7 | 11.5435216828 | 11.5129966958 | 11.4225358663 | 11.5752893725
8 | 11.5236136682 | 11.4970692787 | 11.4109905276 | 11.5768318539