I would like to compare the learning dynamics of rats in a behavioral test (2 groups, 16 trials). Normally, I would use an rm-ANOVA, but the data distribution is non-normal.
Noguchi, K., Gel, Y., Brunner, E. , Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software 50, Iss. 12.
The theory is described in:
Brunner, E. and Puri, M.L. (2001). Nonparametric Methods in Factorial Designs. Statistical Papers 42, 1-52.
If you send me an e-mail then I can send you the papers.
Data distribution is not necessarily to be normal. Do you have ordinal or discrete data? RM-ANOVA is a very restricted analysis which depends on sphericity which is hardly satisfied. Instead, I recommend mixed effects models.
Since Friedman test is often criticized, you can also follow below approach. However, it still depends on the answer to question: if your data is seriously violating assumptions? You can find a lot of useful informations on this kind of models in:
Zuur et al. 2009. Mixed effects models and extensions in ecology with R.
The Friedman test (and Quade) is not in general the equivalent of repeated measures anova.
It handles only unreplicated complete block design.
It this case, if you have multiple rats, multiple groups, and multiple times, there's no way to get the data into the Friedman test.
* * *
To reiterate points made by Mehmet:
One consideration: Is the dependent variable really a continuous measurement variable? That is, if it's really count, ordinal, proportion, etc., there are more appropriate models to use, that may get you out of the non-normal residuals problem.
Also: You want to be looking at the distribution of the residuals of the analysis, not the raw data.
Noguchi, K., Gel, Y., Brunner, E. , Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software 50, Iss. 12.
The theory is described in:
Brunner, E. and Puri, M.L. (2001). Nonparametric Methods in Factorial Designs. Statistical Papers 42, 1-52.
If you send me an e-mail then I can send you the papers.
Dear Edgar Brunner, I just came across your post and found the article very interesting! Is there any way to add a whole-plot factor to the function, i.e. for comparisons with three independent factors and one repeated measures variable? Thanks in advance!
von der Theorie her ist das alles möglich. Das ist nur noch nicht in dem R-Paket vorhanden, das im Wesentlichen Frank Konietschke geschrieben hat. Seine E-Mail Adresse ist [email protected]
Wir wollen dieses Paket schon seit längerem neu schreiben - aber uns fehlt leider die Zeit dazu. Schreiben Sie doch Frank einfach mal eine E-Mail und fragen ihn, ob er vielleicht zufällig schon ein Update "in der Hinterhand" hat.
Aber insgesamt 4 Faktoren ist schon eine ganze Menge in einem Modell! Wie wollen Sie das alles interpretieren? Das sind 4 Haupt effekte, 6 Zweifach-Interaktionen, 4 Dreifach-Interaktionen und eine Vierfach-Interaktion.
Wenn eine Interaktion signifikant wird, müssen Sie ohnedies das Design aufsplitten. Und der F2-LD-F1 ist ja im Paket vorhanden. - Können Sie das nicht inhaltlich sinnvoll aufsplitten? Mein Rat ist: einfache Experimente durchführen und mit den dadurch beantworteten Fragen dann weiter Versuche planen.
Haben Sie denn überhaupt genug Wiederholungen in jeder Whole-Plot Faktorstufe? - Sie können mir genre eine E-Mail auf meinem normalen E-Mail Accont schreiben, dann unterhalten wir uns da oder ich biete Ihnen eine Skype-Unterhaltung an. Meine E-Mail ist: [email protected]
Hallo Herr Brunner, vielen Dank für Ihre freundliche und ausführliche Antwort! Gerne komme ich auf Ihr Angebot zurück und werde Ihnen über Ihre e-mail-Adresse schreiben. Viele Grüße, Ricarda Blum
How to do post hoc (pairwise comparison) analysis using nparLD? I used a F1-LD-F1 (repeated measures scores ~ group:time) model and have results, but, unable to figure out the correct way to do pairwise comparison. Looking for some guidance on the same. I have gone through multiple articles and none comes out clear with the method or sample code. Some use mctp.rm(), some use nparLD, but, not clear on the approach. Thank you.
You can use the function mctp.paired in the R-package nparcomp. You can see this in the paper: nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals, authors: Frank Konietschke, Marius Placzek, Frank Schaarschmidt, Ludwig A. Hothorn (2015), Journal of Statistical Software, 10.18637/jss.v064.i09
Edgar Brunner What about a post hoc for a F1-LD-F2 (2 different measures, 7 times, 3 groups). I've got all effects and interactions significant, but I am finding difficult to identify alll meaningful results. Thanks in advance
I had answered this question already earlier. Hier is again my recommendation:
You can use the function mctp.paired in the R-package nparcomp. You can see this in the paper: nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals, authors: Frank Konietschke, Marius Placzek, Frank Schaarschmidt, Ludwig A. Hothorn (2015), Journal of Statistical Software, 10.18637/jss.v064.i09
Apologies for a lengthy question. But, I hereby request some clarifications.
Please correct me if I am wrong in my approach.
My data has 4 treatment groups(group1 to group4), each group measured for a score at 4 repeated intervals (one pre-treatment(t1), 3 post treatment(t2, t3, t4)).
I used the following code to get the F1-LD-F1 model results:
I get so many requests and questions from all over the world. I am sorry that I cannot perform statistical consulting for the whole world. So, please read the recommended books, papers, and programme descriptions. These include:
Research Papers
Konietschke, F., Hothorn, L. A., Brunner, E. (2012). Rank-based multiple test procedures and simultaneous confidence intervals. The Electronic Journal of Statistics 6, 737-758.
Pauly, M., Brunner, E., and Konietschke, F. (2015). Asymptotic Permutation Tests in General Factorial Designs. Journal of the Royal Statistical Society - Series B, 77,461–473. DOI: 10.1111/rssb.12073
Friedrich, S., Brunner, E., and Pauly, M. (2017). Permuting longitudinal data despite of the dependencies. Journal of Multivariate Analysis 153, 255-265.
Brunner, E., Konietschke, F., Pauly, M., and Puri, M.L. (2017). Rank-Based Procedures in Factorial Designs: Hypotheses about Nonparametric Treatment Effects. Journal of the Royal Statistical Society Series B, Journal of the Royal Statistical Society Series B 79, 1463–1485.
Happ, M., Bathke, A., and Brunner, E. (2018). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in Medicine 38, 363-375.
Software Papers
Noguchi, K., Gel, Y., Brunner, E. , Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software 50, Iss. 12.
Konietschke, F., Friedrich, S., Brunner, E., and Pauly, M. (2019). rankFD: Rank-based tests for general factorial designs. R package version 0.0.3.
Konietschke, F.; Placzek, M.; Schaarschmidt, Frank; Hothorn, Ludwig A.: nparcomp: An R software package for nonparametric multiple comparisons and simultaneous confidence intervals. In: Journal of Statistical Software 64 (2015), Nr. 9, S. 1-17. DOI: http://dx.doi.org/10.18637/jss.v064.i09
Books:
Brunner, E., Domhof S., Langer, F. (2002). Nonparametric Analysis of Longitudinal Data in Factorial Designs. Wiley, New York.
Brunner, E., Bathke, A.C., and Konietschke, F. (2019). Rank- and Pseudo-Rank Procedures for Independent Observations in Factorial Designs – Using R and SAS. Springer Series in Statistics, Springer, Heidelberg. ISBN: 978-3-030-02912-8.
General recommendation:
For questions regarding the analysis of particular data sets, I would like to recommend asking the statistical consulting unit at your university. – Kind regards, Edgar Brunner