Respected researchers,
Is there any non-parametric test equivalent to a repeated measures analysis
of covariance (ANCOVA)?
Similar to what Jos has suggested, but with more theoretical backing, after ordering all data, transform each observation into a normal quantile. Ranks are OK for the one factor model and for main effects, but there is no theoretical support for ranks when interaction terms are present (see text by W. CONOVER on nonparametric statistics).
There is a good explanation of the use of ranks in ANCOVA in a Google Groups discussion at this link.
https://groups.google.com/forum/#!topic/comp.soft-sys.stat.spss/HoY2A7ZO2Dw
The advice at that source state the same reference.
"If you definitely are not happy with ANOVA/ANCOVA on the raw data, you might consider using ANOVA/ANCOVA on the rank-transformed data. Conover's book on "nonparametric statistics" is a good source of information about this approach."
Conover also points out when it is better to use normal scores.
Respected researchers
My scores are not normally distributed. So, I have conducted Friedman Test and also ANOVA and ANCOVA repeated measures. Can I do this?
Nan: First, make sure that for your experiment and the data that ANOVA, ANCOVA, and a Friedman's Test are the right choices. Ask yourself these questions:
1. Do I have one treatment factor and one blocking factor in the experiment? If the answer is YES, then Friedman's Test, a rank based test for a Randomized Complete Block Design may be the best suited test.
2. Do I have a factorial experiment and do I want to estimate and then test the interactions effects? Then, the ANOVA F test would be suitable.
3. Do I have one or more factors that are not interest to me as experimental factors, and they are really nuisance factors that you are stuck with and that you want to adjust for? Then use ANCOVA and make sure that there is no interaction between the covariates and the treatments.
In Cases 2 and 3 we assume normal data. Here, I would do what I have suggested above in a previous post.
i have toys as my treatment factor and rereading as my control group Prof
We have recently developed the theory for Rank Repeated Measures ANCOVA, published in Communications in Statistics - Theory and Methods:
http://www.tandfonline.com/doi/abs/10.1080/03610926.2015.1014106
There is Quade's RANCOVA; an ANOVA for the Group (or Treatment) effect on the residuals of a regression of ranked posttest on ranked pretest. To accomplish this, 1) rank the pretest and posttest separately over Groups, then 2) run a regression of the ranked posttest on the ranked pretest, 3) run a oneway ANOVA for the Group effect on the residuals of the regression in 2).
If anybody has doubts, this site helps to solve it
https://www-01.ibm.com/support/docview.wss?uid=swg21477497
Dear Mogean,
I suggest that you consider the Generalized Estimating Equation (GEE).
https://www.hindawi.com/journals/as/2014/303728/
Article Improving power in small-sample longitudinal studies when us...
Good luck
Yes, there are some options for the non-parametric approach to the General Linear Models (including AN[C]OVA), all in common use. All of them are available in R, most are available in SAS. Let me enumerate a few of them:
1. Robust rank based ANOVA, aka Aligned Rank Transform (ART)
2. ANCOVA using robust estimator (trimmed means, M-estimators, medians)
3. ATS (ANOVA-Type Statistic), WTS (Wald-Type Statistic), permuted Wald-type statistic (WTPS)
4. Permutation AN(C)OVA (under the null hypothesis) or its approximation via finite resampling
5. GEE (Generalized Estimating Equations)
6. Non-parametric ANCOVA using smoothing
7. Ordinal logistic regression with random effects (subject) will work well too, especially for Likert scales.
All of the mentioned methods are implemented in the R statistical package. ATS is doable in SAS. The links I provided will guide you through the theory and comments on the methods. Some refers to R or SAS codes/packages.
1. ARTool Align-and-rank data for a nonparametric ANOVA (http://depts.washington.edu/madlab/proj/art/)
2. Robust Statistical Methods Using WRS2 (https://cran.r-project.org/web/packages/WRS2/vignettes/WRS2.pdf)
3. Anova-Type Statistics, a good alternative to parametric methods for analyzing repeated data from preclinical experiments (http://www.ncs-conference.org/2010/3B_07.pdf)
4. Nonparametric Tests for the Interaction in Two-way Factorial Designs Using R (https://www.researchgate.net/publication/307936821_Nonparametric_Tests_for_the_Interaction_in_Two-way_Factorial_Designs_Using_R)
5. Modern Robust Statistical Methods (https://pdfs.semanticscholar.org/88cb/15520b2f84fd2a5a09e0341e791f40ab4118.pdf)
6. Nonparametric Methods in Factorial Designs (https://www.researchgate.net/profile/Jos_Feys/post/What_statistical_tests_can_I_use_to_compare_mean_values_for_my_study/attachment/59d6558b79197b80779acad7/AS%3A526088510111744%401502440683536/download/Brunner.pdf)
7. GFD: An R Package for the Analysis of General Factorial Designs (https://www.jstatsoft.org/article/view/v079c01/v79c01.pdf)
8. nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments (https://www.jstatsoft.org/article/view/v050i12/v50i12.pdf)
9. Recent Advances and Trends in Nonparametric Statistics (https://books.google.pl/books?id=28dJqAo3hm8C)
10. Permutation tests for linear models in R (https://cran.r-project.org/web/packages/lmPerm/vignettes/lmPerm.pdf)
11. https://cran.r-project.org/web/packages/fANCOVA/fANCOVA.pdf
12. https://cran.r-project.org/web/packages/sm/index.html
13. https://stats.stackexchange.com/questions/41270/nonparametric-equivalent-of-ancova-for-continuous-dependent-variables
14. https://www.researchgate.net/profile/Patrice_Corneli/post/No_normality_no_homocedasticity_U_Mann-whitney_no_significant_differences_t-test_significant_differences_which_test_should_I_trust2/attachment/5bf4d35a3843b00675462988/AS%3A695248409870336%401542771546117/download/OrdinalexampleR.pdf
15. https://cran.r-project.org/web/packages/ordinal/vignettes/clmm2_tutorial.pdf
16. https://cran.r-project.org/web/packages/repolr/repolr.pdf
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