I am not an R user, but what you'd use as a non-parametric alternative to the repeated measures ANOVA is the Friedman test.

The attached link is for the info on using the Friedman test in R.

I hope this helps

Ariel

https://stat.ethz.ch/R-manual/R-patched/library/stats/html/friedman.test.html

The Friedman Test is a nonparametric alternative to the F tests in a  Randomized Complete Block Design ANOVA. How would it take care of repeated measures?

The Friedman test can be used in a couple different ways. It extends the Wilcoxon signed ranks test to include (1) 2+ time periods of data for a single group, and (2) groups of 3+ matched subjects, with individuals being randomly assigned to each condition.

In my earlier post, I was referring to #1, which is the non-parametric alternative to a repeated measures ANOVA without a comparison group.

Thank you for this clarification, Ariel. I don't use the Friedman test often.

It is not a much often used test, and it has many problems... I'd say that most researchers would not use this as a "go-to" statistical test if the assumptions for ANOVA are met....

What is your stand on using normal quantile transformed data with the repeated ANOVA in place of the Friedman Test? I trust using such transformations to get robust ANOVA (not really nonparametric). The main advantage is keeping things simple, All you need to know is how to use your software package (SPSS, MINITAB, STATA, ...) to transform the raw data to z scores that are Normal (0,1), followed by clicking on repeated measures ANOVA.

Many thanks Ariel ad Raid for your answers & clarification. For data transfomation, I have already tried log2 and didn't work. But, I will try other tranformations and do the analysis again!

Google: van der waerden,  normal quantile transformations, BLOM

I suppose that is a viable possibility, Raid. My particular bias is toward using a GEE model where I can control the family/link functions.

I favor Ariel's approach, though a mixed model GLM allows even more flexibility while accounting for the repeated measures, albeit under specific link and distributional assumptions.

About GLMM: Please have a look at this review.

Many thanks all for all the help. I will go through it soon

Friedman's test is considered the non-parametric alternative to parametric two-factor repeated measures ANOVA, if your data do not satisfy parametric assumptions of normality and homogeneity of variance. It is possible to perform non-parametic ANOVAR using Friedman's test with multiple replicates. That being said, how many levels are there for the whole-plot factor (K) and how many for the within-subject factor of time, i.e., the blocks (B)? How replicate measurements (n) are made for each combination of K levels and Block levels? Are any observations missing?

Friedman's test with replication observations (continued)

Assuming a balanced design with one whole plot factor and one blocking factor (the repeated measures within-subject factor.

At each level of block (one point in time), perform a Kruskal-Walls one-way ANOVA. Rank the observations across treatments with the block. Save the H statistic, the df for the test, and the rank sums for each treatment (i.e., the mean rank x the number of observation). 

Perform the same analysis for each of the remaining blocks.

To calculate the Friedman test statistic, Chi-square sub r, sum the ranks down the blocks for each treatment, then square it.

Sum the squared values for each level of the whole-plot treatment.

Multiply this value by 12/(B n^2 K * [nK +1])

Subtract the value of 3*B(nK +1) from the above total

This is Friedman Chi-square statistic with K - 1 df.

An interaction Chi-square value can be calculated by summing the H-values for the B blocks, then subtracting the Friedman statistic. This test is formalized in the paper by de Kroon and Van Der Laan in Statistica Neerlandica.

The df for the Interaction Chi-square test is (B*[K - 1]) - (K -1)

Dr. Eisinga et al. have provided a very useful reference on significance tests and acquiring exact P-values for the Friedman's test. I wonder how this could be applied to the multiple replicate situation that I have described earlier, not only to the omnibus test statistic (the chi-square test), plus the interaction test, and perhaps, further multiple comparison tests.

With respect to the original question, does the questioner have a balanced design, i.e., no missing values? If so, how is he treating this problem? There are various formal and ad hoc methods of imputation.

Many other presenters have suggested other viable alternatives to be implemented in R.  One problem in R and many other statistical packages or programs, there is no mention or implementation of the multiple observations form of Friedman's test. The first time that I encountered the form of the statistic that I previously described was mentioned in de Kroon and van der Laan's paper and the now sadly out-of-print text (1977) by Leonard Marascuilo and MaryEllen McSweeney.

Hi everyone 

Is it possible to looking to the similarities between 4 slides which belong to the one case using  friedman test ?! 

I am not sure what question you are asking? Could you please clarify what your experiment entails?

Of course 

i am studying the heterogenity in breast cancer. I have 55 cases each case has 4 slides. My hypothesis is the reading of 4 slides is similar or different. 

Thanks 

Okay, so you have 4 slides per subject. Slides of what?

Slides of tumour tissue  each slide have score

Is an ordinal ranking over 1 to 5, for example, or is the range of responses broader>

the score of the slide range from 1 to 100 % 

the slides are randomly ordered. 

Thanks 

If the slides are randomly ordered, how is this part of a repeated measures ANOVA?

I did not use ANOVA . I used freidman test  to see if they are similar or different. My question is it is a right test or not . 

Many thanks