Is there a non-parametric alternative to Two-Way Repeated Measures Anova? I am currently comparing the EEG funcional connectivity measured at 14 electrodes and 4 frequency bands between highly and lowly hypnotic susceptible individuals. I extracted the coherence and the absolute imaginary coherency for all 91 possible connections. As a design for statistical analysis, I chose a two way repeated measures anova. With the within subject variable Condition(no hypnosis, hypnosis) and the between subject variables Group(highly susceptible (7), lowly susceptible (9)) and Connection(different connections between the electrodes(91)).
Unfortunately I am far from meeting the requirements for normality and equality of error variances. Even with ln(x+1), log(x+1), sqrt(x), 1/x transformation.
Does anyone have an idea, which design of non-parametric tests would fit here? 
In the foto you can see the structure of my data set for one frequency band.
Any help would be greatly appreciated.
Many thanks.
 A: There are a couple of approaches that may be helpful.
First, if you can determine the distribution of your data, a generalized linear model (possibly as a mixed-effects model to account for the repeated measures) may work. The distribution of the data may be inferred from the nature of the data. (That is, if it is positive values that might be skewed, perhaps Gamma; if it count data, perhaps a negative binomial; if it is proportion data between 0 and 1, beta. You can look up these distributions on, say, Wikipedia.)  There are also tools that can match the (conditional- or residual-) data to these distributions. (See, for example, the fitdistrplus R package).
Second, for a general non-parametric approach that can handle interactions and repeated measures (mixed effects) designs, there's aligned ranks transformation anova. The ARTool software can be run in R or Windows.  It's a very flexible approach, but it has limitations. Read the documentation.
Finally, if you are really into transformations, you might try some more flexible approaches.  Box-Cox transformation is useful because it takes into the account the whole model.  (But you'd have to simplify your model to a general linear model.) On single variables, there's Tukey's ladder of transformations, and the occasionally miraculous normal scores transformation.
Also, sometimes changing your model helps. If there is another factor or interaction you can include, sometimes that makes a huge difference.
