How to set up Fieldtrip 

To perform a 2-way balanced, independent (between units of observation) permutation ANOVA:

1.) put the ft_statfun_indepAnova2way.m file into the statfun folder of your current Fieldtrip version

2.) the actual ANOVA calculations are done by the core function anova_cell_mod (adapted from Arnaud Delorme’s resampling statistical toolkit, https://de.mathworks.com/matlabcentral/fileexchange/27960-resampling-statistical-toolkit), which needs to go into the privat subfolder of the statfun folder 

3.) Next, you’ll have to modify some Fieldtrip functions. Note that the line numbers given below might be slightly different in your Fieldtrip version. They should give you an idea where to look, though.

In ft_statistics_montecarlo:
1. around line 120 (where the defaults for the main function are set), add the following line to set the default effect of interest to be the interaction:
cfg.fac = ft_getopt(cfg, 'fac','iaxb');

2. starting at line 213, replace the assignment 

resample = resampledesign(cfg, design);
 
with

if isfield(cfg,'resample') 
   resample = cfg.resample; 
else 
   resample = resampledesign(cfg, design); 
end

This will allow you to use some pre-computed, more complex permutation matrices (not necessary for an independent 2-way ANOVA, but e.g. for group x condition interactions in a mixed design) 

3. at approximately line 229 add
 
tmpcfg.fac = cfg.fac; 

This configuration struct field will be used to indicate the factor or interaction of interest. This can be 'a' (first factor), 'b' (second factor) or 'iaxb' for the interaction

4. then go to resampledesign (in the private folder of your Fieldtrip version) and change line 130 from 

resample = cat(2, blockres{:}); 
to 
resample(:,cat(2, blocksel{:})) = cat(2, blockres{:}); 

See the following bug note: http://bugzilla.fcdonders.nl/show_bug.cgi?id=1546

Now your Fieldtrip version is set up and ready to run permutation ANOVAs.

You can take a look at the example script and the Sim_indepANOVA_* files (using FtSimLink_indepANOVA; you might want to decrease the number of Monte Carlo simulation to 10 in order to avoid very long running times). Before running the simulation scripts make sure that a copy of anova_cell_mod and the dummy structure are in your working directory (this won’t be necessary if you later run your own analysis in Fieldtrip). The set-up of the design matrix and of the independent and control variables cfg.ivar and cfg.cvar follows the same logic as for one-factorial designs in Fieldtrip (check out the tutorial http://www.fieldtriptoolbox.org/tutorial/cluster_permutation_timelock and http://www.fieldtriptoolbox.org/faq/how_can_i_use_the_ivar_uvar_wvar_and_cvar_options_to_precisely_control_the_permutations?s[]=design&s[]=matrix).


The Sim_indepANOVA_* files exemplify how to perform exact permutation tests with restricted permutations and approximate tests on either the raw data or the residuals under a reduced model as described in ‘Permutation tests for multi-factorial analysis of variance. Marti Anderson and Cajo Ter Braak. Journal of Statistical Computation and Simulation Vol. 73, Iss. 2, 2003.  

You'll have to run the permutation ANOVA for each effect separately by specifying cfg.fac = 'a', 'b' or 'iaxb'.