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Why is there only one p-Value for the friedman test although it's a two way design

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Jonas on 20 Apr 2021
Commented: Jonas on 2 May 2021
like already in the title: i was searching for something like the 2 way anova but without the normal distribution requirement. the friedman test allows a two way layout but i only get 1 p-valie. but i want to know the impact of rows and column.
What am I misunderstanding? best regards
Jonas on 2 May 2021
actually i also used the parametric 2 way anova in the end instead of anova ;) but the original question remained and i was happy with the answer i accepted below. but tahbk you for providing some additional information and helping me a bit more in detail regarding this topic!

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Accepted Answer

Shashank Gupta
Shashank Gupta on 22 Apr 2021
Hi Jonas,
Friedman test in MATLAB as you pointed out give only one p-value which is associated with the column effect. Friedman effect cannot be used for interactions between the row and column factors. Although there are some workaround for separately finding out the p-values for row and column effect.
Test for column effect :-
p = friedman(x)
Test for row effect :-
% For data matrix with no replication, row effect can simply be done by
% taking transpose.
p = friedman(x');
% If the data matrix has replication then it is slightly complicated, below
% is one such template that can be done.
x = reshape(x, [3 2 3]); % First convert the data into 3 dimension data, with the first dimension representing the replicates
x = permute(x, [1 3 2]); % swapping the other two dimensions
x = reshape(x, [9 2]); % restoring the two-dimensional shape
p = friedman(x, 3);
I hope this helps.
  1 Comment
Jonas on 23 Apr 2021
many thanks, i saw this dimension swapping already somewhere, but that was a point in time where i didn't need it yet. Couldn't find it in the aftermath. Thank you very much!

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