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Which test should I use for hypothesis testing on more than two dependent non-parametric data?

The Friedman's test seems to be the option, as I have read in several books and webs, but, when I look for it on MatLab, here, it says:

Friedman's test makes the following assumptions about the data in X:

All data come from populations having the same continuous distribution, apart from possibly different locations due to column and row effects.

All observations are mutually independent.

Should I trust MatLab information? or is it that "observations being mutually independent" is different to independent samples? What does that mean then?

Should I then use Friedman's test with my dependent data? I am really confused.

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    $\begingroup$ Conditional on the blocking factor, they're independent. If you don't condition on it, they're dependent. $\endgroup$ – Glen_b -Reinstate Monica Sep 3 '16 at 15:54
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I'll assume your dependent variable is continuous and your independent variables are categorical. Otherwise, you can't use Friedman's test.

There is nothing wrong in Matlab's description, mutually independent just means each pair of your observations are independent.

If your experiment is repeated (or paired), and you're interested in testing for the treatment effects, then you can use it.

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