How to do factorial analysis for a non-normal and heteroscedastic data? I designed a field experiment with 4 independent factors but data is not normal and heteroscedastic.  Friedman test (agricolae package) from R only fits for rbd.  Can anybody suggest how to analyze my data please?
 A: Package vegan implements some permutation testing procedures using a distance based approach.  For factor analysis, you should take a look at section 5 of the documentation.  There's also more information in the paper:


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*On distance-based permutation tests for between-group comparisons (Reiss et al, 2010)


You might also be interested in skimming this table:


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*Choosing the Correct Statistical Test
A: The Skillings-Mack test  is a general Friedman-type test that can be used in almost any block design with an arbitrary missing-data structure. It's part of the asbio package for R, and there's a user-written package skilmack for Stata.
Skillings, J. H., and G. A. Mack. 1981. On the use of a Friedman-type statistic in balanced and unbalanced block designs. Technometrics 23: 171-177. 
Aho, K. asbio: A collection of statistical tools for biologists. Version 0.3-24. 2010-9-18. Comprehensive R Archive Network (CRAN) 2010-09-19.
Chatfield, M. and Mander, A. The Skillings–Mack test (Friedman test when there are missing data). Stata Journal 9(2):299-305. 
A: As you suggest you "designed" an experiment, it would be better if can you give a description of your design and data set. Even if the data is heteroscedastic and non-normal, probably some variable transformations might help and you may be able to take advantage of the design. The t-test is fairly robust to the normality assumptions.
