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Can I use Bray-Curtis distance when performing MRPP (Multi-response Permutation Procedures) or MRBP (Blocked Multi-response Permutation Procedures)?

[See Ch 24 of McCune & Grace (2002) for explanation of MRPP & MRBP].

Typically, according to McCune & Grace and the literature they cite, Euclidean, Squared Euclidean and Sorensen distance are most often used for these procedures. My question is whether Bray-Curtis Distance would also be appropriate?

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You can use non-euclidean distances such as Bray-Curtis if you use Pseudo-F as your test statistic (see Reiss et al 2010, Biometrics, Vol. 66 (2), pp. 636-643).

"the pseudo-F statistic is a generalization of the classical F statistic that can be calculated directly from the distance matrix D, whether or not D is Euclidean."

The authors of the vegan package in R recommend using the function "adonis", which uses a permutation test with pseudo-F ratios, rather than mrpp. You might want to look into using adonis instead.

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