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5 of 5 people found the following review helpful
4.0 out of 5 stars Take a look, and consult Good, July 24, 2011
This review is from: Comparing Groups: Randomization and Bootstrap Methods Using R (Hardcover)
I feel bad about docking a star from a thoughtful and helpful book, but my appreciation of "Comparing groups" does not reach the "I love it" level. Standing in the way are occasional difficult-to-understand or could-be-presented-better passages, and a feeling that, were the writing "tightened up", one would be left with a fairly thin introductory book, priced at $90. (Note that the titular randomization and bootstrap methods only begin in Chapter 6: the first 100+ pages are taken up by introduction to R and basic EDA). One cannot claim competence in the subject based on "Comparing groups" alone, and needs to go further, assisted by the book's references. Phillip Good's books are a sensible first port of call; selected pages of "Data analysis using regression and multilevel/hierarchical models" by Andrew Gelman and Jennifer Hill are likely to provide an important complementary perspective. Unlike those, "Comparing groups" is better checked out from the library, rather than bought.
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Showing 1-1 of 1 posts in this discussion
Initial post: Jul 24, 2011 9:36:24 AM PDT
An important paragraph from p. 174 says:

"The randomization/permutation test and the bootstrap test were introduced in the previous two chapters as methods to test for group differences. Which should be used? From a statistical theory point of view, the difference between the two methods is that the randomization method is conditioned on the marginal distribution under the null hypothesis. This means each permutation of the data will have the same marginal distribution. *The bootstrap method allows the marginal distribution to vary, meaning the marginal distribution changes with each replicate data set.* If repeated samples were drawn from a larger population, variation would be expected in the marginal distribution, even under the null hypothesis of no difference. The variation in the marginal distribution is not expected; however, there is only one sample from which groups are being randomly assigned so long as the null hypothesis is true. Thus the choice of the method comes down to whether one should condition on the marginal distribution or not".

Can someone (authors?) please explain to me what the highlighted sentence means? What multiple marginal distributions are there?
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