Could we use sign-flipping method to implement two-sample tests?

[xuyangwen]

Dear Anderson,

I have been using PALM to implement second-level analyses for many years. I am writing to ask you one of my doubts about the choice between the two permutation methods in PALM.

My question is: could we use the sign-flipping method (instead of the permutation method shuffling the labels) to conduct a two-sample test comparing two independent groups?

In you paper Winkler et al. (2014), you said:

Page 383: Independent and symmetric errors (ISE) can be considered for measurements that arise, for instance, from differences between two groups if the variances are not assumed to be the same. Page 384: The choice between EE and ISE depends on the knowledge of, or assumptions about, the error terms. Although the EE does not require symmetry for the distribution of the error terms, it requires that the variances and covariances of the error terms are all equal, or have a structure that is compatible with the definition of exchangeability blocks (discussed below).

Does it mean when the variance of the two groups are not euqual, it would be better to use sign-filpping method to implement two-sample test comparing two idependent groups?

Looking forward to your answer and thank you for yout time.

Best regard, Yangwen

[andersonwinkler]

Hi Yangwen,

Yes, if variances aren't the same, we'd use sign-flippings (but the residuals must be symmetric around zero, which is often the case, but not always). We'd also use the Aspin-Welch's "v" statistic (this is accomplished by supplying a file with variance groups, with the option "-v").

All the best,

Anderson

[xuyangwen]

Hi Anderson,

Thank you very much for your answer and providing another way to address the unequal variances problem I did not notice before.

All the best, Yangwen