I have a data set with small number of samples and large number of variables. I did hypothesis testing (T test) on each of the variable and got a number of p values. However, the variables are correlated to each other and FDR correction (Benjamini–Hochberg procedure) assumes that tests are independent or positively regression dependent.

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From the paper of BY (2001), http://projecteuclid.org/euclid.aos/1013699998, it seems to me that BY proves that BH procedure also work well in data set where variables are independent or positively regression dependent to each other. But they also mentioned that there may other form of dependency that BH procedure won't work very well. From http://www.math.tau.ac.il/~yekutiel/papers/JSPI%20–%20Dani.pdf, Y extents the BH procedure to BY procedure to meet the situation of non-positive regression dependency. My question is that what is positive regression dependency and what is non-positive regression dependency? An few examples would be greatly helpful!

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#### Best Answer

You're looking for the Benjamini-Yekutieli procedure:

Benjamini, Yoav; Yekutieli, Daniel. The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29 (2001), no. 4, 1165–1188. doi:10.1214/aos/1013699998. http://projecteuclid.org/euclid.aos/1013699998

The procedure is available in R using the `method = "BY"`

option in `p.adjust()`

. For more info, try `?p.adjust`

.

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