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help > RE: Strange p values
May 9, 2016 03:05 PM | Jon Dudley
RE: Strange p values
Hi Alice,
*Edit: part of my response seems to keep getting chopped off when I hit submit,
This is normal. For a vector of N p-values sorted from smallest to largest, one can compute the FDR-corrected p-values (sometimes called q-values) as: q(i)=p(i)N/i. Simply doing this, however, means your new vector of q-values might not be monotonic, i.e. q(i) might be greater than q(i+1) even though necessarily p(i)<=p(i+1), which can result in an incorrectly set false discovery rate. To accommodate for this, your vector of q-values can be adjusted such that q*(i) is the minimum q(k) where k>=i. Accordingly, you will typically have many duplicate FDR-corrected p-values.
For example, say I have 10 p-values:
0.003, 0.005, 0.03, 0.04, 0.12, 0.14, 0.15, 0.16, 0.17, 0.2
I can compute 10 q-values as p(i)N/i:
0.030, 0.025, 0.10, 0.10, 0.24, 0.233, 0.214, 0.2, 0.189, 0.2
I then enforce monotonicity by setting q*(i) to the smallest q(k), k>=i:
0.025, 0.025, 0.10, 0.10, 0.189, 0.189, 0.189, 0.189, 0.189, 0.2
See Yekutieli and Benjamini (1999) for more detail.
*Edit: part of my response seems to keep getting chopped off when I hit submit,
This is normal. For a vector of N p-values sorted from smallest to largest, one can compute the FDR-corrected p-values (sometimes called q-values) as: q(i)=p(i)N/i. Simply doing this, however, means your new vector of q-values might not be monotonic, i.e. q(i) might be greater than q(i+1) even though necessarily p(i)<=p(i+1), which can result in an incorrectly set false discovery rate. To accommodate for this, your vector of q-values can be adjusted such that q*(i) is the minimum q(k) where k>=i. Accordingly, you will typically have many duplicate FDR-corrected p-values.
For example, say I have 10 p-values:
0.003, 0.005, 0.03, 0.04, 0.12, 0.14, 0.15, 0.16, 0.17, 0.2
I can compute 10 q-values as p(i)N/i:
0.030, 0.025, 0.10, 0.10, 0.24, 0.233, 0.214, 0.2, 0.189, 0.2
I then enforce monotonicity by setting q*(i) to the smallest q(k), k>=i:
0.025, 0.025, 0.10, 0.10, 0.189, 0.189, 0.189, 0.189, 0.189, 0.2
See Yekutieli and Benjamini (1999) for more detail.
Threaded View
Title | Author | Date |
---|---|---|
Alice Yo | May 9, 2016 | |
Jon Dudley | May 9, 2016 | |
Alice Yo | May 11, 2016 | |
Jon Dudley | May 9, 2016 | |