Hi Livio,
FDR.m program is based on the step-up algorithm of FDR control. This
programs generates a common threshold for all the comparisons in a single
step. However, the deifinitions 'step-up' or 'step-down' make more sense
when you translate the procedure in a step-wise algorithm, which for a
step-up procedure is:
First, arrange the p-values{P1 P2 P3.PC} in ascending order corresponding
to null hypotheses, {H1 H2 H3.HC}. Then, compare the following inequality,
in reverse sequential order, starting from the last p-value(or the least
significant value), PC.
Pi < = a * i / C (Starting from i=C)
Continue comparing until you reach a hypothesis Hk for which the above
inequality is true. Finally, reject all the hypotheses having p-values less
than or equal to Pk, which are H1 to Hk.
For details, you can refer to Benjamini's homepage
http://www.math.tau.ac.il/%7Eroee/index.htm . It has links to other versions
of FDR control methods too , including a step-down version.
I would also recommend http://www.sph.umich.edu/~nichols/Docs/FWEfNI.pdf
by Hayasaka et al, to know the difference between step-down and step-up
methods.
I hope it helps,
Archana
----- Original Message -----
From: "livio finos" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Thursday, March 31, 2005 12:32 AM
Subject: [SPM] step-down FDR?
> Dear Nichols, dear all,
> having a look on your FDR.m function I see:
>
> pID = p(max(find(p<=I/V*q/cVID)));
>
> Does it mean, we are performing an FDR procedure in a step-down
> fashion? I mean, in this way we are starting from the less significant
> p-value, then going down to the most significant, then rejecting all
> the remaining hypotheses after the first hypothesis is rejected (with
> a fdr correction).
> indeed we do not impose monotonicity. is it right?
> As an example, consider the vector:
>
> p=[.01 .01 .03 .05 .3 .31 .32 .4 .5 .6];
> and q=.5;
>
> pID (p-value threshold based on independence or positive dependence) = .4
>
>
> the ans to p<=I/V*q/cVID, is
> 1 1 1 1 0 0 1 1 0 0.
>
> this mean that the values .3 and .31 do not respect the criteria,
> altought thei are rejected.
>
> there exist some work proving that this step-down procedure control the
> FDR?
>
> thanks.
> livio
>
|