If you sort the (masked) p-values in a volume from smallest
(most significant) to largest and index them from 1 to N say,
then as i goes from N down to 1,
q_i = minimum (for m >= i) of N * p_m / m
Ignoring the "minimum" aspect, this means q is basically
p * N / i. But p*N/i is not necessarily a decreasing curve,
as is seen in your case. If the curve ever bottoms out (when
moving from right to left), then q is assigned to the minimum
value (from the right).
Once the curve bottoms out, even as p continues to decrease,
q will not.
The curve will bottom out if there are not enough small p-values.
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To make it more clear, view it from the side of the data.
Suppose there are 1000 voxels in your mask and you set p = 0.02.
Then 20 false positives are expected (1000 * 0.02).
If you still have 100 voxels that survive that threshold, then
q will be 0.2 (20/100), the expected fraction of false positives
(assuming there is no minimum issue), equal to the number of
expected false positives divided by the total number of apparent
positives.
But what happens when you drop p down to 0.01 and the number of
surviving voxels drops down to 40? Then the expected fraction
of false positives would be 10 (=0.01*1000) / 40, or 0.25. So
at a lower p-value your q-value would actually increase from 0.2
to 0.25.
But the q-values are not allowed to increase as the p-values
decrease (the minimum attribute), so maybe your q curve would
bottom out around 0.2.
- rick
