= Research Overview =
`fdr` is a simple program which takes in a p-value image and uses FDR ( False Discovery Rate ) theory to carry out multiple comparison correction. For detail on FDR theory see [[http://www-personal.umich.edu/~nichols/FDR/|Tom Nichols' FDR page]].

'''Outputs:'''

 * The main output from FDR is the threshold to apply to the p-value image. Everything below this threshold is significant. If nothing is significant then the threshold will be 0.  This threshold is written as text to standard output.

 * A thresholded image (with `--othresh`)

 * A "q-rate" image (with `-o`) which is effectively the FDR version of a corrected p-value (such that values less than 0.05 would typically be considered significant).

'''Options:'''

 * `--positivecorr` uses a normalisation that assumes the samples are positively correlated - this is the default
 * `--independent` uses a normalisation that assumes all samples are independent (NB: the normalisation is the same as for `--positivecorr`)
 * `--conservative` uses the more general normalisation of (1+1/2+1/3+...+1/N), suitable for any dependence between samples ['''not recommended''']

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'''Examples:'''

The p-value image fed into fdr can be produced in a number of ways.

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== Use with FEAT ==
Change directory into the stats subdirectory. It is then necessary to convert a give cope and varcope image into a p-value image. For example:

{{{ttologp -logpout logp1 varcope1 cope1 `cat dof`}}}

 . (this outputs the log(p) image)

`fslmaths logp1 -exp p1`

 . (this creates the p-value image)

`fdr -i p1 -m ../mask -q 0.05`

 . `Probability Threshold is: ` `0.00339819` (this tells you the FDR threshold - p-values below 0.00339819 are significant)

`fslmaths p1 -mul -1 -add 1 -thr .99660181 -mas ../mask thresh_1_minus_p1`

 . (this creates a 1-p image for ease of display, thresholds that at 1-thresh and then remasks)

Note that if you are looking at a cope created by FLAME fixed-effects, the correct dof is not in the "dof" text file, but in the tdof_t1 image.

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== Use with randomise ==
Output from `randomise` can be fed directly into `fdr`; use the voxel-based thresholding, uncorrected for multiple comparisons, i.e. a `*_vox_p_tstat*` image. This images stores values as 1-p rather than p (where p is the p-value from 0 to 1).  That is, 1 is most significant in a 1-p image (and it is arranged this way to make display and thresholding simple). Therefore `fdr` needs to know that it is a 1-p image. Thus an example would be:

`fdr -i grot_vox_p_tstat1 --oneminusp -m mask -q 0.05 --othresh=thresh_grot_vox_p_tstat1`

where the input image, `grot_vox_p_tstat1`, contains 1-p values, as output by `randomise`.  Note that the name of this image should be changed to whatever you have called your image.

The output from `fdr` gives you a p-value threshold ('''not''' a 1-p value) that can be applied to the p-values, as well as a thresholded image, `thresh_grot_vox_p_tstat1`, where all non-significant voxels are given a value of 1-p=0 and significant voxels still contain the original 1-p values.

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