AFNI Command of the Week: cdf

Not necessarily a neuroimaging-specific tool, cdf simply converts between p-values and t-statistics (or F-statistics) using the cumulative distribution function. Supply the test that you did, followed by the t-statistic (or p-value) and degrees of freedom, e.g.:

cdf -t2p fitt 3.4 15
p = 0.00396 #A t-statstic of 3.4 with 15 degrees of freedom yields a p-value of 0.00396

cdf -p2t fitt 0.001 30
t = 3.65 #We would need a t-statistic of 3.65 or greater to reach a p-value of 0.001

Degrees of freedom can be found by using 3dinfo on a statistical dataset, and then looking at the value of "statpar" associated with your statistical test of interest. Degrees of freedom can also be calculated as the number of time points minus the number of regressors in your model; for example, if you have 1200 time points and 40 regressors, then the degrees of freedom will be 1200-40 = 1160. In the following X-matrix (generated by the command "aiv X.jpg"), the first 25 columns represent regressors accounting for any drift during that run; the next nine columns are the regressors of interest; and the last six columns are motion regressors.


The degrees of freedom in neuroimaging data can be a little tricky to interpret, as FMRI time series are temporally autocorrelated; in other words, the value of one time point can be predicted, to a degree, by neighboring timepoints. Therefore, using ordinary GLM estimation techniques can lead to an inflated degrees of freedom. To rectify this, instead of using 3dDeconvolve, use 3dREMLfit, which will attempt to account for this autocorrelation.