Usage: 3dTcorrelate [options] xset yset

Computes the correlation coefficient between corresponding voxel
time series in two input 3D+time datasets 'xset' and 'yset', and
stores the output in a new 1 sub-brick dataset.


-pearson    = Correlation is the normal Pearson (product moment)
              correlation coefficient [this is the default method].
-spearman   = Correlation is the Spearman (rank) correlation
-quadrant   = Correlation is the quadrant correlation coefficient.
-ktaub      = Correlation is Kendall's tau_b coefficient.
              ++ For 'continuous' or finely-discretized data, tau_b
                 and rank correlation are nearly equivalent.
-covariance = Covariance instead of correlation. That would be
              the Pearson correlation without scaling by the product
              of the standard deviations.
-partial z   = Partial Pearson's Correlation of X & Y, adjusting for Z
              Supply dataset z to be taken into account after '-partial'.
              ** EXPERIMENTAL **
-ycoef      = Least squares coefficient that best fits y(t) to x(t),
              after detrending.  That is, if yd(t) is the detrended
              y(t) and xd(t) is the detrended x(t), then the ycoef
              value is from the OLSQ fit to xd(t) = ycoef * y(t) + error.

-Fisher     = Apply the 'Fisher' (inverse hyperbolic tangent = arctanh)
              transformation to (correlation) results.
              ++ It does NOT make sense to use this with '-ktaub', but if
                  you want to do it, the program will not stop you.
              ++ This option does not apply to '-covariance' or '-ycoef'.

-polort m = Remove polynomical trend of order 'm', for m=-1..9.
              [default is m=1; removal is by least squares].
              Using m=-1 means no detrending; this is only useful
              for data/information that has been pre-processed.

-ort r.1D = Also detrend using the columns of the 1D file 'r.1D'.
              Only one -ort option can be given.  If you want to use
              more than one, create a temporary file using 1dcat.

-autoclip = Clip off low-intensity regions in the two datasets,
-automask =  so that the correlation is only computed between
             high-intensity (presumably brain) voxels.  The
             intensity level is determined the same way that
             3dClipLevel works.
         ** At present, this program does not have a '-mask'
            option. Maybe someday?

-zcensor  = Omit (censor out) any time points where the xset
             volume is all zero OR where the yset volume is all
             zero (in mask). Please note that using -zcensor
             with any detrending is unlikely to be useful.
         ** That is, you should use '-polort -1' with this
             option, and NOT use '-ort'.
          *  In fact, using '-zcensor' will set polort = -1,
             and if you insist on using detrending, you will
             have to put the '-polort' option AFTER '-zcensor.
         ** Since correlation is calculated from the sum
             of the point-by-point products xset(t)*yset(t),
             why censor out points where xset or yset is 0?
             Because the denominator of correlation is from
             the sum of xset(t)*xset(t) and yset(t)*yset(t)
             and unless the t-points where the datasets are
             censored are BOTH zero at the same time, the
             denominator will be incorrect.
         ** [RWCox - Dec 2019, day of Our Lady of Guadalupe]
            [for P Molfese and E Finn]

-prefix p = Save output into dataset with prefix 'p'
             [default prefix is 'Tcorr'].


* The output dataset is functional bucket type, with just one
   sub-brick, stored in floating point format.

* Because both time series are detrended prior to correlation,
   the results will not be identical to using FIM or FIM+ to
   calculate correlations (whose ideal vector is not detrended).

* Also see 3dTcorr1D if you want to correlate each voxel time series
   in a dataset xset with a single 1D time series file, instead of
   separately with time series from another 3D+time dataset.

* https://en.wikipedia.org/wiki/Correlation
* https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
* https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
* https://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient
* https://en.wikipedia.org/wiki/Partial_correlation

-- RWCox - Aug 2001++

++ Compile date = Oct 13 2022 {AFNI_22.3.03:linux_ubuntu_16_64}