Anatomical Dataset Types
========================
First, you must realize that I (and therefore AFNI) consider
the raw functional image time series to be "anatomical" data.
Only after processing does it show functional information.
For this reason you should create your 3D+time datasets as
one of the anatomical types.

No AFNI program (at this time) uses the actual anatomical
dataset type (e.g., SPGR or EPI) for any purpose.  This type
information is only for your convenience.

Functional Dataset Types
========================
In contrast, the functional dataset type is very meaningful
to the AFNI software.  At present (23 July 1997), there are 11
functional dataset types.  (The first five are documented in
"afni_plugins.ps".)

The first type ("fim") stores a single number per voxel.  All the
others store 2 numbers per voxel.  The second type ("fith") is
obsolescent, and will not be discussed further here.

The remaining types differ in the interpretation given to their
second sub-brick values.  In each case, the second value is
used as a threshold for functional color overlay.  The main
difference is the statistical interpretation given to each
functional type.  The types are

 Name  Type Index     Distribution        Auxiliary Parameters [stataux]
 ----  -------------  -----------------  -----------------------------------
 fico  FUNC_COR_TYPE  Correlation Coeff. # Samples, # Fit Param, # Ort Param
 fitt  FUNC_TT_TYPE   Student t          Degrees-of-Freedom (DOF)
 fift  FUNC_FT_TYPE   F ratio            Numerator DOF, Denominator DOF
 fizt  FUNC_ZT_TYPE   Standard Normal    -- none --
 fict  FUNC_CT_TYPE   Chi-Squared        DOF
 fibt  FUNC_BT_TYPE   Incomplete Beta    Parameters "a" and "b"
 fibn  FUNC_BN_TYPE   Binomial           # Trials, Probability per trial
 figt  FUNC_GT_TYPE   Gamma              Shape, Scale
 fipt  FUNC_PT_TYPE   Poisson            Mean

These were chosen because the needed CDF and inverse CDF routines
are found in the "cdf" library from the University of Texas.

When creating a dataset of these types, you will probably want to
store the threshold sub-brick as shorts, to save disk space.  You then
need to attach a scale factor to that sub-brick so that AFNI programs
will deal with it properly.  If you store it as shorts, but do not
supply a scale factor, AFNI will supply one.

 Name  Short Scale  Slider Top
 ----  -----------  ----------
 fico    0.0001          1.0
 fitt    0.001          10.0
 fift    0.01          100.0
 fizt    0.001          10.0
 fict    0.01          100.0
 fibt    0.0001          1.0
 fibn    0.01          100.0
 figt    0.001          10.0
 fipt    0.01          100.0

The default scale factor is useful for some types, such as the fico and
fibt datasets, where the natural ranges of these thresholds is fixed to
[-1,1] and [0,1], respectively.  For other types, the default scale factor
may not always be useful.  It is a good practice to create an explicit
scale factor for threshold sub-bricks, even if the default is acceptable.

The table above also gives the default value that AFNI will use for the
range of the threshold slider.  AFNI now allows the user to set the range
of this slider to be from 0 to 10**N, where N=0, 1, 2, or 3.  This is to
allow for dataset types where the range of the threshold may vary
substantially, depending on the auxiliary parameters.  The user can now
switch the range of the threshold slider to encompass the threshold range
shown to the right of the overlay color selector/slider.  At this time
there is no way to have the range of the threshold slider set automatically
to match the values in the dataset -- the user must make the switch
manually.

Distributional Notes
====================
fico: (Correlation coefficient)**2 is incomplete-beta distributed, so
      the fibt type is somewhat redundant, but was included since the
      "cdf" library had the needed function just lying there.

fizt: This is N(0,1) distributed, so there are no parameters.

fibn: The "p-value" computed and displayed by AFNI is the probability
      that a binomial deviate will be larger than the threshold value.

figt: The PDF of the gamma distribution is proportional to
         x**(Shape-1) * exp(-Scale * x)
      (for x >= 0).

fipt: The "p-value" is the probability that a Poisson deviate is larger
      than the threshold value.

For more details, see Abramowitz and Stegun (the sacred book for
applied mathematicians), or other books on classical probability
distributions.

The "p-values" for fico, fitt, and fizt datasets are 2-sided: that is,
the value displayed by AFNI (below the slider) is the probability that
the absolute value of such a deviate will exceed the threshold value
on the slider.  The "p-values" for the other types are 1-sided: that is,
the value displayed by AFNI is the probability that the value of the
deviate will exceed the threshold value.  (Of course, these probabilities
are computed under the appropriate null hypothesis, and assuming that
the distributional model holds exactly.  The latter assumption, in
particular, is fairly dubious.)

Finally, only the fico, fitt, fift, fizt, and fict types have actually
been tested.  The others remain to be verified.

Bucket Dataset Types (new in Dec 1997)
======================================
The new bucket dataset types (`abuc' == ANAT_BUCK_TYPE, and
`fbuc' == FUNC_BUCK_TYPE) can contain an arbitrary number of sub-bricks.
In an fbuc dataset, each sub-brick can have one of the statistical types
described above attached to it.

================================
Robert W. Cox, PhD
Biophysics Research Institute
Medical College of Wisconsin
