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F-to-Log

The standard dual-state CTF SAM output for each voxel in the brain volume is a pseudo-F ratio. Given an active window A and a control window C, the ratio is A/C-1 if A>C, and 1-C/A if C>A. The advantage of this ratio is that it produces a symmetric distribution centered at zero -— the disadvantage, however, is that the distribution can have long tails if there are large differences between A and C in some voxels. This can be alleviated by using a log ratio instead, namely log(A/C), which is also symmetric about zero and has shorter tails. The use of the log ratio may eliminate the need to normalize individual volumes to z-scores because of the relative lack of outliers. A log scale is commonly used in science for power measures such as the Richter scale and decibels. The following AFNI 3dcalc command will make the conversion from pseudo-F to log ratios.

Usage

3dcalc -a input+orig -expr 'log10(step(a)*(a+1)+step(-a)/(-a+1))' -prefix output

log10 is base 10; use log for the natural logarithm.