Both R^2 and F are measurements of significance of the signal change linearly related to the reference time series, relative to the noise level left after the signal change is subtracted from the data time series. As such, they are essentially both of the form
(signal change)^2 / noise variance
In fact, R^2 and F are related by a formula that you can derive from the equations in Doug Ward's 3dDeconvolve manual [afni.nimh.nih.gov]. Define the following symbols
* r = R^2 statistic
* F = F statistic
* d1 = df_F
* d2 = df_B - df_F
* SSE(B) and SSE(F) = sum of squared errors in the Baseline and Full models, as defined in Doug's manual.
Then we have
r = (SSE(SSE(F))/SSE(B) and
F = (SSE(SSE(F))/SSE(F) * d1/d2, which implies
F = r/(1-r) * d1/d2
Thus, R^2 and F contain exactly the same information, if you assume the degrees-of-freedom of the models are known. In 3dDeconvolve, these values are computed from the number of data points and number of regressors, so they are not dependent on the data values in any way (just on the number of data values and the dimensionality of the models).

But what should one display as the color map? This depends on what you want to communicate. Either R^2 or F^2 will do to communicate significance of activation. Neither is suited for communicating amount of activation. The reason is that the standard models for BOLD activation (I assume that's what we are talking about) indicate that the percent signal change is more-or-less linearly related to the oxygenation state of the blood, and this in turn is related (perhaps not-so-linearly) to the amount of neuronal activity in the vicinity. Thus, the signal change -- the numerator of the statistics -- is causally related to the neuronal activity in some partially-understood way. But the denominator -- the noise level -- is not related to the neuronal activity, as far as anyone guesses at this time. Thus, for amount of activation, you should display the percent signal change.

At least, that's my opinion.

bob cox