I suspect that it's not the Boolean expression but the need to refresh the object after the radio button's value that's the cause of your trouble.
Say your radio button has the values "yes" "no" and "other" and you want a text field to appear when "other" is selected:
LayoutTable::radioButtonField ≠ "other"
is all you need for your Boolean expression.
But an OnObjectModify trigger on the radio button field to run this script may also be needed:
Refresh Object ["Hidden Text Field" ]
where you select the text field while in layout mode and use the Inspector's name box to give it an object name and you then use that name in place of "hidden text field".
PhilModJunk - Thanks so much for the reply. That's helpful. Being new to all of this, it can get quite confusing.