I am basing my question and example on Jason\'s answer in this question
I am trying to avoid using an eventListener, and just to call handleClick
There are a few things to change in your edited version:
You've taken the suggestion of using document.myform['whichThing'] a bit too literally. Your form is named "aye", so the code to access the whichThing radio buttons should use that name: `document.aye['whichThing'].
There's no such thing as an action attribute for the tag. Use onclick instead:
Obtaining and cancelling an Event object in a browser is a very involved process. It varies a lot by browser type and version. IE and Firefox handle these things very differently, so a simple event.preventDefault() won't work... in fact, the event variable probably won't even be defined because this is an onclick handler from a tag. This is why Stephen above is trying so hard to suggest a framework. I realize you want to know the mechanics, and I recommend google for that. In this case, as a simple workaround, use return false in the onclick tag as in number 2 above (or return false from the function as stephen suggested).
Because of #3, get rid of everything not the alert statement in your handler.
The code should now look like:
function handleClick()
{
alert("Favorite weird creature: "+getRadioButtonValue(document.aye['whichThing']));
}