it is always good to restrict the DOM search. so better to use a parent also, so that the entire DOM won't be traversed.
IT IS VERY FAST
<div id="radioBtnDiv">
<input name="myButton" type="radio" class="radioClass" value="manual" checked="checked"/>
<input name="myButton" type="radio" class="radioClass" value="auto" checked="checked"/>
</div>
$("input[name='myButton']",$('#radioBtnDiv')).change(
function(e)
{
// your stuffs go here
});