I found @Piyush's answer helpful, and just to add to it, if you programatically create a select, then there is an important way to get this behavior that may not be obvious. Let's say you have a function and you create a new select:
var changeitem = function (sel) {
console.log(sel.selectedIndex);
}
var newSelect = document.createElement('select');
newSelect.id = 'newselect';
The normal behavior may be to say
newSelect.onchange = changeitem;
But this does not really allow you to specify that argument passed in, so instead you may do this:
newSelect.setAttribute('onchange', 'changeitem(this)');
And you are able to set the parameter. If you do it the first way, then the argument you'll get to your onchange
function will be browser dependent. The second way seems to work cross-browser just fine.